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

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%.

Full text

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:
=ℎ
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]
Elongation
at break [%]
ABS-M30
1040
2180-2230
26-31
2-7
Verowhite
1170
2000-3000
50-65
10-25
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. 3–9, 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, 670–77.
[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, 414–25.
[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. (27–29 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, 48–65.
[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.79 506–18.
[14] Mueller J, Shea K and Daraio C 2015 Mechanical properties of parts fabricated with inkjet 3D
printing through efficient experimental design, Mater. Des. 86 902–12.