ArticlePDF Available

Topology optimization through stiffness/weight ratio analysis for a three-point bending test of additive manufactured parts

Authors:

Abstract and Figures

Topology Optimization (TO) is a technique that allows for increasingly efficient designs and its objective is to maximize the performance of mechanical systems or structure in a variety of fields. Attempts to employ TO for parts manufactured with conventional methods such as casting, forging, injection moulding, CNC machining and the like could not lead to desired optimum results due to the existing manufacturing constraints regarding geometrical complexity. Currently, additive manufacturing (AM) techniques allow the fabrication of more complex shapes which in principle will lead to improved performances through application of the TO concept. This study focuses on structural optimization of additive manufactured parts of thermoplastic parts based on analysis of the stiffness/weight (mass) ratio for a beam subjected to a three-point bending load. The experimental work is done on optimization of parts manufactured by Fused Deposition Modelling (FDM) technology and finally compared with an identical model manufactured using Polyjet 3D printer. Different TO software are compared to conduct the optimization, and a module of SolidWorks 2018 from Dassault Systems is chosen for the topology optimization for the final experiment. The study focuses on the results on stiffness/mass ratios, paying attention to the influence of different printing parameters on the test results. An increase of stiffness/weight ratio of 31.7% was predicted by software while experiments showed an increase of just 27.04%.
Content may be subject to copyright.
IOP Conference Series: Materials Science and Engineering
PAPER • OPEN ACCESS
Topology optimization through stiffness/weight ratio analysis for a three-
point bending test of additive manufactured parts
To cite this article: A A Garcia-Granada et al 2019 IOP Conf. Ser.: Mater. Sci. Eng. 700 012012
View the article online for updates and enhancements.
This content was downloaded from IP address 178.171.23.41 on 26/11/2019 at 13:32
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution
of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Published under licence by IOP Publishing Ltd
COTech
IOP Conf. Series: Materials Science and Engineering 700 (2019) 012012
IOP Publishing
doi:10.1088/1757-899X/700/1/012012
1
Topology optimization through stiffness/weight ratio analysis
for a three-point bending test of additive manufactured parts
A A Garcia-Granada1, *, J Catafal-Pedragosa1,2 and H G Lemu2
1 GEPI-IQS Grup Enginyeria Producte Industrial, Universitat Ramon Llull, Via
Augusta, 390. 08017, Barcelona, Spain.
2 Department of Mechanical and Structural Engineering and Materials Science,
University of Stavanger, Norway.
* Corresponding author: andres.garcia@iqs.url.edu
Abstract. Topology Optimization (TO) is a technique that allows for increasingly efficient
designs and its objective is to maximize the performance of mechanical systems or structure in
a variety of fields. Attempts to employ TO for parts manufactured with conventional methods
such as casting, forging, injection moulding, CNC machining and the like could not lead to
desired optimum results due to the existing manufacturing constraints regarding geometrical
complexity. Currently, additive manufacturing (AM) techniques allow the fabrication of more
complex shapes which in principle will lead to improved performances through application of
the TO concept. This study focuses on structural optimization of additive manufactured parts of
thermoplastic parts based on analysis of the stiffness/weight (mass) ratio for a beam subjected to
a three-point bending load. The experimental work is done on optimization of parts manufactured
by Fused Deposition Modelling (FDM) technology and finally compared with an identical model
manufactured using Polyjet 3D printer. Different TO software are compared to conduct the
optimization, and a module of SolidWorks 2018 from Dassault Systems is chosen for the
topology optimization for the final experiment. The study focuses on the results on stiffness/mass
ratios, paying attention to the influence of different printing parameters on the test results. An
increase of stiffness/weight ratio of 31.7% was predicted by software while experiments showed
an increase of just 27.04%.
1. Introduction
Topology optimization is a type of structural optimization that is used as a tool or technique in areas that
need reduction of weight in a component by optimal distribution of mass (weight) and hence leads to
improved stiffness to weight ratio. The optimization technique produces shapes by removal of materials
from regions where the component shows low levels of stress under loading conditions. Such shapes
can be complex and hence difficult to manufacture using the traditional manufacturing techniques. With
the current opportunities provided by additive manufacturing, however, the difficulty of fabrication of
complex shapes is not an issue, and hence topology optimized design can be realized. As additive
manufacturing is a technology that is not yet fully mature, it requires detailed studies of several aspects
to understand the material behavior under loading conditions. In this introduction, a brief literature
review is reported to understand the previous work on material characterization of additive
manufactured parts and also on topology optimization.
COTech
IOP Conf. Series: Materials Science and Engineering 700 (2019) 012012
IOP Publishing
doi:10.1088/1757-899X/700/1/012012
2
In order to perform a proper topology optimization, the optimization software needs to rely on
material properties verified for each additive manufacturing strategy. In Akessa et al. [1], for instance,
a study was conducted to characterize the mechanical properties of ABS-M30 material using rectangular
samples that were subjected to 3-point bending tests. The samples were manufactured by varying the air
gap, raster width and raster angle. A similar study was reported by Gebisa and Lemu [2] in which the
effects of varying the FDM process parameters on the flexural properties of ULTEM 9085 were
investigated. The objective of this study was to consider all possible combinations of parameters; air
gap, raster width, raster angle, contour number and contour width.
According to other recent studies carried out by Domingo-Espin et al. [3], anisotropic material
properties should be considered when using FEA simulation of FDM parts exceeding the elastic region
limit. From this study, conclusions were achieved using tests and simulations of an “L” shaped cantilever
beam with bending and torsion for polycarbonate materials. Furthermore, dynamic properties were
studied as described by Domingo-Espin et al. [4], where a simple prismatic part was loaded using a
dynamic mechanical analysis (DMA). Results showed that the building parameters, namely nozzle
diameter, number of contours and distance between rasters can control the elastic behavior of the FDM
manufactured part, being the number of contours the most influential parameter. Test parameters, such
as amplitude, frequency and temperature, showed a great influence on the damping capacity of the part.
Creep behaviour of polycarbonate (PC) parts manufactured using FDM process were studied by
Salazar-Martín et al. [5] using experimental method focusing on the effect of three process parameters:
(1) part build orientation, (2) raster to raster air gap, and (3) number of contours. The study was
conducted on the primary and secondary creep behaviour. It was found that increasing the density of the
sample, by increasing number of countours and reducing air gap, causes creep strain to decrease. The
study also shows the significance of arranging the deposited filaments in the same direction the sample
is loaded. The influence of FDM manufacturing parameters on mode I fracture properties has been
recently studied by Sedigi et al. [6] to explore how a part can hold deformation energy beyond elastic
limits, taking into account plasticity and crack locations.
Other additive manufacturing techniques have been studied to understand the influence of
manufacturing parameters on material properties. For example, Morales-Planas et al. [7] studied the
influence of different manufacturing parameters such as part orientation on mechanical properties of
Multi Jet Fusion PA12 focused on achieving the right design for watertightness, strength and tolerances.
Once material properties are well studied, a topology optimization can be performed taking into account
these values and a literature review on topology optimization is provided.
A review on topology optimization was performed by Hassani et al. [8] already in year 1998 and is
continuously reviewed due to the growth of software and hardware developments. For example,
Campbell et al. [9] provided a review of numerical optimization techniques for meta-device design for
optical materials. In this paper, the literature review focused on lightweight design considering topology
optimization needs for the best stiffness to weight ratio. Gebisa and Lemu [10] reported a case study on
topology optimized design for additive manufacturing. An engine bracket was topologically redesigned
to reduce its weight considering fabrication in AM. The study results show that topology optimization
is a powerful technique to reduce the weight of a structural product while maintaining the design
requirements if additive manufacturing is considered.
Faskhutdinov et al. [11] reported a study done on the topology optimization of a jet engine part with
Selective Laser Melting (SLM) technology where the process of TO is described. The optimization is
the process of choice of the best option imaginable. That decision is done based on some dependent
values (design data) and a target function. The values of design data are found at which the target
function has a minimum. While there may be a number of targets, one will have to have priority on
others, as not all of them may be compatible. Then, topology optimization allows finding an optimal
material distribution in a given design space under the certain loads and boundary conditions. Recently,
Wang et al. [12] worked on lightweight design for robots by integrating topology optimization and
parametric system optimization using TOSCA software. Their target was to maintain the deformations
of the end-effector of a serial painting robot reducing the mass of components.
COTech
IOP Conf. Series: Materials Science and Engineering 700 (2019) 012012
IOP Publishing
doi:10.1088/1757-899X/700/1/012012
3
The objective of the work reported in this article is to conduct topology optimization of 3D printed
parts of thermoplastic materials for improved stiffness to mass ratio using both experimental test (3-
point bending test) and optimization software.
2. Materials and Methods
2.1. Three-point bending test
A three-point bending test is defined as a starting point for the topology optimization reported herein.
This is because tensile tests are not adequate as they provide a uniform stress distribution across the
section of the specimen and therefore the optimization is limited to a reduction of cross section. Three-
point bending test is relatively simple to conduct in a common laboratory facility. It creates different
stress values across the thickness of the specimen and provides room for topology optimization.
In this study, the stiffness to mass ratio is used as a parameter of optimization. Stiffness for a constant
section specimen of a simple supported beam under transverse load is theoretically calculated as follows
based on pure bending:
=
=48
3 (1)
where k is stiffness, F is applied force, y is displacement in loading direction, E is Young modulus,
I is section inertia and L is span length. For the same beam loading, maximum stress (
σ
) is obtained at
the middle of the specimen and theoretically expressed as follows:
=
8 (2)
where h is section height of the specimen.
Theoretical equation for stress does not include stress concentrations near supports but test is defined
to obtain fracture on lower parts of specimen. Therefore, in classical engineering optimization,
increasing inertia will improve stiffness and at the same time reduce maximum stress avoiding plasticity
and fracture with the exception of stress concentration effects if new shapes involve sharp edges.
2.2. Simulation software for topology optimization
Software for topology optimization is growing very fast together with the rapid increase in
computational speed and hardware capacity. As a result, many modelling and simulation tools are
incorporating topology optimization modules in their software package. In this study, a module of
SolidWorks 2018 from Dassault Systems is chosen for the topology optimization. The software allows
the definition of boundary conditions similar to the three-point bending test setup and provides design
rules to select surfaces that should be defined as design features and non-design features. The design
features are subjected to material removal if not contributing to load sharing while the non-design
features should be kept as they are in initial design, regardless of the stress level acting on them. The
software also allows the definition of other rules such as the optimization criteria. The optimization
criteria in this case is defined based on the best stiffness to mass ratio with a load of 50 N, considering
the material anywhere in the beam remains within the elastic region.
2.3. Additive fabrication and testing machine
Fortus 450mc machine from Stratasys (Figure 1(a)), FDM technology, is chosen to fabricate original
and optimized parts using ABS M30 material. According to the material data, the density is around
1040 kg/m3, Young’s modulus between 2180 and 2230 MPa and yield strength between 26 and 31 MPa
with elongation at break between 2 and 7%, depending on the orientation of the part (Table 1) [13]. For
model slicing and machine control, the pre-processor software of the machine, Insight® 12.2, was used.
Raster and contour width were set to 0.4064 mm with just one contour and 0 mm air gap between
contours. Two orientations were chosen, flat and edge and for each orientation two angles 0º and 45º
were chosen.
COTech
IOP Conf. Series: Materials Science and Engineering 700 (2019) 012012
IOP Publishing
doi:10.1088/1757-899X/700/1/012012
4
Optimized parts required support material for overhanging areas. The FDM process of the machine
uses support material referred to as SR20, which dissolves at 70±3 °C and removed from the
manufactured part. The solvent is a water solution with additions of sodium hydroxide and sodium
carbonate. Two sample designs, i.e. rectangular samples and optimized samples were printed and tested.
Four variations with different parameters where designed for each sample, and three specimens for each
variation were tested. In other words, a total of 12 + 12 = 24 ABS specimens were tested.
Table 1. Properties for ABS- M30 and Verowhite (from [13] and [14]).
Density
[kg/m
3
]
Young’s modulus
[MPa]
Yield stress
[MPa]
ABS-M30
1040
2180-2230
26-31
Verowhite
1170
2000-3000
50-65
In order to compare the results with another printing technology, the identical designs were
manufactured using an Objet30 Prime machine from Stratasys (Figure 1 (b)) which is based on Polyjet
technology. This machine cures acrylic liquid by using ultraviolet lamps which can provide high
accuracy with layers of 0.015 mm. The material used for this study was VeroWhite [14]. According to
the material manufacturer, this material has the material properties given in Table 1. A total of 10 + 10
= 20 samples from Verowhite material were manufactured with the same manufacturing conditions to
check repeatability. Finally specimens where tested using three-point bending test on an Instron 5985
(Figure 1 (c)) where displacement and force where recorded. Span length for the beam supports was set
to 100 mm with a velocity of 1mm/min.
Figure 1. Machines used for additive manufacturing machine and testing (a) Fortus 450mc
FDM machine (b) Objet 30 Prime Polyject machine and (c) Instron 5985 tensile test machine.
3. Results and discussion
The original geometry considered for this project is shown in Figure 2, where two small extensions were
provided to a rectangular beam to avoid falling from the three-point bending supports. Theoretical
calculation are provided with equation (1) and equation (2) ignoring these extensions. From theoretical
calculations, the following values are obtained: mass, m = 20.8 g, stiffness, k = 640 N/mm (at E = 2000
MPa) and stress, σ = 1.875 MPa (for F = 50 N), which is below 26 MPa for the lowest yield stress and
without considering stress concentration effects.
(a)
(b)
(c)
COTech
IOP Conf. Series: Materials Science and Engineering 700 (2019) 012012
IOP Publishing
doi:10.1088/1757-899X/700/1/012012
5
Figure 2. Original geometry to be optimized for a three point bend.
Once the samples are defined, topology optimization was performed to achieve an improvement in
the stiffness/mass ratio. Figure 3 (a) shows the optimized model, i.e. after removing unwanted material
but with sharp edges. Then, a smooth optimized geometry is generated (Figure 3 (b)) upon generating
soft cure transitions. In this optimization process, the mass is reduced from 20.8 g down to 9.1 g. Since
the section is not constant or of regular shape, theoretical calculations are not possible for stiffness and
strength.
Figure 3. Optimized part (a) with rough surfaces as optimized and (b) smoothed surface
geometry created base on optimized shape.
The original and the optimized parts are then manufactured with both machines. Figure 4 (a) shows
the specimen manufactured using ABS-M30 material and SR20 support. After the support material is
removed, the specimen is three-point bending tested as illustrated in Figure 4 (b).
Figure 4. Optimized part (a) as manufactured with material support material and (b) under
three-point bending test.
The same procedure was repeated for the specimens fabricated from Verowhite material. Object30
Prime allows fabrication of parts which are closer to CAD geometry as it allows much smaller layer
thickness. This means, it is possible to get a smoother surface in this case compared with that of Fortus
450mc machine. As shown in Figure 5(a), the fracture started from the top connection between front
and bottom face but low friction led to sliding of the test sample (Figure 5(b)) with conditions dissimilar
to the case in topology optimization, which is defined with ideal conditions where the load is placed in
the middle and lower supports are always in the same place. Figures 6(a) and (b) show von Mises stress
distribution for the original design and the optimized shape, respectively. In both figures, stress is much
higher at the load point (middle of the beam) and at the support points (locations of boundary
conditions), thus attention is paid to points in the lower part of the middle section of the specimen where
fracture is expected to happen.
(a)
(b)
(a)
(b)
COTech
IOP Conf. Series: Materials Science and Engineering 700 (2019) 012012
IOP Publishing
doi:10.1088/1757-899X/700/1/012012
6
Figure 5. Optimized structure tested with unstable sliding support.
Figure 6. von Mises stress for 1 mm displacement for (a) original shape and (b) optimized shape.
Finally, Figure 7 shows results for all ABS-M30 tests for both original and optimized designs for
each fabrication condition. The difference in stiffness to mass ratio for all orientations ranged from
18590 to 20830 N/m/g for original part and from 23460 to 26960 N/m/g for optimized parts. Comparison
of all scenarios is provided in Table 2.
Figure 7. Test results for several printing directions for Fortus 450mc.
Analyzing all scenarios, it can be observed that the increase in stiffness to mass (ky /m) ratio varies
from 12.61% increase in the worst case to 45.03% in the best case. The achieved average increase in
stiffness to mass ratio is 27.04%. This is very important since the layer orientation of real complex 3D
components cannot be controlled for each location and therefore it is important to expect that
improvement is achieved for any combination of orientations. Table 3 gives summarized values of the
average mass, loads, displacements and stiffness.
0
500
1000
1500
2000
2500
0 2 4 6 8 10 12 14 16
Load (N)
Displacement (mm)
3-point Bending Test
(a)
(b)
COTech
IOP Conf. Series: Materials Science and Engineering 700 (2019) 012012
IOP Publishing
doi:10.1088/1757-899X/700/1/012012
7
Table 2. Stiffness comparison of ABS-M30 for different scenarios.
Stiffness to mass (ky /m) ratio (N/m/g)
Average
value
Lowest
value
Highest
value
Worst case
optimization
Best case
optimization
Rectangular
1.975E+04
1.859E+04
2.083E+04
2.083E+04
1.859E+04
Optimized
2.509E+04
2.346E+04
2.696E+04
2.346E+04
2.696E+04
k
y
/m increase after
optimization
27.04%
26.19%
29.43%
12.61%
45.03%
Table 3. Average values for each sample design.
Mass
(g)
Max. load
(N)
Displ. at max.
load (mm)
Load at 1 mm
displ. (N)
k
y
(N/m)
k
y
/m
(N/m/g)
Rectangular
19.71
1847
10.06
389.2
3.892E+05
1.975E+04
Optimized
8.87
906
3.43
222.6
2.226E+05
2.509E+04
Furthermore, fracture is also analyzed for each specimen and fabrication orientation. Figure 8 shows
fractured parts from edge fabrication ((a) and (b)) and flat fabrication ((c) and (d)). For each sample
shown, the upper part is 0º and the lower part is 45º. Original parts are shown on the left and optimized
parts on the right. Fracture is complete for flat orientations while fracture is produced on the bottom of
the specimen (as expected) for edge manufactured components.
Figure 8. Fracture of original samples (left a and c) and optimized samples (right b and d).
Results are compared with predictions made by optimization software. In the simulations for
optimization, a Young´s modulus of 1526 MPa was used for a better fitting to test data. 3D tetrahedral
elements of side length 1 mm were used to obtain 12 elements per each mm3 with 4 Jacobian points for
each element. Therefore, for the original shape a total of 130087 nodes and 187218 elements were used
to be eliminated during the optimization process and to define the light weight structure. However, the
importance of optimization simulations is the reduction of weight using reliable material data. As given
(a)
(b)
(c)
(d)
COTech
IOP Conf. Series: Materials Science and Engineering 700 (2019) 012012
IOP Publishing
doi:10.1088/1757-899X/700/1/012012
8
in Table 2, this varies depending on the material orientation. Comparison of the stress results of the
optimized model with the original model is given in Table 4. This comparison shows that optimization
software (FEA) resulted a 31.7% improvement in stiffness to mass ratio (with the same Young’s
modulus) while average results for the 3-point bending tests gave a 27.04% improvement. These
percentage improvements between the simulation approach and experimental test approach have no
significant difference.
Table 4. Comparison of FEA simulations with tests.
Stiffness to mass (ky /m) ratio (N/m/g)
FEA
(E =1526 MPa)
3-point bending
test (average)
Difference
Rectangular 2E+04 1.975E+04 1.25%
Optimized
2.634E+04
2.509E+04
4.75%
Improvement of ky /m
after optimization 31.7% 27.04%
The work was repeated using another printer having better resolution. In this case, 10 samples for
original design and 10 samples for optimized design were manufactured using Verowhite material and
an Object30 Prime printer. For the last samples of Verowhite material, the support was not mechanically
removed after solvent exposition for 24 hours in order to avoid possible damage to the structure. The
weight of components is shown in Figure 9. Average values of each printing direction are taken for
ABS-M30 samples. The weight of the Verowhite original design is very close to the computer aided
design weight of 24.10 g considering density of 1170 kg/m3 while ABS-M30 designs do not reach the
expected density due to accuracy in layers and trajectories.
Figure 9. Mass comparison for Verowhite and ABS-M30.
0
5
10
15
20
25
30
12345678910
Mass (g)
Verowhite-original Verowhite-optimized
ABS30-original ABS30-optimized
COTech
IOP Conf. Series: Materials Science and Engineering 700 (2019) 012012
IOP Publishing
doi:10.1088/1757-899X/700/1/012012
9
On the other hand, Verowhite optimized shapes do not show any improvements in the stiffness to
mass ratios as shown in Figure 10. A possible reason for this can be the sling of the Verowhite
components that place the load in a point far from the center of the specimen due to a surface that looks
like a polished surface. If focused on the original structures, the curves are very similar for ABS-M30
and Verowhite if the weights are normalized. The ABS 30 model, however, has shown improvement in
stiffness to mass ratio. In both cases, for ABS-M30 and Verowhite, the optimized shape can take less
deformation and less energy when compared to original designs.
Figure 10. Comparison Verowhite to ABS-M30.
4. Conclusions
In this paper, a study focusing on topology optimization of additive manufactured part using Fortus
450mc (FDM technology) and Polyjet Object30 Primeis machines is reported. The selected part is tested
using three-point bending test. The optimization targets maximum (improved) stiffness to mass ratio. It
is observed that the obtained stiffness to mass ratio varies with printing orientation. For the ABS-M30
FDM manufactured parts, the topology optimized part under three-point bending test resulted in an
average improvement in stiffness to mass ratio of 27.04%, worst case improvement of 12.61% and best
case improvement of 45.03%. Similar design geometry was used to compare the optimized part performs
by using Verowhite material printed in a Polyjet Objet30 Prime machine. It is observed that the part
manufactured by Polyjet Objet30 Prime machine gives better accurate geometry compared with ABS-
M30 using FDM Fortus 450mc. The part manufactured using Verowhite showed no improvement in
stiffness to mass ratio. One reason for this lack of improvement is the glossy surface of the manufactured
part when the support material is removed. The sliding of the test specimen under the three-point
bending supports due to the glossy surface led to inaccuracies in the test results. It has also been observed
that the optimized shapes provide a lower fracture displacement and absorb less energy when compared
to original shapes.
Acknowledgements
This work has been performed within the Ris3Cat PlastFun (COMRDI16-1-0018) project (Plastic with
functionalized surfaces), funded by ERDF through the Programa Operatiu de Catalunya 2014-2020.
-20
0
20
40
60
80
100
120
-2 0 2 4 6 8 10 12 14 16 18
Normalised force (N/g)
Displacement (mm)
Verowhite-original1 Verowhite-optimized1
ABS-M30-original1 ABS-M30-optimized1
COTech
IOP Conf. Series: Materials Science and Engineering 700 (2019) 012012
IOP Publishing
doi:10.1088/1757-899X/700/1/012012
10
References
[1] Akessa A D, Lemu H G and Gebisa A W 2017 Mechanical property characterization of additive
manufactured ABS material using design of experiment approach, In: Proc. ASME 2017 Inter.
Mech. Eng. Congress and Exposition (Nov. 39, 2017, Tampa, Florida, USA), IMECE2017-
70144, V014T07A004.
[2] Gebisa A W and Lemu H G 2018 Investigating effects of Fused-Deposition Modeling (FDM)
processing parameters on flexural properties of ULTEM 9085 using designed experiment,
Mater. 11(4), 500.
[3] Domingo-Espin M, Puigoriol-Forcada J M, Garcia-Granada A A, Llumà J, Borros S, and Reyes
G 2015 Mechanical property characterization and simulation of fused deposition modeling
Polycarbonate parts, Mater. Des. 83, 67077.
[4] Domingo-Espin M, Borros S, Agullo N, Amador A, Garcia-Granada A A, and Reyes G 2014
Influence of building parameters on the dynamic mechanical properties of polycarbonate fused
deposition modeling parts, 3D Print. Addit. Manuf. 1(2), 70–7.
[5] Salazar-Martín A G, Pérez M A, García-Granada A A, Reyes G and Puigoriol-Forcada J M 2018
A study of creep in polycarbonate fused deposition modelling parts, Mater. Des. 141, 41425.
[6] Sedighi I, Ayatollahi M R, Bahrami B, Pérez-Martínez M A and Garcia-Granada A A 2019
Mechanical behavior of an additively manufactured polycarbonate specimen: tensile, flexural
and mode I fracture properties, Rapid Prototyp. J., 25, 2019.
[7] Morales-Planas S, Minguella-Canela J, Lluma-Fuentes J, Travieso-Rodriguez J and García-
Granada A A 2018 Multi Jet Fusion PA12 manufacturing parameters for watertightness,
strength and tolerances, Mater. 11(8), 1472.
[8] Hassani B and Hinton E 1998 A review of homogenization and topology optimization I
homogenization theory for media with periodic structure, Comput. Struct., 69(6), 707–17.
[9] Campbell S D, Sell D, Jenkins R P, Whiting E B, Fan J A and Werner D H 2019 Review of
numerical optimization techniques for meta-device design, Opt. Mater. Express, 9(4) 1842
63.
[10] Gebisa A W and Lemu H G 2017 A case study on topology optimized design for additive
manufacturing, Proc. of 1st COTech Conf. (Stavanger: Nov 30 Dec 1, 2017) Eds H G Lemu
et al. (IOP Conference Series: Material Science and Engineering), 276(1), 12026.
[11] Faskhutdinov R N, Dubrovskaya A S, Dongauzer K A, Maksimov P V and Trufanov N A 2017
Topology optimization of a gas-turbine engine part, In: Proc. Int. Conf. Mech. Eng., Autom.
Control Syst. (2729 Oct. 2016, Tomsk, Russian Federation): IOP conf. series: Mat. Sci. Eng.
177(1), 12077.
[12] Wang X, Zhang D, Zhao C, Zhang P, Zhang Y and Cai Y 2019 Optimal design of lightweight
serial robots by integrating topology optimization and parametric system optimization, Mech.
Mach. Theory, 132, 4865.
[13] Croccolo D, De Agostinis M and Olmi G 2013 Experimental characterization and analytical
modelling of the mechanical behaviour of fused deposition processed parts made of ABS-
M30, Comput. Mater. Sci.79 50618.
[14] Mueller J, Shea K and Daraio C 2015 Mechanical properties of parts fabricated with inkjet 3D
printing through efficient experimental design, Mater. Des. 86 90212.
... Also, it has been demonstrated that the density of the specimen has a rather large effect on the characteristics of the printed parts [2][3][4]6,[8][9][10][11]. Moreover, the raster path in each layer [12][13][14][15][16] and the printing direction of the whole specimen [17][18][19][20][21] have major influences on the properties of the final products, including the basic and more specific mechanical properties. ...
... ABS has also been investigated for toughness [2], maximum elongation [2,14], shear strength [15], Poisson's ratio [14] and torsion properties [26]. In a few studies, general lattice structures [27] as well as more specific and applicable structures [18] have been printed and tested using ABS. Other polymers have also been tested less commonly in the form of additively manufactured parts. ...
Article
Mechanical components produced by the 3D-printing technique contain small voids by nature, which make them susceptible to fracture. Therefore, understanding the fracture behavior of these components improves the applicability of this manufacturing method. In this study, the effect of layer orientation is investigated on the mixed-mode I/II fracture behavior of additively manufactured poly-carbonate produced using a fused deposition modelling (FDM) printer. A total of 48 semi-circular bend (SCB) specimens with different mode mixities and printing orientations are tested. The curves for the maximum tangential stress (MTS) and the generalized MTS (GMTS) criteria are then produced using the mode I fracture properties for the weakest and the strongest direction of the printed material. This results in two failure curves for each of the criteria. Comparing the mixed-mode fracture toughness data with these curves, it is observed that all the data are placed between the two GMTS curves (regarding error bands). As an engineering approach, the band created by the GMTS curves, called the GMTS range, is suggested as an acceptable band for use in engineering designs. Furthermore, in a more detailed analysis, the fracture paths of the specimens are correlated with the position of the experimental data in the GMTS range. Three different fracture modes occur during the tests depending on the layer orientation and mode mixity of the sample. The inter-layer and the cross-layer modes correspond to the data points on the lower and upper fracture curves, while the data points in the middle represent the samples undergoing the crack multi-kinking mode.
... Illustration of optimization process [8] The optimization is started by giving an initial input or basic idea. This is very important because usually faces nonconvex optimization problems which results in high local optimal topologies. ...
Article
Full-text available
In the present time, there are many challenges in the production of industrial parts. Due to the constantly rising prices of materials and energy, it is necessary to constantly look for ways to optimize production costs and optimize material consumption. There is great pressure on economical production, i. to produce products with the lowest costs given the expected and necessary properties. With the introduction of additive manufacturing technologies into practice and the production of parts for end use comes the introduction of methods for optimizing the shape of the part and the required amount of material for its production. We call this method Topological Optimization. The presented article describes the preparation of topologically optimized parts and a comparison of their strength properties with respect to the original and the original part.
... Looking specifically at fracture properties, the effects of building parameters on 3D printing with acrylonitrile butadiene styrene (ABS) (Hart and Wetzel, 2017;García-Domínguez et al., 2020;Garcia-Granada et al., 2019;McLouth et al., 2017), polylactic acid (PLA) (Chac on et al., 2017;Torres et al., 2016) and polycarbonate (PC) (Sedighi et al., 2020b;Cantrell et al., 2017;Domingo-Espin et al., 2015;Bahrami et al., 2020) have been studied in the literature. These research studies show that the stacking (layer) direction has a significant effect on the mechanical properties of parts produced using fused deposition modeling. ...
Article
Purpose The purpose of this paper is to study the Mode I fracture behavior of polycarbonate (PC) parts produced using fused deposition modeling (FDM). The focus of this study is on samples printed along the out-of-plane direction with different raster angles. Design/methodology/approach Tensile and Mode I fracture tests were conducted. Semi-circular bend specimens were used for the fracture tests, which were printed in four different raster patterns of (0/90), (15/−75) (30/−60) and (45/−45). Moreover, the finite element method (FEM) was used to determine the applicability of linear elastic fracture mechanics (LEFM) for the printed PC parts. The fracture toughness results, as well as the fracture path and the fracture surfaces, were studied to describe the fracture behavior of the samples. Findings Finite element results confirm that the use of LEFM is allowed for the tested PC samples. The fracture toughness results show that changing the direction of the printed rasters can have an effect of up to 50% on the fracture toughness of the printed parts, with the (+45/−45) and (0/90) orientations having the highest and lowest resistance to crack propagation, respectively. Moreover, except for the (0/90) orientation, the other samples have higher crack resistance compared to the bulk material. The fracture toughness of the tested PC depends more on the toughness of the printed sample, rather than its tensile strength. Originality/value The toughness and the energy absorption capability of the printed samples (with different raster patterns) were identified as the main properties affecting the fracture toughness of the AM PC parts. Because the fracture resistance of almost all the samples was higher than that of the base material, it is evident that by choosing the right raster patterns for 3D-printed parts, very high resistance to crack growth may be obtained. Also, using FEM and comparing the size of the plastic zones, it was concluded that, although the tensile curves show nonlinearity, LEFM is still applicable for the printed parts.
Article
Full-text available
Topology Optimisation is a broad concept deemed to encapsulate different processes for computationally determining structural materials optimal layouts. Among such techniques, Discrete Optimisation has a consistent record in Civil and Structural Engineering. In contrast, the Optimisation of Continua recently emerged as a critical asset for fostering the employment of Additive Manufacturing, as one can observe in several other industrial fields. With the purpose of filling the need for a systematic review both on the Topology Optimisation recent applications in structural steel design and on its emerging advances that can be brought from other industrial fields, this article critically analyses scientific publications from the year 2015 to 2020. Over six hundred documents, including Research, Review and Conference articles, added to Research Projects and Patents, attained from different sources were found significant after eligibility verifications and therefore, herein depicted. The discussion focused on Topology Optimisation recent approaches, methods, and fields of application and deepened the analysis of structural steel design and design for Additive Manufacturing. Significant findings can be found in summarising the state-of-the-art in profuse tables, identifying the recent developments and research trends, as well as discussing the path for disseminating Topology Optimisation in steel construction.
Article
Full-text available
The aim of this paper is to explore the watertightness behaviour for high pressure applications using Multi Jet Fusion technology and polyamide 12 as a material. We report an efficient solution for manufacturing functional prototypes and final parts for water pressure applications and provide manufacturing rules for engineers in the pressurized product development process for up to 10 MPa of nominal pressure. The research findings show manufacturers the possibility of using additive manufacturing as an alternative to traditional manufacturing. Water leakage was studied using different printing orientations and wall thicknesses for a range of pressure values. An industrial ball valve was printed and validated with the ISO 9393 standard as also meeting tolerance requirements. This paper is a pioneering approach to the additive manufacturing of high-performance fluid handling components. This approach solves the problem of leakage caused by porosity in additive manufacturing technologies.
Article
Full-text available
Fused-deposition modeling (FDM), one of the additive manufacturing (AM) technologies, is an advanced digital manufacturing technique that produces parts by heating, extruding and depositing filaments of thermoplastic polymers. The properties of FDM-produced parts apparently depend on the processing parameters. These processing parameters have conflicting advantages that need to be investigated. This article focuses on an investigation into the effect of these parameters on the flexural properties of FDM-produced parts. The investigation is carried out on high-performance ULTEM 9085 material, as this material is relatively new and has potential application in the aerospace, military and automotive industries. Five parameters: air gap, raster width, raster angle, contour number, and contour width, with a full factorial design of the experiment, are considered for the investigation. From the investigation, it is revealed that raster angle and raster width have the greatest effect on the flexural properties of the material. The optimal levels of the process parameters achieved are: air gap of 0.000 mm, raster width of 0.7814 mm, raster angle of 0°, contour number of 5, and contour width of 0.7814 mm, leading to a flexural strength of 127 MPa, a flexural modulus of 2400 MPa, and 0.081 flexural strain.
Conference Paper
Full-text available
Additive manufacturing technology is a process of joining materials to make objects from 3D model data, usually layer upon layer, contrary to conventional manufacturing technologies, which mostly use subtractive process. The technology has developed from the earlier days of rapid prototyping to sophisticated rapid manufacturing in the last 20 years and can create parts directly from CAD model without the use of tooling. This technology is predicted to revolutionize many sectors of manufacturing by reducing component lead-time, material waste, energy usage, etc. Though there is significant progress in the field, there are still a number of challenges including characterization of mechanical properties. This paper presents a study conducted to characterize the mechanical properties of ABS-M30 materials whose specimens are fabricated using different printing parameters. To understand the mechanical properties, it is vital to study the effects of the printing parameters on 3D printed parts. For this purpose, Design of Experiment (DOE) is used. The printing parameters of the machine (Fortus 450mc Fused Deposition Modeling (FDM) machine) such as raster orientation, air gap, and raster width, were examined to test Tensile strengths and 3-point bend strength of the tested specimens. The study shows that, raster orientation and air gap has more effect on mechanical properties of ABS-M30 products where raster width has less effect.
Article
Full-text available
Topology optimization is an optimization method that employs mathematical tools to optimize material distribution in a part to be designed. Earlier developments of topology optimization considered conventional manufacturing techniques that have limitations in producing complex geometries. This has hindered the topology optimization efforts not to fully be realized. With the emergence of additive manufacturing (AM) technologies, the technology that builds a part layer upon a layer directly from three dimensional (3D) model data of the part, however, producing complex shape geometry is no longer an issue. Realization of topology optimization through AM provides full design freedom for the design engineers. The article focuses on topologically optimized design approach for additive manufacturing with a case study on lightweight design of jet engine bracket. The study result shows that topology optimization is a powerful design technique to reduce the weight of a product while maintaining the design requirements if additive manufacturing is considered.
Article
Full-text available
One of the key goals of aerospace industry is a reduction of the gas turbine engine weight. The solution of this task consists in the design of gas turbine engine components with reduced weight retaining their functional capabilities. Topology optimization of the part geometry leads to an efficient weight reduction. A complex geometry can be achieved in a single operation with the Selective Laser Melting technology. It should be noted that the complexity of structural features design does not affect the product cost in this case. Let us consider a step-by-step procedure of topology optimization by an example of a gas turbine engine part.
Article
Purpose The purpose of this paper is to investigate the effect of layer orientation on the tensile, flexural and fracture behavior of additively manufactured (AM) polycarbonate (PC) produced using fused deposition modeling (FDM). Design/methodology/approach An experimental approach is undertaken and a total number of 48 tests are conducted. Two types of tensile specimens are used and their mechanical behavior and fracture surfaces are studied. Also, circular parts with different layer orientations are printed and two semi-circular bending (SCB) samples are extracted from each part. Finally, the results of samples with different build directions are compared to one another to better understand the mechanical behavior of additively manufactured PC. Findings The results demonstrate anisotropy in the tensile, flexural and fracture behavior of the additively manufactured PC parts with the latter being less anisotropic compared to the first two. It is also demonstrated that the anisotropy of the elastic modulus is small and can be neglected. Tensile strength ranges from 40 MPa to 53 MPa. At the end, mode I fracture toughness prediction curves are provided for different directions of the FDM samples. Fracture toughness ranges from 1.93 to 2.37 MPa.mm 1/2 . Originality/value The SCB specimen, a very suitable geometry for characterizing anisotropic materials, was used to characterize FDM parts for the first time. Also, the fracture properties of the AM PC have not been studied by the researchers in the past. Therefore, fracture toughness prediction curves are presented for this anisotropic material. These curves can be very suitable for designing parts that are going to be produced by 3D printing. Moreover, the effect of the area to perimeter ratio on the tensile properties of the printed parts is investigated.
Article
Optimization techniques have been indispensable for designing high-performance meta-devices targeted to a wide range of applications. In fact, today optimization is no longer an afterthought and is a fundamental tool for many optical and RF designers. Still, many devices presented in recent literature do not take advantage of optimization techniques. This paper seeks to address this by presenting both an introduction to and a review of several of the most popular techniques currently used for meta-device design. Additionally, emerging techniques like topology optimization and multi-objective optimization and their context to device design are thoroughly discussed. Moreover, attention is given to future directions in meta-device optimization such as surrogate-modeling and deep learning which have the potential to disrupt the fields of optical and radio frequency (RF) inverse-design. Finally, many design examples from the literature are presented and a flow-chart that provides guidance on how best to apply these optimization algorithms to a given problem is provided for the reader.
Article
Topology optimization is proven significant for improving the performance of mechanical systems. However, when it is utilized for the optimal design of industrial robots, there are still many challenges such as complicated variable configurations of robots and computational expensiveness. Therefore, this paper presents an integrated optimal design method for lightweight serial robots by the use of part-level topology optimization and parametric system optimization. Firstly, the finite element analysis (FEA) and virtual joint method (VJM) are combined to construct the stiffness model of the robot, based on which deformations of the end-effector (EE) are analyzed. Then, typical robot configurations and load conditions are determined for the optimizations. Secondly, topology optimizations of main structure components i.e. the part-level optimizations are implemented with TOSCA software, and the stiffness-mass metamodels i.e. relationships between the stiffness and mass of these components are constructed. Finally, the system optimization of the robot is obtained by determining the mass division into different components with the robot stiffness model and metamodels. The optimal design of a serial painting robot is implemented to demonstrate the effectiveness of the proposed method.
Article
This paper presents an experimental investigation on the influence of process parameters such as part orientation, air gap and number of contours along with their interactions on the creep behaviour of fused deposition modelling (FDM) processed polycarbonate (PC) parts. Due to the lack of creep curve data with parts processed by FDM, this research gives a first quantitative approach to the time-dependent mechanical properties. This study not only varies significant process parameters viz., part build orientation, raster to raster air gap and number of contours, but also applies different loads to the samples to further understand primary and secondary creep behaviour for PC, providing the creep curves. Furthermore, two mathematical models are used to fit the experimental data, which can be used in numerical modelling. The first model is the well-documented and commonly used Bailey-Norton equation. As a second model, the fractional Voigt Maxwell in series (FVMS) is proposed to use. This model applies fractional calculus to reduce the number of parameters to be calculated. Conclusions obtained about how process parameters affect the creep behaviour are in agreement with previous research in mechanical properties of FDM parts.