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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 eﬃciency 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

aﬀordable, 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 3oﬀers 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

eﬃciency 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 eﬀectively 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 diﬃculty is that the constraints are

not easy to establish in diﬀerent engineering problems, or diﬀerent working conditions, diﬀerent

Appl. Sci. 2019,9, 5322 3 of 24

backgrounds, and diﬀerent 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;

Xgj

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 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:

Min f (X)(1)

S.t. gj(X)=0, j=1, 2, · · · ,p

gj(X)≤0, j=p+1, p+2, · · · ,m

XL≤X≤XU

(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, stiﬀness 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 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.

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

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 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.

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 [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 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 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 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 eﬀect 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 diﬀerent 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 stiﬀness of the body

is analyzed. The thickness of the body parts that are insensitive to the modality and stiﬀness 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 diﬀerent types of stiﬀened plate structures were compared. It was found that

the material consumption of the W-type stiﬀened plate structure was less and the comprehensive

mechanical properties were better. The W-type stiﬀeners 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 eﬀect 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 eﬀective.

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 stiﬀness constraints. Finally, the nonlinear

optimization model was approximated by sequential linear programming, and a good lightweight

eﬀect 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 oﬀ-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-oﬀs 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 diﬀerent 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 eﬀects of Mises, Tsai-Hill, and Tsai-Wu failure criteria and three

diﬀerent 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 diﬃculties

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 diﬃcult due to the implicit boundary representation formulation

and the use of an unstructured mesh. Second, the computing cost of the GA is practically aﬀordable 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, eﬃciency, 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. Diﬀerent

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 diﬀerent 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 diﬀerent angles. Kim et al. [

51

] applied topology optimization in thin-walled beam section design

for the ﬁrst time successfully. The cross section of the diﬀerent 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 eﬃciency

and eﬃciency 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 eﬀective 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 diﬀerential equation

(PDE) into a system of ordinary diﬀerential 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 stiﬀness 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 diﬀerential equation, which indirectly realizes the dynamic evolution of the structure boundary

topology and shape. The normal motion velocity in the partial diﬀerential equation is established

based on the shape sensitivity analysis result of the optimized objective function, combining ﬁnite

element method and ﬁnite diﬀerence 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 suﬀer 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 eﬃciency. 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 diﬀerent 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 stiﬀened 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 stiﬀness 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 stiﬀness 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 stiﬀness, this formulation has evidently shown that the coordination of

multipoint displacements and the eﬀect of shape-preserving can be successfully achieved. Cai et al. [

69

]

proposed an eﬃcient 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

eﬀective 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 diﬃculties 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 eﬀectively. 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

eﬀectively 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 eﬃciency 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 stiﬀness 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 eﬀectiveness 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 eﬃciency [

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 eﬀectively 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 diﬃcult 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 diﬀerence between the diﬀerence 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-eﬃciency 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 stiﬀness 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

stiﬀness 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 stiﬀened 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 stiﬀeners

to grow or atrophy with respect to the loads applied. The proposed growth-based method could

generate a distinct stiﬀener layout, which is diﬀerent to those produced by the conventional topology

optimization methods, and thus oﬀers unique possibilities of improving the design eﬃciency 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 eﬃciency, 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 stiﬀness 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 stiﬀness 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 eﬃcient 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

eﬀectively 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 eﬃciency. 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-eﬃciency 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 eﬀective 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 eﬀectively 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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