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Lightweight Research in Engineering: A Review

Authors:

Abstract

In the field of mechanical equipment manufacturing, the focus of research and development is not on weight reduction, but on how to choose between the rigidity and performance of components (such as strength or flexibility). For this contradiction, lightweight is one of the best solutions. The problems associated with lightweight were initially considered and systematically studied in aircraft manufacturing in engineering. Therefore, lightweight has been greatly developed in aviation research and has played an increasingly important role in construction machinery. This paper presents a brief description of the current status of lightweight in machinery by reviewing some significant progress made in the last decades. Potential research topics are also discussed from the four aspects of material, structure, bionics, and manufacturing, and they forecast the development trend of lightweight in the future construction machinery. The entire body of literature about the field is not covered due to the limitation of the length of paper. The scope of this review is limited and closely related to the development of lightweight technology in engineering applications.
applied
sciences
Review
Lightweight Research in Engineering: A Review
Jiao Wang 1, Yan Li 1, * , Gang Hu 2and Mingshun Yang 1
1School of Mechanical and Precision Instrument Engineering, Xi’an University of Technology,
Xi’an 710048, China; wjiao91@163.com (J.W.); yangmingshun@xaut.edu.cn (M.Y.)
2Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710054, China;
hg_xaut@xaut.edu.cn
*Correspondence: jyxy-ly@xaut.edu.cn
Received: 14 October 2019; Accepted: 3 December 2019; Published: 6 December 2019


Abstract:
In the field of mechanical equipment manufacturing, the focus of research and development
is not on weight reduction, but on how to choose between the rigidity and performance of components
(such as strength or flexibility). For this contradiction, lightweight is one of the best solutions. The
problems associated with lightweight were initially considered and systematically studied in aircraft
manufacturing in engineering. Therefore, lightweight has been greatly developed in aviation research
and has played an increasingly important role in construction machinery. This paper presents a brief
description of the current status of lightweight in machinery by reviewing some significant progress
made in the last decades. Potential research topics are also discussed from the four aspects of material,
structure, bionics, and manufacturing, and they forecast the development trend of lightweight in the
future construction machinery. The entire body of literature about the field is not covered due to
the limitation of the length of paper. The scope of this review is limited and closely related to the
development of lightweight technology in engineering applications.
Keywords: lightweight; topology; structure optimization; bionics; manufacturing; engineering
1. Introduction
Lightweight is a multidisciplinary engineering science that consists of knowledge bases in the fields
of materials mechanics, computational technology, materials science, and manufacturing technology.
The goal of lightweight is to minimize the structural weight under certain boundary conditions while
meeting certain life and reliability requirements. Lightweight is one of the most important laws for the
growth of nature. In nature, the essence of lightweight is to achieve maximum eciency with minimal
consumption. In the field of science and engineering, lightweight is a discipline that is both traditional
and new. In modern society, the requirements for lightweight are not only technically achievable and
aordable, but also sustainable.
This paper presents a brief description of the current status of structural optimization by reviewing
some significant progress made in the last decades. Since the length of this paper is limited, it does not
cover the entire body of literature for the field. The scope of this review is limited and closely related
to the authors0own research interests.
The paper is organized as follows: lightweight research background and significance are introduced
in Section 2. Section 3oers a survey of the lightweight mathematical model and solution. Lightweight
pathways and research progress are briefly discussed in Section 4and mainly includes four aspects:
material, structure, bionics and manufacturing technology, and 3D printing. Section 5concludes the
paper with some personal perspectives on the future development of lightweight.
Appl. Sci. 2019,9, 5322; doi:10.3390/app9245322 www.mdpi.com/journal/applsci
Appl. Sci. 2019,9, 5322 2 of 24
2. Lightweight Research Background and Significance
In the field of mechanical equipment manufacturing, the focus of research and development
is not on weight reduction, but on how to choose between the rigidity and performance of moving
components. For this contradiction, lightweight technology is the most one of the good solutions [
1
].
For example, lightweight components enable faster machining speeds, higher precision and longer
life for mechanical equipment, while lightweight robots move faster, more agilely and with higher
precision. Under the requirements of lightweight, mechanical equipment can also use smaller and
more economical drive systems, to enhance the market competitiveness of products.
The problems associated with lightweight first appeared in aircraft manufacturing and the
aerospace industry [
2
]. While mastering theoretical knowledge, rich design experience is also
indispensable. Increasingly high demands have prompted lightweight engineers to continually learn
and apply all new technologies and knowledge in a targeted manner, to address the lightweight system
issues they face. The iconic breakthrough in this field is to make full use of the carrying capacity of the
skin and replace the truss structure with an unstructured structure. The principle of solid wall and
shell generated from the aerospace manufacturing field has spread to high-performance locomotives
and ships and the field of shipbuilding, large wind-power plants, automobile body manufacturing,
and machine tool manufacturing.
It is estimated that by 2020, the market value of lightweight in the German electronics industry
and machinery manufacturing industry will reach 40 billion euros. The new concept of material
and structure optimization design technology has been applied to an unprecedented scale in the
European and American aviation and aerospace industries. For example, the optimization design of
the leading-edge rib of the Airbus A380 wing, through the application of topology, size, and shape
optimization technology, the overall weight reduction of the aircraft reaches 500 kg. Similar major
technologies have been used by other major aircraft manufacturers in Europe and the United States.
Experience has shown that typical optimization designs for individual structural components can
achieve at least 20% weight loss on a classic design basis. The lightweight design of aerospace vehicles
has great economic performance, which can reduce the manufacturing cost and improve the resource
utilization, while ensuring the design requirements [3,4].
The structural cost (materials for steel, concrete, masonry, etc.) accounts for more than 50%
of the main construction cost, and structural optimization can reduce the total construction cost by
10% to 35%. This invisible total profit is very large, has basically no risk, and can be easily obtained
through small optimization investment, which is helpful for reducing corporate investment, increasing
corporate profits, and improving capital turnover, and has great economic value design optimization.
According to calculations, when a car loses 10 kg, and the fuel consumption per 100 km decreases
by an average of 0.51 L, the carbon dioxide emissions are reduced by 12 g/km. The current car still has
about 35% weight-loss potential. If lightweight material substitution is used to do this, it is equivalent
to about 1 kg of aluminum instead of 2 kg of steel, and the load-carrying capacity is unchanged. In the
field of machinery manufacturing alone, the German industry
0
s annual reduction in carbon dioxide
emissions through lightweight measures is equivalent to a year
0
s total carbon dioxide emissions
in a large German city. Lightweight design helps reduce aircraft fuel consumption. The energy
eciency of the fuel depends mainly on the power of the engine and the total mass of the fuselage.
Therefore, reducing the weight of the fuselage can significantly improve the power density, carrying
capacity, reliability, and running speed of the aircraft, while maintaining the same performance and
cost. Reducing fuel consumption can also reduce greenhouse gas emissions eectively and make
aircrafts more environmentally friendly.
3. Lightweight Mathematical Model and Solution
The problem of lightweight ultimately comes down to the maximum and minimum problem
of solving the objective function under certain constraints. The diculty is that the constraints are
not easy to establish in dierent engineering problems, or dierent working conditions, dierent
Appl. Sci. 2019,9, 5322 3 of 24
backgrounds, and dierent hard requirements. The current solution steps can be roughly simplified,
as shown in Figure 1.
Appl. Sci. 2019, 9, x FOR PEER REVIEW 3 of 24
backgrounds, and different hard requirements. The current solution steps can be roughly simplified,
as shown in Figure 1.
Figure 1. The current solution steps.
There are generally two modeling ideas of structural optimization methods [1,5]: One is to seek
structural stiffness maximization (minimum compliance) under volume or mass constraints, and
the other is to seek structural minimum volume or mass under stiffness constraints. Mathematical
modeling is the first step in lightweight. Regardless of whether the optimization is a static problem, a
dynamic problem, or a shape, size, and topology problem, it can generally be expressed in the form
of nonlinear programming. The standard nonlinear programming model is as follows:
 
XMin f
(1)
 
 
UL XXX
mppjX
pjXtS
,,,,g
,,,,g ..
j
j
210
210
(2)
where,
 
Xf
is the objective function, generally taking the structural weight;
is the
constraint function, which may include the physical equation and the coordination equations, static
or dynamic strength, stiffness limit, etc.;
 
T
N
XXXX ,,,
21
is the design variable; and
U
X
and
L
X
are the upper and lower limits of
X
, respectively. It is necessary to make the following
explanation about the model:
Design variables can be either continuous or discrete. For engineering structure design, the
variables are usually a lot.
The objective function and the constraint function are continuously differentiable in most cases
and may also be noncontinuous and nondifferentiable.
The constraint function is usually implicit and has a nonlinear nature. The degree of
nonlinearity is different for different problems or different design points of the same problem.
Because the constraint conditions in complex engineering may be very diverse, the degree of
nonlinearity and linearity are also different for the structure’s design. At the same time, our
solution was obtained through iterative optimization. For the optimization result, different
variables are grouped with different requirements. Due to the fact that each set of variables
must be fully analyzed, one by one, the amount of calculations is usually very large. Therefore,
the number of times structural analysis is usually an important indicator of the efficiency of an
optimization method [1].
After the lightweight approach and the mathematical model are determined, we need to solve
the model. In recent years, there have been many methods for solving lightweight optimization
problems, such as mathematical programming, optimization criterion method, emerging
meta-heuristic bionic optimization algorithm, etc., which have attracted many experts and scholars,
and have been widely used in engineering field.
Figure 1. The current solution steps.
There are generally two modeling ideas of structural optimization methods [
1
,
5
]: One is to seek
structural stiness maximization (minimum compliance) under volume or mass constraints, and
the other is to seek structural minimum volume or mass under stiness constraints. Mathematical
modeling is the first step in lightweight. Regardless of whether the optimization is a static problem,
a dynamic problem, or a shape, size, and topology problem, it can generally be expressed in the form
of nonlinear programming. The standard nonlinear programming model is as follows:
Min f (X)(1)
S.t. gj(X)=0, j=1, 2, · · · ,p
gj(X)0, j=p+1, p+2, · · · ,m
XLXXU
(2)
where,
f(X)
is the objective function, generally taking the structural weight;
gj(X)
is the constraint
function, which may include the physical equation and the coordination equations, static or dynamic
strength, stiness limit, etc.;
X=X1,X2,· · · ,XNT
is the design variable; and
XU
and
XL
are the upper
and lower limits of
X
, respectively. It is necessary to make the following explanation about the model:
Design variables can be either continuous or discrete. For engineering structure design, the
variables are usually a lot.
The objective function and the constraint function are continuously dierentiable in most cases
and may also be noncontinuous and nondierentiable.
The constraint function is usually implicit and has a nonlinear nature. The degree of nonlinearity
is dierent for dierent problems or dierent design points of the same problem. Because the
constraint conditions in complex engineering may be very diverse, the degree of nonlinearity and
linearity are also dierent for the structure’s design. At the same time, our solution was obtained
through iterative optimization. For the optimization result, dierent variables are grouped with
dierent requirements. Due to the fact that each set of variables must be fully analyzed, one by
one, the amount of calculations is usually very large. Therefore, the number of times structural
analysis is usually an important indicator of the eciency of an optimization method [1].
After the lightweight approach and the mathematical model are determined, we need to solve the
model. In recent years, there have been many methods for solving lightweight optimization problems,
such as mathematical programming, optimization criterion method, emerging meta-heuristic bionic
optimization algorithm, etc., which have attracted many experts and scholars, and have been widely
used in engineering field.
From the point of view of engineering and mechanics, the criterion method [
6
] oers some
criteria that should be met when the structure reaches the optimal design (such as synchronous failure
Appl. Sci. 2019,9, 5322 4 of 24
criterion, full stress criterion, energy criterion, etc.). Then the solution satisfying these criteria is
obtained by the iterative method. The method is characterized by fast convergence, no direct relation
between the number of times of reanalysis and the number of design variables, and a small amount of
calculation. However, it is limited in its application, which is mainly applicable to the case where the
structural layout and geometric shape have been determined. Although the standard method has its
shortcomings, from the perspective of engineering application, it is more convenient. The simplest
criterion method is the synchronous failure criterion method and the full stress criterion method.
The structural optimization [
7
] problem is summarized into a mathematical programming problem,
and then solved by mathematical programming. The mathematical programming methods commonly
used in structural optimization are nonlinear programming, and sometimes linear programming.
In special cases, dynamic programming, geometric programming, integer programming, or random
programming may be used.
Heuristic algorithms have been a solution trend in recent years. These algorithms include genetic
algorithm (GA), neural network algorithm, simulated annealing algorithm, fruit fly algorithm [
8
],
artificial bee colony algorithm [
9
], particle swarm algorithm [
10
] (PSO), ant colony optimization
algorithm [
11
], Cuckoo search algorithm [
12
], multi-island genetic algorithm [
13
], and the new raindrop
algorithm [
14
]. The algorithm is simple and easy to implement, and it has few parameters. It has
great advantages in dealing with many engineering problems and has also been applied in the field of
structural optimization.
The development of lightweight software systems is as important as basic method research, and
software is a tool for lightweight and the actual structure. The aviation industry first stimulated the
development of structural optimization, and it is also the main industry for developing and applying
structural optimization software. After the zero-sensitivity analysis and finite element modeling ideas
are taken into consideration, there are many existing software programs, such as ANSYS Workbench,
SolidWorks, Optistruct, Adams, Abaqus, Hyperworks, UG, ISIGHT, TOSCA, CATIA, and ADINA.
4. Lightweight Pathways and Research Progress
Increasing the payload and lightweight design of the aircraft structure, the integration of materials,
structure, and manufacturing process is the eternal driving force to lead the optimization design theory
and technology development. Therefore, according to lightweight design objects, such as automobiles,
airplanes, folding electric vehicles, various beams, etc., under the condition of ensuring the basic
performance of various lightweight objects, the quality can be reduced via the following ways (see the
Figure 2).
Appl. Sci. 2019, 9, x FOR PEER REVIEW 4 of 24
From the point of view of engineering and mechanics, the criterion method [6]offers some
criteria that should be met when the structure reaches the optimal design (such as synchronous
failure criterion, full stress criterion, energy criterion, etc.). Then the solution satisfying these criteria
is obtained by the iterative method. The method is characterized by fast convergence, no direct
relation between the number of times of reanalysis and the number of design variables, and a small
amount of calculation. However, it is limited in its application, which is mainly applicable to the case
where the structural layout and geometric shape have been determined. Although the standard
method has its shortcomings, from the perspective of engineering application, it is more convenient.
The simplest criterion method is the synchronous failure criterion method and the full stress
criterion method.
The structural optimization [7] problem is summarized into a mathematical programming
problem, and then solved by mathematical programming. The mathematical programming
methods commonly used in structural optimization are nonlinear programming, and sometimes
linear programming. In special cases, dynamic programming, geometric programming, integer
programming, or random programming may be used.
Heuristic algorithms have been a solution trend in recent years. These algorithms include
genetic algorithm (GA), neural network algorithm, simulated annealing algorithm, fruit fly
algorithm [8], artificial bee colony algorithm [9], particle swarm algorithm [10] (PSO), ant colony
ny optimization algorithm [11], Cuckoo search algorithm [12], multi-island genetic algorithm [13],
and the new raindrop algorithm [14]. The algorithm is simple and easy to implement, and it has few
parameters. It has great advantages in dealing with many engineering problems and has also been
applied in the field of structural optimization.
The development of lightweight software systems is as important as basic method research, and
software is a tool for lightweight and the actual structure. The aviation industry first stimulated the
development of structural optimization, and it is also the main industry for developing and
applying structural optimization software. After the zero-sensitivity analysis and finite element
modeling ideas are taken into consideration, there are many existing software programs, such as
ANSYS Workbench, SolidWorks, Optistruct, Adams, Abaqus, Hyperworks, UG, ISIGHT, TOSCA,
CATIA, and ADINA.
4. Lightweight Pathways and Research Progress
Increasing the payload and lightweight design of the aircraft structure, the integration of
materials, structure, and manufacturing process is the eternal driving force to lead the optimization
design theory and technology development. Therefore, according to lightweight design objects, such
as automobiles, airplanes, folding electric vehicles, various beams, etc., under the condition of
ensuring the basic performance of various lightweight objects, the quality can be reduced via the
following ways (see the Figure 2).
Figure 2. Lightweight approaches.
Figure 2. Lightweight approaches.
Lightweight is divided into lightweight materials, lightweight manufacturing, and lightweight
structure. The lightweight material is lightened by the use of lightweight materials, to ensure
structural performance. Typical applications are in the medical, automotive, and aerospace industries.
Lightweight construction is designed to meet the requirements by improving structural design. The
Appl. Sci. 2019,9, 5322 5 of 24
application of structural optimization technology to achieve lighter weight is superior to the former
two in terms of low cost, short cycle, easy implementation, and light-weighting eect. In recent years,
it has been widely used in the field of engineering machinery lightweight.
A detailed classification of lightweight technologies is shown in Figure 3.
Appl. Sci. 2019, 9, x FOR PEER REVIEW 5 of 24
Lightweight is divided into lightweight materials, lightweight manufacturing, and lightweight
structure. The lightweight material is lightened by the use of lightweight materials, to ensure
structural performance. Typical applications are in the medical, automotive, and aerospace
industries. Lightweight construction is designed to meet the requirements by improving structural
design. The application of structural optimization technology to achieve lighter weight is superior to
the former two in terms of low cost, short cycle, easy implementation, and light-weighting effect. In
recent years, it has been widely used in the field of engineering machinery lightweight.
A detailed classification of lightweight technologies is shown in Figure 3.
Figure 3. Lightweight technologies.
4.1. Material Lightweight
The key to lightweight materials is to find new materials with superior mechanical properties
that can replace raw materials. Generally, the density of new materials is lower than the raw
materials, and the strength is higher than the raw materials. Since it is related to important factors
such as product performance and price, the choice of materials for the product is critical.
High-strength steels, aluminum alloys, magnesium alloys, plastics, and composite materials are all
lightweight materials [1518]. Lai et al. [19] focus on the recent experience achieved by Fiat in
introducing HSS up to reach a share higher than 60% in weight applying and developing new
methodologies to solve in the design phase any criticality arising from the use of this material. It is
possible to create a lightweight material made with gypsum and EPS [20] waste with enhanced
mechanical properties, low density, and outstanding thermal behavior. However, the use of coarse
EPS waste has a negative effect on the Shore C surface hardness, especially with latex and fibers. Liu
et al. [10] proposed a structural optimization method for commercial front bumper system made of
carbon fiber composite materials, which combined Kriging modeling technology with improved
PSO algorithm to find the optimal strength and crash-worthiness requirements, to achieve weight
reduction in 2016. In 2017, Zaiß et al. proposed new concepts for quality assurance of lightweight
material. This provided a way of thinking for lightweight technology [21]. A lightweight, injectable,
high-rigidity plastic composite to replace the aluminum in the chassis of the chassis was developed
[22]. In 2018, Ma et al. [23] used HC70E and DOMEX700W to replace the traditional Q235E, which
h reduced the container quality by 19.2%. The carbon fiber composite materials, aramid fiber
materials, and Balsa wood were used by Zhong et al. [24] in order to light the four-rotor UAV
fuselage. The lightweight material was selected, and the weight analysis of the trailer chassis and
trailer structure was carried out. It was found that the weight of the trailer structure was
significantly reduced by 73.61%, thereby reducing the fuel consumption and preventing carbon
dioxide emissions from environmental pollution [25]. Lightweight concrete has recently been
Figure 3. Lightweight technologies.
4.1. Material Lightweight
The key to lightweight materials is to find new materials with superior mechanical properties that
can replace raw materials. Generally, the density of new materials is lower than the raw materials,
and the strength is higher than the raw materials. Since it is related to important factors such as
product performance and price, the choice of materials for the product is critical. High-strength
steels, aluminum alloys, magnesium alloys, plastics, and composite materials are all lightweight
materials [
15
18
]. Lai et al. [
19
] focus on the recent experience achieved by Fiat in introducing HSS up
to reach a share higher than 60% in weight applying and developing new methodologies to solve in the
design phase any criticality arising from the use of this material. It is possible to create a lightweight
material made with gypsum and EPS [
20
] waste with enhanced mechanical properties, low density,
and outstanding thermal behavior. However, the use of coarse EPS waste has a negative eect on
the Shore C surface hardness, especially with latex and fibers. Liu et al. [
10
] proposed a structural
optimization method for commercial front bumper system made of carbon fiber composite materials,
which combined Kriging modeling technology with improved PSO algorithm to find the optimal
strength and crash-worthiness requirements, to achieve weight reduction in 2016. In 2017, Zaiß et
al. proposed new concepts for quality assurance of lightweight material. This provided a way of
thinking for lightweight technology [
21
]. A lightweight, injectable, high-rigidity plastic composite to
replace the aluminum in the chassis of the chassis was developed [
22
]. In 2018, Ma et al. [
23
] used
HC70E and DOMEX700W to replace the traditional Q235E, which reduced the container quality by
19.2%. The carbon fiber composite materials, aramid fiber materials, and Balsa wood were used by
Zhong et al. [24]
in order to light the four-rotor UAV fuselage. The lightweight material was selected,
and the weight analysis of the trailer chassis and trailer structure was carried out. It was found that
the weight of the trailer structure was significantly reduced by 73.61%, thereby reducing the fuel
consumption and preventing carbon dioxide emissions from environmental pollution [
25
]. Lightweight
concrete has recently been introduced into structural engineering applications in Thailand in order to
study the performance of porous lightweight concrete [26].
Appl. Sci. 2019,9, 5322 6 of 24
4.2. Structure Lightweight
Lightweight structure is a comprehensive analysis of the overall physical layout of each structural
parameter of the product under the premise of satisfying the functional requirements and safety
performance of the product, achieving the eect of quality reduction and stable performance.
Lightweight structure is the best distribution of materials in the structure. It mainly includes
structural topology optimization, shape optimization, size optimization, topography optimization,
free shape optimization, etc. In recent years, combining them for lightweight design has become a
mainstream practice.
4.2.1. Size Lightweight
Size lightweight refers to the optimization of the basic dimension structure by means of mechanical
analysis. It means that the basic shape and size of the components have been determined, and the
functions of the products have also been realized in order to improve performance and reduce costs.
Many dierent types of sizes can be selected for optimization, and we can optimize the critical size
(dimensions) of the product. Generally, the optimal size selection is based on the required functional
and mechanical properties constraints to select the optimal combination from a certain limited range.
A lightweight design method for automobile body structure based on sensitivity analysis and
side collision was proposed [
27
]. The thickness of the body structure parts is taken as the design
variable, the modality and rigidity of the body-in-white are the constraints, and the body-in-white
mass is the minimum. The sensitivity of the part thickness to the modality and stiness of the body
is analyzed. The thickness of the body parts that are insensitive to the modality and stiness of the
vehicle body and the crashworthiness are selected to optimize the calculation with the minimum body
mass. The result of the optimization reduced the body by 14.8 kg. The simulation calculation of the
side collision is carried out on the lightweight vehicle and occupant restraint system, and compared
with the results before the lightweight, the vehicle crashworthiness and the safety of the occupant
are compared and checked, according to the collision result. The thickness of the body parts was
readjusted. The results show that the lightweight body meets the requirements of collision safety, and
the dummy
0
s C-NCAP score is acceptable. In 2014, Shi et al. [
28
] established the multidisciplinary
design optimization model of the vehicle door, analyzed the sensitivity of the design variables, removed
the design variables that had less influence on the structure, constructed the approximate response
surface of each performance, and applied the genetic algorithm based on the response surface for
multidisciplinary optimization. Zhang et al. [
29
] used the three-dimensional SolidWorks drawing
software to establish a three-dimensional model of the gantry machining center. The key dimension
sensitivity analysis of the V-shaped rib beam structure was carried out, and the beam size design was
carried out by the extreme dimension adjustment method. During 2015, the shape and size of the
ship
0
s bottom slab and the upper building slab were optimized, to seek the optimal distribution of
materials. Based on the above mentioned data, the volume fraction is set as the restriction condition of
the model, and the structural natural frequency is set as the objective function [
30
].
Wang et al. [31]
took the wall thickness length and transition angle of each section of hollow half-axle of automobile
steering drive axle as design variables, the minimized quality of half-axle as optimization objective,
and the second-order constrained mode frequency and equivalent stress at the end corner transition
of half-axle spline as constraints, established a lightweight optimization model of half-axle. A
combination of
10 design
variables and three levels of numerical simulation tests was obtained by
using an orthogonal experimental design. The response surface approximation model was established
by the least-squares method, and the model was optimized by the sequence quadratic programming
algorithm.
Liu et al. [32]
carried out a study on the optimization of the machine tool column topology.
According to the results of the material distribution, the basic shape of the machine tool column
was designed. Five dierent types of stiened plate structures were compared. It was found that
the material consumption of the W-type stiened plate structure was less and the comprehensive
mechanical properties were better. The W-type stieners were selected to optimize the layout and
Appl. Sci. 2019,9, 5322 7 of 24
size of the column, and the lightweight design of the column structure was realized. Chen et al. [
33
]
used the correlation analysis method to analyze the influence of design variables such as 90 position
shapes and thicknesses on the structural rigidity of the SUV body-in-white, and selected the design
variables with lightweight potential. Then, the multiperformance optimization design of the 30 design
variables was carried out and finally achieved a good lightweight eect in 2016. In 2017, Wang et al. [
34
]
established the optimization mathematical model for the cross-section size of the frame longitudinal
beam, and the finite element analysis software programs were used to carry out modal analysis of
the optimized frame solid model in order to verify its dynamic characteristics meet the dynamic
requirements, which indicated that the lightweight optimization design is reasonable and eective.
For the lightweight design of satellite structures,
Li et al. [35]
considered the manufacturing process
constraints of augmented materials comprehensively, applied the topological optimization method to
find the optimal path of force transmission in the feasible design space of structures, abstracted the
corresponding truss structure on the basis of this method, and then applied the dimension optimization
method to design the optimal truss member cross-section size. Finally, considering the optimal rod
size and structural processing constraints, geometric reconstruction is carried out in order to obtain a
structural design scheme for additive manufacturing. In 2018, Ma et al. [
36
] studied the lightweight
design of the Chinese University Student Formula Race Car frame through size optimization under
the premise of satisfying the frequency, strength, and stiness constraints. Finally, the nonlinear
optimization model was approximated by sequential linear programming, and a good lightweight
eect was achieved. Jiang et al. [
37
] established a mathematical model with the minimum span beam
as the objective function, the allowable stress of the beam as the constraint, and the unit thickness as
the variables in the optimization of the spar size. By taking the volume of spar as objective function,
the allowable stress of the spar as constraint, and web thickness as design variable, size optimization is
conducted for the main spar and the rear spar. Subsequently, Xu et al. [
6
] took a midsize o-road vehicle
frame as the optimization object, used the experimental design method to carry out the sensitivity
analysis of design variables, and established the structural optimization model based on the necessary
trade-os of design variables. Simultaneously, the multi-island genetic optimization algorithm was
used to calculate the natural frequencies of the frame under the three conditions of maximum stress,
displacement and free mode, so as to optimize the discrete sizes of the frame plates under the constraints
of natural frequencies, geometric sizes, and strength. Deng et al. [
38
] took the folding electric vehicle
and main folding frame for the object and used SolidWorks to establish a simplified three-dimensional
model of the main folding frame, which was imported into the ANSYS Workbench for static analysis.
Lightweight design of the main folding frame connecting rod by topology optimization and size
optimization under the static-load, sudden-braking, sharp-turn conditions. Zhang et al. [
39
] used a
horizontal machining center bed as the research object, and used the wall thickness of the bed and the
longitudinal thickness, the lateral thickness of the rib as the design parameters, and carried out an
orthogonal test on the test data by least-squares method. The response surface model of the bed mass,
maximum deformation, maximum stress, and the first four natural frequencies are obtained. Taking
the minimum bed mass as the optimization goal, the maximum deformation amount, the maximum
stress, and the first four natural frequencies remain unchanged, and the objective function is solved by
the stepwise quadratic programming method, to complete the size optimization. The optimization
results show that the bed quality is reduced by 5.01% when the static and dynamic characteristics of
the bed are basically unchanged.
4.2.2. Shape Lightweight
Shape optimization structure can further improve the product
0
s superiority and the performance
of the product by further improving the topography and shape characteristics of parts under the
condition of the overall topological relationship being roughly determined. For example, in the
same part of the hole, whether the rectangle is suitable, or the circular is more superior, that is shape
optimization. The dierent sections of the boom were analyzed, from the quadrilateral section to the
Appl. Sci. 2019,9, 5322 8 of 24
nine-sided section and the large rounded corner section, and obtained the influence of the section
shape on the function, stability, and expansion of the boom, which has a certain reference value for
other scholars to study the shape optimization structure [40].
Based on the curve-surface equation, geometric design variable parametric mapping definition of
the new method, and shape optimization design problem design variables less and more constraints,
experts took the shape optimization design of two squirrel cage elastic support slots as an research
object, the optimization design of squirrel cage elastic support slots with single symmetry, double
symmetry, and ellipse periodic distribution was obtained. The slots were found to be excellent, and the
shape is narrow at both ends [
41
]. Zhang et al. [
42
] proposed a new method of hole-shape optimization
on general composite surface. The method of parameter mapping was used to optimize the hole shape
on the surface structure, and the failure function value on the hole circumference curve was selected as
the optimization design objective. The eects of Mises, Tsai-Hill, and Tsai-Wu failure criteria and three
dierent material systems on the optimization results are compared when elliptic function is used to
describe the hole shape. Finally, an example of spline function to describe the hole shape was given in
2011. Developing new methodologies for shape optimization of openings on three-dimensional curved
panels that are used widely in aeronautical and aerospace engineering. To circumvent the diculties
associated with the hole boundary shape parameterization, a virtual punching method that exploits
Boolean operations of the CAD modeler was proposed [
43
] for the definition of shape design variables.
Compared with the parametric mapping method developed previously, the virtual punching method
was shown to be an implicit boundary representation for this specific kind of structure. Instead, the
parametric mapping method was based on the explicit boundary representation. A zero-order genetic
algorithm (GA) was correspondingly implemented into the design procedure of the virtual punching
method in order to execute the optimization process for two reasons. First, it makes it possible to avoid
sensitivity analysis that is relatively dicult due to the implicit boundary representation formulation
and the use of an unstructured mesh. Second, the computing cost of the GA is practically aordable in
shape optimization because often only a small number of design variables are involved. Numerical
tests are carried out for typical examples of the stress concentration minimization around openings on
the curved panels in 2012. Zhang et al. [
29
] used the three-dimensional SolidWorks drawing software
to establish a three-dimensional model of the Longmen Machining Center. Based on the original beam
structure, the well-shaped ribbed plate (original beam structure), ten-shaped ribbed plate, X-shaped
ribbed plate, and V-shaped of beam structure schemes were designed. The ANSYS software is used to
compare and determine the V-shaped rib beam structure as the optimal solution. Isogeometric Analysis
uses NURBS to achieve seamless connection of computer-aided geometric design (CAD), finite element
analysis (FEA), and structural optimization [
44
]. This method uses the NURBS control point of the
geometric model boundary as a design variable, which greatly simplifies the optimization process.
However, due to the large changes in the design variables during the optimization process, the adjacent
control points are too close or too far apart, resulting in grid overlap and malformation, reduced
computational accuracy, and even interruption of the iterative process in 2013. Taking the rotating shell
structure as the object, Sun et al. [
45
] derived the parameterized expression of the opening boundary of
the rotating shell based on hyperelliptic equation and coordinate mapping transformation, and carried
out the study on the dynamic optimization of the opening shape in 2015. In order to improve the
precision, eciency, and convergence of structural optimization calculation, the quasi-equal-arc length
method and the sequence response surface approximation modeling method (SRSM) based on uniform
design are proposed to achieve the precise approximation of spatial hyperelliptic curves respectively,
which have certain application value for the design of structural shape optimization in time-consuming
engineering. Simultaneously, Zhang et al. [
46
] discussed the extended shape optimization problem of
support structures, namely Dirichlet boundary and free boundary simultaneous optimization. Dierent
from traditional FEM, weighted B-spline finite element method and the level set function were applied
as structural analysis tools to consider Dirichlet boundary conditions automatically compensates for
displacement field shape optimization. In 2018, aiming at the lightweight design of the steering wheel
Appl. Sci. 2019,9, 5322 9 of 24
of a certain model [
47
], the hybrid analysis model of the steering wheel skeleton beam body was
established. The skeleton section was parameterized, and the non-sensitive parameters identified by
the sensitivity analysis of dierent section shape parameters were used as design variables, and the
performance evaluation index was used as the constraint condition to carry out the lightweight design
of the steering wheel skeleton. Zhang [
48
] studied the excellent properties of honeycomb structure with
high strength, light weight, energy absorption, shock absorption, sound insulation and heat insulation.
Shape optimization was performed from three angles of the thickened joint, nonregular hexagon and
gradient edge thickness honeycomb structure. From the theoretical analysis and experiment, the
compressive and flexural properties of three honeycomb structures were explored. It is one of the most
widely used structures in lightweight design. Ma et al. [
23
] optimized the structural design of the side
plate assembly by changing the reinforced steel shape and the shape of cross section, and optimized
the structural design of the automobile cargo box guard plate assembly by reducing the number of
reinforcing steel bars and changing the position of reinforcing steel bars.
4.2.3. Topology Lightweight
Topology optimization is used to determine the distribution of materials by analyzing the
distribution of structural forces. Reducing or simply removing material in places with small forces,
retaining or adding materials to areas with large forces or complex forces. In the case of meeting
the mechanical constraints of the material, the material is distributed as much as possible to reduce
the structural quality reasonably. Actually, the structural topology design [
49
] seeks the optimal
distribution of materials within the design area, i.e., it should be determined which points of the
space are material points and which points remain as holes. Structural topology optimization
includes topology optimization of discrete structures and topology optimization of continuous variable
structures [
50
]. In recent years, some progress has been made in structural topology optimization
design, and topology optimization of truss structures in engineering is the most studied. Back to the
truss theory proposed by Michell et al. in 1904, this theory can only be used for single-case conditions
and relies on the selection of appropriate strain fields, which cannot be applied to engineering practice.
In 1964, the ground structure approach was proposed, and numerical methods were introduced. Since
then, the study of topology optimization has revived, and some analytical and numerical theories have
been proposed. At present, the numerical methods for continuous structure topology optimization
include: level set method, branch and bound, steepest descent method, homogenization method,
variable thickness method, variable density method, progressive structure optimization method, and
so on.
Before 2010, topology optimization developed rapidly, and many experts studied and expanded it
from dierent angles. Kim et al. [
51
] applied topology optimization in thin-walled beam section design
for the first time successfully. The cross section of the dierent thin-walled beams is very useful for
identifying the orientation and position of the reinforcement. In proposing topological optimization
problems, a simple power law is applied to the relationship between the density of elements with holes
and the mechanical properties of the elements. Wang et al. [
52
] proposed a new method for topological
optimization of level set models with structural boundaries embedded in scalar functions of higher
dimensions. Allaire et al. [
5
] proposed a new numerical method based on the combination of classical
shape derivatives and forward propagation level set methods. This level set model can flexibly handle
complex topological changes and succinctly describe the boundary shape of the structure. Topological
changes, fidelity, and automation of boundary representations can be handled and compared to
other methods based on boundary changes or homogenization. In this paper, only direct and linear
velocities are achieved, and nonlinear speed functions may greatly increase computational eciency
and eciency of fast fusion. Based on previous research, Wang et al. [
53
] combined the Radial Basis
Function (RBF) with the traditional level set method to construct a more eective structural topology
optimization method. RBF implicit modeling with multiquadric (MQ) splines was developed to
define the implicit level set function with a high level of accuracy and smoothness. An RBF-level set
Appl. Sci. 2019,9, 5322 10 of 24
optimization method was proposed to transform the Hamilton–Jacobi partial dierential equation
(PDE) into a system of ordinary dierential equations (ODEs) over the entire design domain of the
method of lines. Subsequently, Guo et al. [
54
] reviewed the development history and research status
of structural topology optimization from two aspects, discrete structure topology optimization and
continuum structure topology optimization, and put forward the research direction of topology
optimization in theory, practical application, expansion, and software research. At the same time,
Chen et al. [
55
] proposed a level set method for structural stiness topology optimization by implicitly
embedding the boundary of the structure into a zero-level set model of a high one-dimensional scalar
function. The dynamic motion of the level set function is controlled by a Hamiltonian–Jacobi-type
partial dierential equation, which indirectly realizes the dynamic evolution of the structure boundary
topology and shape. The normal motion velocity in the partial dierential equation is established
based on the shape sensitivity analysis result of the optimized objective function, combining finite
element method and finite dierence method, to realize numerical calculation of the elastic equilibrium
equation and the Hamilton–Jacobi equation. The method can optimize the topology and shape of
the structural design boundary and obtain the smooth boundary form simultaneously. There is no
intermediate density material phenomenon like the homogenization method or the density function
penalty method and the chessboard format numerical calculation singularity problem. Luo et al. [
56
]
proposed a new semi-implicit level set method for structural shape and topology optimization. The
structure boundary is implicitly expressed as the zero-level set of high-dimensional scalar functions,
including appropriate time-marching schemes, to achieve discrete level set processing. The main
feature of the present method is it does not suer from any time-step size restriction, as all terms
relevant to stability are discretized in an implicit manner. The semi-implicit scheme with additive
operator splitting treats all coordinate axes equally in arbitrary dimensions with good rotational
invariance. Hence, the present scheme for the level set equations is stable for any practical time steps
and numerically easy to implement with high eciency. Liu et al. [
57
] took the engine hood of a certain
type of vehicle as the research object, and took the topology optimization method as the guidance,
designed three dierent schemes (original structural optimization, small hole reconstruction, and
overall reconstruction) to optimize the structure of the hood, and analyzed its mechanical properties.
Based on the original structure, the topology optimization of the uniformly distributed holes in the
part with less load on the structure is relatively conservative, and the lightweight margin is small, but
the feasibility is large. In the original structural scheme, some holes have been dug in the cover plate
in order to reduce the weight, and the holes in the original structure cannot be rearranged, so that
fewer parts can be lightened, which limits the topology optimization design. Therefore, the small
holes in the original structure of the cover plate are filled, leaving only three large pairs of holes in
the cover plate structure, and then topology optimization is performed, and the holes on the inner
plate are rearranged according to the optimization result. All the holes in the original hood structure
are filled, and then analyzed by topology optimization software to re-divide and design the overall
structure. The topography of the outer ring of the cover plate is unlikely, and the outer ring of the cover
plate may have an assembly relationship with other parts of the body. Therefore, in the optimization
scheme, the outer-ring structure of the cover plate is separated, and as an untreated structure, only the
internal structure is optimized. Many scholars [
58
60
] optimized the stiened layout of thermoelastic
structures and thin-walled structures under inertial load successively. Qiu et al. [
61
,
62
] carried out
topological optimization of size-dependent sandwich structure and functionally graded material
structure respectively.
Kang et al. [
63
] proposed a topology optimization based on node nonlocal density interpolation
structure, which avoided the checkerboard pattern and the “island” phenomenon successfully. In this
method, design variable points can be positioned at any locations in the design domain and may not
necessarily coincide with elemental nodes in 2011. By using the Shepard family of interpolants, the
density value of any given computational point is interpolated by design variable values within a certain
circular influence domain of the point. Liu et al. [
64
] studied the structural topology optimization
Appl. Sci. 2019,9, 5322 11 of 24
design problem under the condition of simple harmonic load, with the specified displacement response
amplitude of the structure as the design target and the structural volume as the constraint. The
variable density method and the sensitivity filtering method are used to optimize the topology of the
dynamic displacement response. In order to eliminate the local modal phenomena that are prone to
appear in the dynamic topology optimization problem, a polynomial interpolation model of material
properties is introduced, and the sensitivity redistribution method is adopted to avoid the checkerboard
phenomenon in the topology optimization process in 2012. The SIMP mode was established [
65
]
according to the variable density method in order to meet the requirements of high modality and high
lightweight of the workpiece square mirror in 2013. The maximum stiness or strain energy is often
used as the objective function of optimization, and the volume constraint of the whole structure is the
optimal constraint. It can be transformed into the objective function with the minimum volume under
the given structural stiness constraint. Assume that the material density is constant within the cell
and is used as a design variable, while the material properties are used. The exponential function of
density is simulated. The exponential function relationship of relative density has greatly improved
the elimination of checkerboard phenomenon and numerical stability. Yang et al. [
66
] conducted a
finite element analysis on the bonnet of a car under four common conditions (the forward bending
conditions, lateral bending conditions, torsional bending conditions, and constrained mode conditions).
The topology optimization method was adopted to optimize the central area of the inner hood of the
hood with the minimum weighted strain energy as the optimization target. Optimize the area of the
hood ribs, and export the STL file with OSS mooth, regenerate the surface, import it into CATIA, modify
the model according to the topology-optimized shape and material distribution path, and obtain the
topology-optimized hood. The hood plate with optimized topology is obtained, and high-strength
steel, aluminum alloy, and magnesium alloy are selected as replacement materials, respectively. In 2014,
the optimized aluminum alloy solution with topological structure was the optimal lightweight solution.
Zhang et al. [
67
] researched on various simultaneous topology optimization methods extended from
standard formulas discussed the scalability and accessibility of topology optimization. Zhu et al. [
68
]
introduced the AWE method to maintain the topology optimization formula for the extended shape
retention of the specific local domain configuration. Compared with the standard topology optimization
design maximizing structural stiness, this formulation has evidently shown that the coordination of
multipoint displacements and the eect of shape-preserving can be successfully achieved. Cai et al. [
69
]
proposed an ecient and flexible design method, which integrates B-spline finite element method
and level set function to solve stress-constrained shape and topology-optimization problems. Any
structure of complex geometry is embedded within an extended, regular, and fixed Eulerian mesh, no
matter how the structure is optimized. High-order B-spline shape functions are further implemented
to ensure precisions of stress analysis and sensitivity analysis. The parameters involved, rather than
the conventional discrete form of LSF, are used directly as design variables, to simplify the numerical
calculation process. Specifically, LSF is constructed by an R function that combines cubic splines
into implicit functions, providing flexibility for shape optimization within a fixed grid frame, while
compactly supported radial basis functions (CS-RBF). It is used as an implicit function stress-constrained
topology optimization function to calculate stress and stress sensitivity with high precision. Zhang and
Yang [
30
] took the ship floor frame and superstructure frame as the research object. In order to improve
the space layout of the top of the cabin, the topology of the superstructure frame was optimized, and
the optimal distribution of materials was sought. The structure type and structure of the topology
optimization were obtained. The type makes the material distribution more reasonable. In 2016,
Zhu et al. [
70
] explored the latest advances about topology optimization techniques for aircraft and
aerospace structural design. Lee et al. [
71
] proposed a novel P-norm correction method and a maximum
stress-constrained topology optimization lightweight design. The modified P-norm correction method
to overcome the limitation of conventional P-norm methods by employing the lower bound P-norm
stress curve. Zheng et al. [
72
] used the method of topology optimization and size optimization to
optimize the frame structure of FSAE racing car, and verified the lightweight design of L-shaped and
Appl. Sci. 2019,9, 5322 12 of 24
cantilever beams with yield strength constraints. In order to avoid gray areas, Zhou et al. [
73
] proposed
an approximate symbolic distance function to regulate LSF and KS functions. The bounded normalized
attribute of KS functions is a symbolic distance function or a normalized first order approximation. The
novelty lies in the fact that many arbitrarily shaped engineering features are considered basic design
primitives. The Kreisselmeier–Steinhauser (KS) function of Boolean operations is used as LSF, which
uses implicit functions to ensure smooth description and topological changes of basic features and the
entire structure. Second, using the modified Heaviside function to smooth the transition of the air-solid
material at a fixed point. To calculate the mesh, a narrow-band integration scheme was developed for
eective sensitivity analysis. Level Set Method (LSM) to describe design geometry and Extended Finite
Element Method (XFEM) were used to solve control equations and measure design performance [
74
].
Chen et al. [75]
introduced the application of topology in bridge design. The basic principles of
structural topology optimization are systematically illustrated from three aspects: physical model,
mathematical model, and optimization algorithm. This paper introduces the application of topology
optimization technology, to find the structure of bridge structure, and shows the structure derivation
process and optimization results in topology optimization. In view of the diculties faced by the
current structural topology optimization technology in the bridge type finding, the direction of future
research is discussed. Zhu et al. [
76
] proposed a conformation-preserving topological optimization
design method to suppress the warping deformation of local structural domains. The optimization
results showed that the constraint of local strain energy on the shape-holding domain could suppress the
warping deformation in complex projects eectively. In 2017, Zhang et al. [
77
] introduced the free curve
of closed B-spline as the structural topology optimization of basic design elements in order to realize
topology optimization with a small number of design variables. Complex shape of design domain is
rigorously modeled by means of level-set description and Boolean operation. Topology optimization
is carried out conveniently within the framework of fixed grid. Computing accuracy is ensured
eectively with the use of finite cell method. Xie et al. [
78
] established a simplified vehicle model for
the front longitudinal beam of electric vehicles and used the Kriging method, genetic algorithm, and
fruit fly optimization algorithm to lightly design the front longitudinal beam. Teng et al. [
79
] proposed
a progressive structural topology optimization model with the objective of maximizing the natural
frequencies of specific modes and minimizing the weighting function of dynamic compliance in order
to achieve multi-objective dynamic structural topology optimization design. Gao et al. [
80
] studied the
topological optimization of a given fixed boundary continuum under uniform force. The variance of the
reaction forces at the boundary between the elastic solid and its foundation is firstly introduced as the
evaluation criterion of the uniformity of the reaction forces. Then, the standard formulation of optimal
topology design is improved by introducing the variance constraint of the reaction forces. Sensitivity
analysis of the latter is carried out based on the adjoint method. In 2018, Picelli et al. [
81
] proposed
a horizontal set method to solve the problem of minimum stress and stress-constrained shape and
topology optimization. This method solved the sub-optimization problem in each iteration in order to
obtain the best boundary velocity.
Zhu et al. [82]
focused on the dynamic response structure topology
optimization method under harmonic fundamental acceleration excitation. In the dynamic response
analysis, we propose using the large mass method (LMM) in which artificial large mass values are
attributed to each driven nodal degree of freedom (DOF), which can thus transform the base acceleration
excitations into force excitations. Mode displacement method (MDM) and mode acceleration method
(MAM) are then used to calculate the harmonic responses and the design sensitivities due to their
balances between computing eciency and accuracy especially when frequency bands are taken into
account.
Wang et al. [83]
took the support frame of photovoltaic panel cleaning robot as an example
and proposed a lightweight design method based on the combination of topological optimization
and response surface method. A numerical simulation experiment combination of seven design
variables is obtained by using the Box–Behnken experimental design. Furthermore, a response surface
approximation model for the bearer frame is established based on quadratic polynomial regression
equations. An iteration optimization is conducted on the model with multi-objective genetic algorithm,
Appl. Sci. 2019,9, 5322 13 of 24
the multi-objective genetic algorithm to carry out iterative optimization calculation on the approximate
model.
Hou et al. [84]
used Sines standard to deal with fatigue constraints based on the background
of pressure topology optimization in order to avoid the failure of connection area in multi-fastener
connection design. Q-P relaxation was used to solve the singularity problem related to stress constraints
in order to achieve the purpose of topology optimization. Subsequently, Wang and Ruan [85] carried
out lightweight design of the steering vertical arm about commercial vehicle based on the topology
optimization technology of HyperWorks. On the basis of the results of the topology optimization of
the vertical arm, the second design of the vertical arm was carried out. By comparing the structure
of the vertical arm before and after optimization, it was found that the weight of the new structure
was reduced by 13.02%, while the original strength and stiness remained basically unchanged.
Huang et al. [86]
established a mathematical model for topological optimization of a naval gun bracket
by homogenization method theory, which takes the cell density of a microstructure as the design
variable, the minimum compliance as the objective function, and the volume function as the constraint
function. It implements the topology optimization process with ANSYS finite element software. In
addition, it is an important step to make the optimization result manufacturable. This also provides
a design idea for general mechanical structure problems.
Bai et al. [87]
carried out the topological
optimization design of the rack and obtained the optimum material distribution of the rack structure.
Referring to the optimized structure, the frame model is rebuilt, and the finite element analysis is
carried out to verify the reliability of the results, which improves the utilization rate of materials under
the condition of meeting the requirements. Shen et al. [
88
] took the smallest flexibility of a harvester
gearbox shell as the objective function, combined with the variable density method and Lagrange
multiplier method in order to optimize the gearbox topology, removed some redundant materials, and
designed reinforcing ribs. In order to realize the lightweight design of the cold-end fan blade in the case
of bird impact, Wu et al. [
89
] started from the point of structural topology optimization calculation, met
the strength requirements of airworthiness regulations, while reducing the mass by 37.9%. It has certain
practical reference value and broad application prospects in dynamic optimization of engineering
structures. Level set-based optimization for two-dimensional structural configurations with thin
members is presented. A structural domain with thin thickness is defined as a narrow band region on
the zero-level contour [
90
] of the level set function. No additional constraints or penalty functional
is required to enforce semi-uniformity in member thickness. An improved topology optimization
approach named adaptive bubble method (ABM) was proposed to overcome the shortcomings of the
traditional bubble method, such as the frequent remeshing operation and the tedious merge process of
holes [
91
]. Recently, an algorithm [
92
] combining solid isotropic material with penalty (SIMP) and
bidirectional evolutionary structure optimization (BESO) was proposed, while topological optimization
of lightweight cellular materials and structures. An example of a simple support beam and a cantilever
beam demonstrates the eectiveness of the method, but the method assumes the uniqueness of the
microstructure of the lightweight porous material, which is somewhat idealized and is not conducive
to actual demand.
4.2.4. Bionics lightweight
Biological structure is the result of hundreds of millions of years of natural selection and evolution
of life. It has incomparable advantages over the structure of artificial materials [
93
]. Bionics is a
technical imitation of the functions of animals and plants in nature, which provides a bridge between
biology and technology and provides new ideas for solving technical problems. By reproducing
the principles of biology, humans have found many technological solutions. Structural bionics is an
important branch of bionics. It mainly studies the structure, material, and function of organisms and
designs bionic structures.
Mechanical structural bionics mainly imitates the special abilities of organisms; studies the
structure, function, and working principle of organisms; extracts useful configuration features and
transplants these principles into engineering technology; invents superior instruments, devices, or
Appl. Sci. 2019,9, 5322 14 of 24
machines; and creates new technologies to improve their structural eciency [
94
], which is also the
ultimate goal of lightweight design. The function of living things is far superior to any artificially
manufactured machine. Bionics is a discipline that is used to achieve and eectively apply biological
functions in engineering. There are many parts or mechanical designs in the industrial manufacturing
field that are inspired by biology, such as applying the shape or skin structure of a dolphin to
the submarine design principle: imitating the bat
0
s function of ultrasonic positioning and ranging
to produce radar equipment; imitating the shell-built large-span thin-shell building; imitating the
femoral structure to build the column, which eliminates the area where the stress is particularly
concentrated, and can withstand the maximum load with the least building materials. Supporting
human weight-bearing and moving bones, the dense bones in the cross section are distributed around,
and the soft bone marrow fills the lumen. Interestingly, this conclusion is also reflected in many animal
and plant tissues in nature. For example, the stem of many plants that can withstand the strong wind
is a vascular structure with hollow cross section. Therefore, it is possible to apply the idea of structural
bionics to lightweight design, which is dicult to achieve by traditional methods.
Before 2010, Zhang et al. [
95
] studied the porous structure of chicken eggshells, parrot eggshells,
pork bones, mung beans, soybeans, ginkgo biloba, lotus seeds, and apple epidermis. From the point
of view of the distribution of pore density, size, and geometry, the pore of natural structure can be
divided into uniform pore, gradient pore, and multi-hole. The development of an optimal porous
bearing based on the gradient configuration of natural materials also indicates that the biomimetic
porous structure design is expected to be widely developed and applied in the field of materials and
mechanical engineering in the future. Zhou et al. [
96
] established a driving mechanism to flap the wing
angle in a motion cycle for the phenomenon of tilting to the left or to the right caused by the incomplete
symmetry of the flapping wing. The mathematical model of the dierence between the dierence and
the angular velocity, and the optimization of the objective function by the pattern search method under
the constraints of mechanics and bionics. Zhao et al. [
97
] summarized the configuration of light and
high-eciency biological structures and applied them to the structural bionic design of high-speed
machine tool work ribs. Ansys
0
APDL parametric language was used to establish an optimization model
to determine the optimal structural parameters of the workbench ribs. The bionic annular sandwich
rib structure is used in the rib layout of the workbench, and the diagonal ribs are arranged in the
direction of the maximum deformation gradient to realize the weight reduction of the structure and the
improvement of the static and dynamic characteristics. Subsequently,
Qing et al. and Liu et al. [98,99]
introduced the lowest cutting resistance and higher in the cutting process based on the geometry
and excellent biomechanical functions of animal teeth, claw toes, and body surface. The service life
provides the basis for bionic research for the optimization of geometrical parameters and mechanical
properties of cutting tools. Helms et al. [
100
] learned about the biologically inspired engineering
design process and gained a deep understanding of biologically inspired design. At the same year,
Ma et al. [101]
analyzed the structural similarity between Dragonfly membrane fin and aircraft fuselage
reinforcement frame, extracted the structural characteristics that determine the excellent mechanical
properties of dragonfly membrane fin structure(polygon unit and wing angle), and applied them to
the design of aircraft fuselage reinforcement frame.
Liu et al. [102,103]
designed wind turbine blades
based on the characteristics of plant leaf vein distribution and mechanical properties. According to the
high similarity between human respiratory system and engine intake-and-exhaust system, the model
of automobile exhaust manifold was established [
104
107
] by using human bronchus, and verified the
mechanical performance analysis respectively. Meanwhile, Quinn et al. [
108
] discussed how to apply
bionics to engineering. Han et al. [
109
,
110
] of Jilin university conducted dynamic and modal analysis
of bionic surface shape gear.
Shu et al. [
111
] reviewed the research of biological heuristic design in 2011. In 2012,
Cadman et al. [112]
attracted much attention in mechanics and biology because of its unique chemical,
mechanical, and structural properties, based on the special ultralight cell natural material of cuttlebone.
Since the square ribs are stretched between each other during casting cooling, cracks are likely to occur
Appl. Sci. 2019,9, 5322 15 of 24
during cooling or residual internal stress is high after casting, and rupture of the rib may occur due to
impact [
113
]. The honeycomb structure design to improve the dynamic and static stiness of the whole
machine of the moving beam gantry machining center by using bionics principle were adopted. Based
on the characteristics of plant veins and dragonfly-wing veins, structural bionic design of the aircraft
bracket was carried out [
114
]. In the design of the end-face reinforcement ribs, the main reinforcement
ribs are arranged mainly along the stress-gradient direction and the deformation-gradient direction,
the secondary reinforcement ribs are arranged on both sides of the main reinforcement rib, and the
distribution density of the reinforcement ribs is increased in the large stress area. In the design of the
end-face reinforcement ribs, the main reinforcement ribs are arranged mainly along the stress-gradient
direction and the deformation-gradient direction, the secondary reinforcement ribs are arranged on both
sides of the main reinforcement rib, and the distribution density of the reinforcement ribs is increased
in the large stress area. Fu et al. [
115
] proposed a lightweight structure design of the vein-to-rib-cage
beam with reference to the biological vein structure with similar structure, force, and functional
characteristics of the upper flange plate of the crane, mimicking the structural characteristics of the
vein inclination and stagger. Zhao et al. [
4
] studied the research methods and processes of structural
bionics, analyzed the typical application and progress of structural bionics in the field of mechanical
engineering, summarized the role of structural bionics in the field of mechanical applications, and
prospected the development prospects of structural bionics. Based on structural bionics, topology
optimization and dimension optimization design methods, Wang [
116
] carried out optimization design
research on the rotary table of key parts of 4 m NC vertical lathe, aiming at improving structural
stiness and reducing its mass, optimizing the target demand analysis of the rotary table, and finding
the bionic prototype. Based on the excellent bearing performance of the water lily plant, Wang Lian,
we use the fuzzy similarity analysis method to calculate the similarity between Wang Lian and the
rotary table, and determine that Wang Lian works for the rotation, by extracting the configuration
law of the leaf vein structure of Wang Lian, constructing two bionic optimization models of the rotary
table, and performing static analysis. The combination of structural bionics and topology optimization
provides a new idea for obtaining more reasonable structural form of machine-tool parts. Based on
the idea of structural bionic optimization design, combined with topological optimization analysis,
structural bionic optimization design research on the main metal structure of QD75T/31.5 m bridge
crane-box girder were carried out in 2013 [
117
]. Based on the fuzzy similarity theory, the similarity
calculation between the biological prototype and the box-shaped main beam was carried out, and the
bamboo and Wanglian were determined as biological prototypes. The structure and configuration
of two biological prototypes of bamboo and Wanglian were studied and extracted, and then they
were applied to the study of structural bionic optimization design of the box-shaped main girder of
bridge cranes. Two kinds of bionic main girder models were established. The static analysis and
modal analysis of the bionic main beam are carried out. The design results can be used for reference
by crane designers and provided a new design idea for the crane to break through the traditional
experience design. Based on the similarity between the wind turbine and the king palm plant in
terms of configuration and stress environment, the structural properties of the king palm plant are
used to lighten the structure of large wind turbine towers and blades [
118
]. Meng [
119
] explored
and studied the structural bionics design method of engineering machinery, and carried out bionics
design on the structure and chassis structure of engineering machinery. The system combs the various
theoretical theories on which structural bionics depends. It briefly explains the general methods and
processes of structural bionics research and application. It clarifies the relationship between structural
bionics theory and engineering machinery structural design, and it provides a new innovative design
idea for engineering machinery. The bionic structure design and finite element static analysis of the
excavator
0
s stick were carried out based on the hollow structure of the bone dispersion, the ribbed
plate structure of the Wanglian blade and the Xianren column, and the hierarchical structure of the
shell and the bamboo. Liu and Chen [
120
] aimed at the lightweight design requirements of thin-walled
parts, based on the analysis of the shape and configuration of Wang Lian
0
s vein branching structure,
Appl. Sci. 2019,9, 5322 16 of 24
took the aircraft cover prototype as the object, and applied the structural bionic design method, to
carry out the structural bionic lightweight design of the rib distribution form inside the cover plate.
Fu et al. [
121
] used bamboo as a bionic object to optimize the structural design of the transverse
rib of the normal rail box girder, which made the crane box girder structure lighter. Qi et al. [
122
]
studied the structure of bamboo based on bionics principle. Bamboo joints have the function of fixing
bamboo body, increasing the mechanical strength of the stem, making the stem stronger, not easy to
lodge and deform. The lightweight design of tower equipment was discussed. In 2014, Li et al. [
123
]
designed a new method for the layout of reinforced ribs in large machine tools based on the natural
growth principle of plant veins. If we confirm the potential of leaf venation as concept generators for
creating the optimal load-bearing topology for stiened machine-tool structures, then a mathematical
model explaining the optimality of plant morphogenesis is presented. Based on this, an evolutionary
algorithm was developed, which uses three growth strategies to determine the candidate stieners
to grow or atrophy with respect to the loads applied. The proposed growth-based method could
generate a distinct stiener layout, which is dierent to those produced by the conventional topology
optimization methods, and thus oers unique possibilities of improving the design eciency and
commonality for machine-tool development. Huang et al. [
124
] designed the tail swing structure
of the underwater fish robot based on the advantages of high eciency, low noise, high speed, and
high maneuverability of underwater organisms. Chen et al. [
125
] discussed the biological skeleton
of fish bones, leaves, and feathers and carried out a structural layout design of a large aspect-ratio
wing, with the help of bionics theory. Based on structural bionics, You et al. [
126
] used the topological
principle to optimize the design of the rib structure inside the column of nose milling machine. After
the improvement, the quality of the column was reduced and the stiness and mechanical properties
were improved significantly in 2015. In 2016, a bamboo-like tower structure [
127
] was proposed. The
application method of structural bionic design theory in bionic design of tower structure was proposed,
and a bionic tower model for the bamboo-like structure was established. Bamboo was chosen as the
biological prototype, and the similarity between the tower and the bamboo was calculated from the
aspects of structure, function, load, and constraint, which verified the rationality of the biological
selection. The knot-like feature structure of bamboo was extracted and used for tower design. A
bionic tower with five reinforcement sections was proposed, and the geometric model of the tower
was established. It can provide theoretical reference for tower structure design. Bao et al. [
128
]
proposed a bionic design method of lightweight strengthened structure, which studied honeycomb
according to the characteristics of leaf veins and leaves to optimize the shape and distribution of
reinforcing plates. Chen et al. [
129
] pointed out that two biomimetic structures that appeared in
recent years did not meet the requirements according to the characteristics of three-dimensional
lightweight structure of beetle
0
s front wing, which was helpful for the biomimetic application research
of improving the structure of beetle
0
s front wing.
Jia et al. [130]
elaborated the correlation between
structural bionics and structural design of engineering machinery and also provided a new idea
for the innovative design of engineering machinery in 2017. In 2018,
Shan et al. [131]
designed the
bionic robot thigh, according to the CT of the human femur, and established an asymmetric spatial
tetrahedral mesh structure along the vertical stress line inside the thigh, to achieve its weight reduction.
It provides a new idea for the design and manufacture of humanoid robots. Cao et al. [
132
] studied
the structure of lightweight and high-rigidity organisms, designed the frog plate bionic structure
of SCARA manipulator arm by Pro/E three-dimensional software, and used ANSYS Workbench to
analyze the statics and modal analysis to obtain the optimal stiness and lightweight ribbed bionic
II model. Wang et al. [
133
] carried out bionic design based on bamboo and realized lightweight
design of the crane. Compared with the transverse ribs of traditional box girder, the bionic design of
bamboo can correspondingly reduce the number of transverse ribs, which could meet the stability
requirements, as well as the lightweight requirements, while also meeting the strength and toughness
requirements.
Zhao et al. [134]
explored the biomechanical morphology of the leaves and stems
of representative emergent plants by combining experimental and numerical methods, and they
Appl. Sci. 2019,9, 5322 17 of 24
developed an interdisciplinary topological optimization method that combines mechanical properties
and dual ecological constraints. In the two-way evolutionary structure optimization technique, the
proposed biophysical insights are expected to be used to design ecient and advanced structures
(aircraft wings and turbine blades).
4.3. Lightweight Manufacturing Technology and 3D Printing
Lightweight materials are only one aspect of research. When new materials are identified, new
production processing conditions are needed to reduce weight. The organic integration of new material
and new technology into product development not only improves the product performance, but also
eectively shortens the production time and material consumption of the product and shortens the
whole life cycle of the product. The development and research of new technology has pointed out a new
way for lightweight. The optimization of lightweight manufacturing technology can be divided into
cutting, welding, and improvement of other processes of Tox connection. Cutting technology is mainly
considered to adopt advanced equipment or improved process method to improve the machining
accuracy and eciency. In welding technology, besides using advanced welding equipment, good
welding technology can not only improve the welding strength, but also make the appearance of
welding neat and beautiful.
The 3D Kagome lattice structure, 3D pyramid structure, and hexagonal diamond structure
were designed. The selected material was fabricated by using an Objet 350 3D printer and a
polypropylene-based photopolymer called Objet Durus White RGD430 in 2014 [
135
]. In 2016,
Li et al. [136]
proposed a density-aware internal support structure modeling scheme in order to realize
the lightweight modeling of 3D-printing model which conforms to the mechanical characteristics. The
Density-Controllable internal support structure was generated according to the structural analysis.
Simultaneously, Jiang et al. [
137
] proposed a “weak balance” lightweight modeling scheme, to
generate the internal filling structure of 3D printing model. The scheme can generate internal
density-varying fillings based on structural analysis automatically. The lattice structure has many
properties superior to solid materials and traditional structures. It can integrate many functions. Tao
and Leu [138] used AM technology to make a computer-aided design model, which is more complex
than the traditional program, by adding materials layer by layer. In 2017,
Eichenhofer et al. [139]
introduced a new type of additive manufacturing technology for fiber reinforced thermoplastic
composites, namely ultra-lightweight continuous lattice manufacturing, and demonstrated its ability
to characterize anisotropic materials in digital manufacturing structures. Nguyen et al. [
140
] used
topology optimization as an innovative design tool, to facilitate additives manufacturing, by adding
materials layer by layer, to achieve complex geometry. Almost any product can be manufactured,
and the best product structure can be created with the least amount of materials, but can still ensure
the product attributes of machinery. Li et al. [
35
] applied topological optimization method and size
optimization to find the best path of force transmission and the optimum cross-section size of truss
members for the lightweight design of satellite structures. Considering the optimum rod size of
truss members and the constraints of structural processing, geometric reconstruction was carried
out to obtain the structural design scheme for material-added manufacturing to achieve lightweight
design. Sun et al. [
141
] generated honeycomb path trajectories with controllable parameters based on
material and compressive stress analysis. An adaptive generation technology of lightweight honeycomb
3D-printing path was proposed, which provided a new idea for direct printing generation of lightweight
structure with improved local load-carrying performance in 2018. A novel compression-resistant
lattice composite material by introducing a novel optimization method and metallization method was
proposed [
142
], which made a great contribution to lightweight in 2019. Based on the bionics principle,
Shan et al. [
131
] designed the bionic robot thigh according to the CT scan human-femur surface. Using
laser melting technology, the lower thigh of the robot was printed in 3D, without the support of its
internal mesh, in order to verify the manufacturability of the solid and spatial mesh chimera structure.
Appl. Sci. 2019,9, 5322 18 of 24
5. Conclusions and Prospect
This document is only a part of the literature at home and abroad in recent years and is for
reference only. By reading a large number of research literature and books, the optimization problems
of lightweight structure are all generated according to the characteristics of the research objects and
the rigid requirements of researchers. Currently, the modeling ideas are relatively fixed and mature,
and optimization methods are needed to solve this problem, which mainly include size, shape, and
topology optimization. Before 2000, due to the limited technology, the size and shape optimization were
used. After 2000, the topology optimization developed and is still relatively perfect so far. In recent
years, combining these three methods for lightweight research has become part of the mainstream in
engineering. At the same time, the imitation organism has excellent performance, is lightweight, and
has a high-eciency structure, which embodies the optimal distribution of materials and provides
prototypes and methods for the lightweight design of mechanical structures. The best innovation of
the 21st century is the intersection of biology and technology, and lightweight is conducive to saving
materials and protecting the environment. It conforms to the national concept of low carbon, energy
saving, and environmental protection. It benefits the country and the people, and it is more conducive
to enterprises. A large number of theoretical methods and engineering application practices show
that structural lightweight technology not only provides an eective design tool for the development
of aircraft structures, but, more importantly, brings about changes in design concepts. This has
always been the goal pursued by our engineers. In the future, we will continue our research on
lightweight [143]:
The research of lightweight model is limited to engineering software modeling. From the
perspective of mathematics, we can describe the modeling by borrowing mathematical tools
and specific mathematical relations guided by the physical background of the research object in
the future.
Practicality and precision of construction machinery. Combine the specific dynamic and static
problems of the project with lightweight design to make it closer to the actual machine.
Optimization of reliability. The reliability of structure is increasingly becoming an important
indicator of modern structural design. The comprehensive design based on reliability size, shape,
and topology optimization should be a research direction in the future.
The combination of lightweight and additive manufacturing can eectively reduce the risk of
revision and optimization of design, which is a very new trend in the future.
The new intelligent algorithm can be cited to solve the lightweight model.
Multidisciplinary cross-bionic lightweight will also be an exploration trend in mechanical
engineering in the future.
Author Contributions:
Conceptualization, J.W., Y.L., G.H., and M.Y.; methodology, J.W. and Y.L.; formal analysis,
J.W.; investigation, J.W. and Y.L.; resources, Y.L.; data curation, J.W.; writing—original draft preparation, J.W. and
Y.L.; writing—review and editing, J.W., Y.L., G.H., and M.Y.; funding acquisition, Y.L. and G.H.
Funding:
This study was funded by the National Natural Science Foundation of China (51475366, 51475146,
51875454).
Conflicts of Interest: The authors declare that they have no conflict of interest.
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This paper is to present an important issue of fatigue failure in the design of multi-fasteners jointed structure. To avoid failure in the connection area, Sines criterion is utilized. Fatigue constraints are handled in the context of stress based topology optimization. To eliminate the high stresses caused by the finite element modeling, the control volume is defined to evaluate the stress states around the fasteners. The standard topology optimization is extended to minimize the structural compliance with fatigue failure constraints. To address singularity problems related to stress constraints, q-p relaxation is used. P-norm is used as the constraints aggregation scheme. Basing on the above, the design sensitivity of fatigue constraints is derived and calculated. The proposed method is verified by a numerical example of an assembled I-beam. The comparisons of the numerical results have shown the effect of the fatigue constraint.
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