Topology optimization for additive manufacture

247 Pages·2017·31.31 MB·English

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Topology optimization for
additive manufacture
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Topology Optimization for Additive Manufacture

By
Aremu Adedeji

A Doctoral Thesis
Submitted in Partial Fulfillment of the
requirements for the Award of
Doctor of Philosophy
of Loughborough University

Wolfson School of Mechanical and Manufacturing Engineering

March 1, 2013
© by Adedeji Aremu 2013
Acknowledgements
I am grateful to God for the successful completion of this work and for the opportunity to meet
differentpeopleatLoughboroughUniversity. Iwouldliketothankmysupervisorsfortheopportu-
nity to conduct research at a world class university. Thanks to Prof. Ian Ashcroft, Prof. Richard
Hague, Prof. Ricky Wildman and Dr. Chris Tuck. I am also grateful to members of AMRG, for
assisting with yearly oral examinations, administrative and technical issues. These include Prof.
Vadim Silberschmidt, Prof. Jonathan Huntley, Prof. Rob Parkin, Prof. Phil Dickens, Dr. David
Brackett,MarkHardy,MarkEast,PhilipBrindley,JoMason,AndyDean,BridgetShipman,Vince
Scothern and Sally Alldritt. Also, funding provided by the IMCRC made this work possible. I am
grateful to Euge´nie Hunsicker and Joshua Vande Hey for their help and support during the PhD.
Speaking with some other people at international conferences helped overcome obstacles. I am
grateful to Dr. Osvaldo Querin and Prof. David Rosen, their depth of understanding gave the
required insight needed for different tasks. Also, thanks to Darren Engwirda and Dr. Xiaodong
Huang for replying promptly to questions about their work and my examiners Prof. Jeremy Cou-
plandandProf. PeterGoslingfortheirusefuladvice. Iwouldn’twanttoforgetmyundergraduate
supervisor Dr. Leke Oluwole who initially introduced me to the finite element method.
Finally, I would like to appreciate all members of my family for their patience and understand-
ing. These include my father, Dr. Jonathan Aremu, mother, Joy Aremu, my siblings, Bayo, Bola
and Kunle and my wife Favour Aremu. Thanks to my spiritual father, Bishop David Oyedepo, for
his timely messages. May my heavenly father continue to enrich all your families in Jesus name.
i
Abstract
Additivemanufacturing(AM)offersawaytomanufacturehighlycomplexdesignswithpotentially
enhanced performance as it is free from many of the constraints associated with traditional man-
ufacturing. However, current design and optimisation tools, which were developed much earlier
than AM, do not allow efficient exploration of AM’s design space. Among these tools are a set
of numerical methods/algorithms often used in the field of structural optimisation called topology
optimisation (TO). These powerful techniques emerged in the 1980s and have since been used to
achievestructuralsolutionswithsuperiorperformancetothoseofothertypesofstructuraloptimi-
sation. However, such solutions are often constrained during optimisation to minimise structural
complexities, thereby, ensuring that solutions can be manufactured via traditional manufacturing
methods.
With the advent of AM, it is necessary to restructure these techniques to maximise AM’s
capabilities. Such restructuring should involve identification and relaxation of the optimisation
constraints within the TO algorithms that restrict design for AM. These constraints include the
initialdesign,optimisationparametersandmeshcharacteristicsoftheoptimisationproblembeing
solved. AtypicalTOwithcertainmeshcharacteristicswouldinvolvethemovementofanassumed
initial design to another with improved structural performance. It was anticipated that the com-
plexityandperformanceofasolutionwouldbeaffectedbytheoptimisationconstraints. Thiswork
restructured a TO algorithm called the bidirectional evolutionary structural optimisation (BESO)
for AM. MATLAB and MSC Nastran were coupled to study and investigate BESO for both two
and three dimensional problems. It was observed that certain parametric values promote the real-
izationofcomplexstructuresandthiscouldbefurtherenhancedbyincludinganadaptivemeshing
strategy (AMS) in the TO. Such a strategy reduced the degrees of freedom initially required for
this solution quality without the AMS.
ii
Journal, Conferences and
Workshops
1. Aremu A., Ashcroft I., Wildman R., Hague R., Tuck C., and Brackett, D., The effects
of bidirectional evolutionary structural optimisation parameters on an industrial designed
component for additive manufacture, Proceedings of the Institute of Mechanical Engineers,
PartB:JournalofEngineeringManufacture,227(6),DOI:10.1177/0954405412463857,p794-
807, 2013.
2. Aremu A., BrackettD., Ashcroft I., Wildman R., HagueR., Tuck C., Topology Optimisation
Using BESO for Additive Manufacture of a Metal Aerospace Component,The8th ASMOUK
/ IMSSO conference on engineering design optimisation. p26-37, 2010, London.
3. Aremu A., Ashcroft I., Wildman R., Hague R. and Tuck C., Suitability of SIMP and BESO
topology optimisation Algorithms for additive manufacture, 21st Annual International Solid
Freeform Fabrication Symposium, p679-692, 2010, Texas.(Reviewed)
4. AremuA.,AshcroftI.A.,WildmanR.,TuckC.,andHagueR,Investigationoffiniteelement
modelling issues in the application of topological structural optimisation, 20th International
Workshop on Computational Mechanics of Materials. 2010, Loughborough.
5. Aremu A., Brackett D., Ashcroft I., Wildman R., Hague R., Tuck C, An Adaptive Meshing
BasedBESOTopologyOptimisation,9th WorldCongressonStructuralandMultidisciplinary
Optimisation, 2011, Shizuoka.
6. AremuA.,AshcroftI.,WildmanR.,HagueR.,TuckC.,BrackettD.,A hybrid Algorithm for
topology optimisation of Additive Manufactures Structures, 22nd Annual International Solid
Freeform Fabrication Symposium, p279-289, 2011, Texas.(Reviewed)
iii
7. Aremu A., Ashcroft I., Wildman R., Hague R., Tuck C., Brackett D.,An adaptive meshing
algorithm for BESO optimisation of two dimensional parts, 21st International Workshop on
Computational Mechanics of Materials, 2011, Limerick.
iv
Contents
Acknowledgements i
Abstract ii
Journal, Conference And Workshop Pages iii
List Of Figures xi
List Of Tables xiii
Nomenclature xix
1 Introduction 1
1.1 Additive Manufacturing Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Premilinary Work on Design Optimization . . . . . . . . . . . . . . . . . . . . . . . 7
1.3 Structural Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Optimization Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5 Research Hypothesis, Aims and Objectives . . . . . . . . . . . . . . . . . . . . . . 15
1.6 Scope and Thesis Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2 Literature Review: Design for Additive Manufacture and Topology Optimiza-
tion 18
2.1 Design for Additive Manufacture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Definition of Topology Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 History of Topology Optimization Algorithms . . . . . . . . . . . . . . . . . . . . . 23
2.4 Topology Optimization Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.1 Homogenization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.2 Solid Isotropic Microstructure with Penalization . . . . . . . . . . . . . . . 26
2.4.3 Evolutionary Structural Optimization . . . . . . . . . . . . . . . . . . . . . 29
2.4.4 Application of Modern Algorithms for Topology Optimization . . . . . . . . 30
2.5 Commercial Topology Optimization Software . . . . . . . . . . . . . . . . . . . . . 32
2.6 Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.6.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.6.2 Common Linear Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
v
2.6.3 Adaptive Mesh Improvement Strategies . . . . . . . . . . . . . . . . . . . . 38
2.7 Application of Adaptive Meshing in Engineering and Topology Optimization . . . 39
2.8 Evaluation of Research Requirement . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.8.1 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.8.2 Hole Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.8.3 The Starting Design and Mesh Size. . . . . . . . . . . . . . . . . . . . . . . 41
2.8.4 Optimization Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.9 Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.10 Simulation Design and Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.11 Data Collection and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.12 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3 Two Dimensional Parametric, Probabilistic and Adaptive Studies 50
3.1 Theoretical Description of the FM-BESO Algorithm . . . . . . . . . . . . . . . . . 51
3.2 An Implementation Of the BESO Algorithm. . . . . . . . . . . . . . . . . . . . . . 54
3.3 Probabilistic BESO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.4 Benchmarking the Code Performance with the Literature . . . . . . . . . . . . . . 63
3.5 Two Dimensional Parametric Studies . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.5.1 Simulations PS2-1 to PS2-4 . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.5.2 Simulations PS2-5 to PS2-8 . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.5.3 Simulations PS2-9 to PS2-12 . . . . . . . . . . . . . . . . . . . . . . . . . . 70
3.5.4 Discussion and Analysis of Parametric Results . . . . . . . . . . . . . . . . 70
3.6 Probabilistic Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.6.1 Probabilistic Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.6.2 Analysis of Probabilistic Results . . . . . . . . . . . . . . . . . . . . . . . . 79
3.7 A Hybrid Algorithm for Two Dimensional Topology Optimization . . . . . . . . . 82
3.7.1 Modified BESO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
3.7.2 Adaptive Meshing Strategy (AMS) . . . . . . . . . . . . . . . . . . . . . . . 84
3.7.3 Test Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.7.4 Test Of Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
3.7.5 Sensitivity Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
3.7.6 Boundary Smoothness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.8 Benefits and Drawbacks of the Adaptive Meshing Strategy . . . . . . . . . . . . . . 97
3.9 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4 Three Dimensional Studies 99
4.1 A Single Load Case Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
4.2 Results Of Three Dimensional Parametric Analysis . . . . . . . . . . . . . . . . . . 102
4.2.1 Simulation 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.2.2 Simulation 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
4.2.3 Simulation 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.2.4 Simulation 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
4.2.5 Three Dimensional BESO Parameter Relationships . . . . . . . . . . . . . . 111
vi
4.3 A Comparison Of The Two And Three Dimensional Parametric Analysis . . . . . 113
4.4 Experimental Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.4.1 Post Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.4.2 Manufacturing: Selective Laser Sintering. . . . . . . . . . . . . . . . . . . . 119
4.4.3 Mechanical Tester And Rig . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.4.4 Validation Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.4.5 Results And Discussion Of Validation Experiments . . . . . . . . . . . . . . 124
4.4.6 Determination Of Error In Experimental Results . . . . . . . . . . . . . . . 128
4.5 Summary And Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5 A Hybrid Algorithm For Three Dimensional Topology Optimization 133
5.1 Three Dimensional AMS-BESO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.1.1 Boundary Elements Selection . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.1.2 Reduction Of the Design Domain . . . . . . . . . . . . . . . . . . . . . . . . 135
5.1.3 Element Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
5.1.4 Improvement of Mesh Quality . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.2 Three Dimensional AMS-BESO Simulations . . . . . . . . . . . . . . . . . . . . . . 143
5.3 Results from Simulations A3-1, A3-2, A3-2 and A3-4 . . . . . . . . . . . . . . . . . 145
5.3.1 Effects Of Domain Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5.3.2 OptimalTopologiesAndPerformanceForSimulationsA3-1,A3-2,A3-3and
A3-4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.4 Stiffness Determination For A3-1, A3-2, A3-3 and A3-4 . . . . . . . . . . . . . . . 151
5.5 Computational Time For A3-1, A3-2, A3-3 and A3-4 . . . . . . . . . . . . . . . . . 153
5.6 Boundary Smoothness Of Three Dimensional Solutions . . . . . . . . . . . . . . . . 156
5.7 A Comparison of Two and Three Dimensional Adaptive Topologies . . . . . . . . . 157
5.8 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6 Discussion, Conclusion and Recommendation for Further Work 159
6.1 General Summary and Major Findings . . . . . . . . . . . . . . . . . . . . . . . . . 160
6.2 Quantification of Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162
6.3 Structural Integrity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
6.4 Regions Of an Optimal Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
6.5 Computational Efficiency of AMS-BESO . . . . . . . . . . . . . . . . . . . . . . . . 166
6.6 A Comparison with Commercial Software . . . . . . . . . . . . . . . . . . . . . . . 167
6.6.1 Solution of the Three Dimensional Parametric Problem with OptiStruct . . 167
6.6.2 Solution Of the three Dimensional Cantilever Problem With OptiStruct . . 169
6.7 Implication of Results for Additively Manufactured Parts . . . . . . . . . . . . . . 170
6.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.9 Recommendations For Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . 173
List Of References 175
Appendix A: BESO Code Implemented with MATLAB and Nastran 188
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