A review of topology optimization for additive manufacturing: Status and challenges

Abstract Topology optimization was developed as an advanced structural design methodology to generate innovative lightweight and high-performance configurations that are difficult to obtain with conventional ideas. Additive manufacturing is an advanced manufacturing technique building as-designed structures via layer-by-layer joining material, providing an alternative pattern for complex components. The integration of topology optimization and additive manufacturing can make the most of their advantages and potentials, and has wide application prospects in modern manufacturing. This article reviews the main content and applications of the research on the integration of topology optimization and additive manufacturing in recent years, including multi-scale or hierarchical structural optimization design and topology optimization considering additive manufacturing constraints. Meanwhile, some challenges of structural design approaches for additive manufacturing are discussed, such as the performance characterization and scale effects of additively manufactured lattice structures, the anisotropy and fatigue performance of additively manufactured material, and additively manufactured functionally graded material issues, etc. It is shown that in the research of topology optimization for additive manufacturing, the integration of material, structure, process and performance is important to pursue high-performance, multi-functional and lightweight production. This article provides a reference for further related research and aerospace applications.

[1]  Grégoire Allaire,et al.  Structural optimization under overhang constraints imposed by additive manufacturing technologies , 2017, J. Comput. Phys..

[2]  Liang Gao,et al.  Topology optimization for multiscale design of porous composites with multi-domain microstructures , 2019, Computer Methods in Applied Mechanics and Engineering.

[3]  Gengdong Cheng,et al.  Recent development in structural design and optimization , 2010 .

[4]  Yanyan Zhu,et al.  The anisotropy of laser melting deposition additive manufacturing Ti–6.5Al–3.5Mo–1.5Zr–0.3Si titanium alloy , 2015 .

[5]  M. Messner.  Optimal lattice-structured materials , 2016 .

[6]  Tao Zeng,et al.  Thermo-mechanical behavior analysis of 3D braided composites by multiscale finite element method , 2017 .

[7]  Jong-Bong Park,et al.  Design of a C/SiC functionally graded coating for the oxidation protection of C/C composites , 2005 .

[8]  Carl-Johan Thore,et al.  Topology optimization of periodic 3D heat transfer problems with 2D design , 2019, Structural and Multidisciplinary Optimization.

[9]  F. Liou,et al.  Additive manufacturing of functionally graded metallic materials using laser metal deposition , 2020, Additive Manufacturing.

[10]  J. Kruth,et al.  Manufacturing by combining Selective Laser Melting and Selective Laser Erosion/laser re-melting , 2011 .

[11]  Thomas Tröster,et al.  On the fatigue properties of metals manufactured by selective laser melting — The role of ductility , 2014 .

[12]  Lu Zhou,et al.  Topology optimization of self-supporting structures with polygon features for additive manufacturing , 2018, Computer Methods in Applied Mechanics and Engineering.

[13]  Gengdong Cheng,et al.  Multi-scale concurrent material and structural design under mechanical and thermal loads , 2016 .

[14]  M. H. Luxner,et al.  Finite element modeling concepts and linear analyses of 3D regular open cell structures , 2005 .

[15]  Yanan Wang,et al.  Design and experimental validation of self-supporting topologies for additive manufacturing , 2019, Virtual and Physical Prototyping.

[16]  Jihong Zhu,et al.  A comprehensive study of feature definitions with solids and voids for topology optimization , 2017 .

[17]  Vimal Dhokia,et al.  Process planning for additive and subtractive manufacturing technologies , 2015 .

[18]  Junjie Jiang,et al.  Functionally graded porous scaffolds in multiple patterns: New design method, physical and mechanical properties , 2018, Materials & Design.

[19]  Jikai Liu,et al.  Piecewise length scale control for topology optimization with an irregular design domain , 2019, Computer Methods in Applied Mechanics and Engineering.

[20]  Albert C. To,et al.  Efficient Design-Optimization of Variable-Density Hexagonal Cellular Structure by Additive Manufacturing: Theory and Validation , 2015 .

[21]  Mei Yulin,et al.  A level set method for structural topology optimization and its applications , 2004 .

[22]  Hadi Moztarzadeh,et al.  Design and Development of an Additive Manufactured Component by Topology Optimisation , 2017 .

[23]  S. Torquato,et al.  Scale effects on the elastic behavior of periodic andhierarchical two-dimensional composites , 1999 .

[24]  Hang Zhou,et al.  3D Printing of Carbon Nanotubes-Based Microsupercapacitors. , 2017, ACS applied materials & interfaces.

[25]  Helder C. Rodrigues,et al.  A hierarchical model for concurrent material and topology optimisation of three-dimensional structures , 2008 .

[26]  Weihong Zhang,et al.  Functionally graded materials from topology optimisation and stereolithography , 2018, European Polymer Journal.

[27]  Albert J. Shih,et al.  Tissue transformation mold design and stereolithography fabrication , 2017 .

[28]  Lars Krog,et al.  Application of Topology, Sizing and Shape Optimization Methods to Optimal Design of Aircraft Components , 2011 .

[29]  C. Culmone,et al.  Additive manufacturing of medical instruments: A state-of-the-art review , 2019, Additive Manufacturing.

[30]  N. Shamsaei,et al.  Effects of process time interval and heat treatment on the mechanical and microstructural properties of direct laser deposited 316L stainless steel , 2015 .

[31]  S. Torquato,et al.  Design of materials with extreme thermal expansion using a three-phase topology optimization method , 1997 .

[32]  Andrew T. Gaynor,et al.  Three-dimensional projection-based topology optimization for prescribed-angle self-supporting additively manufactured structures , 2018, Additive Manufacturing.

[33]  Bo Wang,et al.  Influence of imperfection distributions for cylindrical stiffened shells with weld lands , 2015 .

[34]  Xu Guo,et al.  Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework , 2014 .

[35]  David W. Rosen,et al.  The Size Matching and Scaling Method: A Synthesis Method for the Design of Mesoscale Cellular Structures , 2010, 2010 International Conference on Manufacturing Automation.

[36]  C. Tuck,et al.  Effect of the build orientation on the mechanical properties and fracture modes of SLM Ti–6Al–4V , 2014 .

[37]  J. Lewis,et al.  3D Printing of Interdigitated Li‐Ion Microbattery Architectures , 2013, Advanced materials.

[38]  Y. Xie,et al.  A simple evolutionary procedure for structural optimization , 1993 .

[39]  G. H. Loh,et al.  An overview of functionally graded additive manufacturing , 2018, Additive Manufacturing.

[40]  Kai Guo,et al.  Optimization of an “area to point” heat conduction problem , 2016 .

[41]  Weihong Zhang,et al.  Note on spatial gradient operators and gradient-based minimum length constraints in SIMP topology optimization , 2019, Structural and Multidisciplinary Optimization.

[42]  Raimund Rolfes,et al.  Robust design of composite cylindrical shells under axial compression — Simulation and validation , 2008 .

[43]  Qi Xia,et al.  Simultaneous optimization of the material properties and the topology of functionally graded structures , 2008, Comput. Aided Des..

[44]  Gursel Alici,et al.  System and process development for coaxial extrusion in fused deposition modelling , 2017 .

[45]  A. Panesar,et al.  Strategies for functionally graded lattice structures derived using topology optimisation for Additive Manufacturing , 2018 .

[46]  Xiaoping Qian,et al.  Undercut and overhang angle control in topology optimization: A density gradient based integral approach , 2017 .

[47]  Josephine V. Carstensen,et al.  Topology-optimized design, construction and experimental evaluation of concrete beams , 2019, Automation in Construction.

[48]  Xu Guo,et al.  Explicit three dimensional topology optimization via Moving Morphable Void (MMV) approach , 2017, 1704.06060.

[49]  Y. Xie,et al.  Topological design of microstructures of cellular materials for maximum bulk or shear modulus , 2011 .

[50]  Zunyi Duan,et al.  Size effect of lattice material and minimum weight design , 2014 .

[51]  David W. Rosen,et al.  Heuristic optimization method for cellular structure design of light weight components , 2013 .

[52]  Jihong Zhu,et al.  Experimental validation of 3D printed material behaviors and their influence on the structural topology design , 2018 .

[53]  Jihong Zhu,et al.  Topology Optimization in Aircraft and Aerospace Structures Design , 2016 .

[54]  Yaoyao Fiona Zhao,et al.  Simulation of elastic properties of solid-lattice hybrid structures fabricated by additive manufacturing , 2017 .

[55]  J. Plocher,et al.  Review on design and structural optimisation in additive manufacturing: Towards next-generation lightweight structures , 2019 .

[56]  James K. Guest,et al.  Achieving minimum length scale in topology optimization using nodal design variables and projection functions , 2004 .

[57]  Lawrence E Murr,et al.  Microstructures and Properties of 17-4 PH Stainless Steel Fabricated by Selective Laser Melting , 2012 .

[58]  Charlie C. L. Wang,et al.  Support slimming for single material based additive manufacturing , 2015, Comput. Aided Des..

[59]  Bo Wang,et al.  Hybrid optimization of hierarchical stiffened shells based on smeared stiffener method and finite element method , 2014 .

[60]  David W. Rosen,et al.  Design for Additive Manufacturing , 2015, Additive Manufacturing Technologies.

[61]  Yongcun Zhang,et al.  Design of conducting paths based on topology optimization , 2008 .

[62]  Yingjie Xu,et al.  A strain energy model for the prediction of the effective coefficient of thermal expansion of composite materials , 2012 .

[63]  Qui X. Lieu,et al.  A multi-resolution approach for multi-material topology optimization based on isogeometric analysis , 2017 .

[64]  G. N. Labeas,et al.  Investigation on the Static Response and Failure Process of Metallic Open Lattice Cellular Structures , 2010 .

[65]  Yi Min Xie,et al.  Topology optimization of 3D continuum structures under geometric self-supporting constraint , 2020 .

[66]  Ernst Rank,et al.  Additive manufacturing in construction: A review on processes, applications, and digital planning methods , 2019, Additive Manufacturing.

[67]  M. Ramulu,et al.  Fatigue performance evaluation of selective laser melted Ti–6Al–4V , 2014 .

[68]  Tong Gao,et al.  An aerospace bracket designed by thermo-elastic topology optimization and manufactured by additive manufacturing , 2020 .

[69]  P. Breitkopf,et al.  Design of materials using topology optimization and energy-based homogenization approach in Matlab , 2015 .

[70]  O. Sigmund,et al.  Minimum length scale in topology optimization by geometric constraints , 2015 .

[71]  Andrew A. Shapiro,et al.  Development and characterization of Ti-6Al-4V to 304L stainless steel gradient components fabricated with laser deposition additive manufacturing , 2016 .

[72]  Y. Xie,et al.  Computational efficiency and validation of bi-directional evolutionary structural optimisation , 2000 .

[73]  Jihong Zhu,et al.  From Topology Optimization Design to Additive Manufacturing: Today’s Success and Tomorrow’s Roadmap , 2020, Archives of Computational Methods in Engineering.

[74]  Zhu Jihong,et al.  Layout optimization of multi-component structures under static loads and random excitations , 2012 .

[75]  Rubén Ansola,et al.  A new overhang constraint for topology optimization of self-supporting structures in additive manufacturing , 2018 .

[76]  M. Shakeri,et al.  A review on optimization of composite structures Part II: Functionally graded materials , 2019, Composite Structures.

[77]  Tao Zeng,et al.  Extended multiscale FE approach for steady-state heat conduction analysis of 3D braided composites , 2017 .

[78]  Ying Liu,et al.  Self-supporting structure design in additive manufacturing through explicit topology optimization , 2017 .

[79]  Adedeji Aremu,et al.  A voxel-based method of constructing and skinning conformal and functionally graded lattice structures suitable for additive manufacturing , 2017 .

[80]  Charlie C. L. Wang,et al.  Support-free volume printing by multi-axis motion , 2018, ACM Trans. Graph..

[81]  Xiaoping Qian,et al.  Simultaneous optimization of build orientation and topology for additive manufacturing , 2020 .

[82]  Ole Sigmund,et al.  On projection methods, convergence and robust formulations in topology optimization , 2011, Structural and Multidisciplinary Optimization.

[83]  P. Breitkopf,et al.  Concurrent topology optimization design of material and structure within FE2 nonlinear multiscale analysis framework , 2014 .

[84]  Xiaoping Qian,et al.  Topology optimization of self-supporting support structures for additive manufacturing , 2018 .

[85]  H. Rodrigues,et al.  Hierarchical optimization of material and structure , 2002 .

[86]  Ramana V. Grandhi,et al.  A survey of structural and multidisciplinary continuum topology optimization: post 2000 , 2014 .

[87]  Shikai Jing,et al.  Design Optimization of Irregular Cellular Structure for Additive Manufacturing , 2017 .

[88]  Xianmin Zhang,et al.  Imposing minimum length scale in moving morphable component (MMC)-based topology optimization using an effective connection status (ECS) control method , 2019, Computer Methods in Applied Mechanics and Engineering.

[89]  James K. Guest,et al.  Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design , 2016 .

[90]  Julián A. Norato,et al.  Fatigue-based topology optimization with non-proportional loads , 2019 .

[91]  Weihong Zhang,et al.  Feature-driven topology optimization method with signed distance function , 2016 .

[92]  Ahmad Barari,et al.  Customization of Automotive Structural Components using Additive Manufacturing and Topology Optimization , 2019, IFAC-PapersOnLine.

[93]  Liang Meng,et al.  An inverse approach to the accurate modelling of 3D-printed sandwich panels with lattice core using beams of variable cross-section , 2020 .

[94]  Yunlong Ma,et al.  Grid-pattern optimization framework of novel hierarchical stiffened shells allowing for imperfection sensitivity , 2017 .

[95]  Weihong Zhang,et al.  Topology Optimal Design of Material Microstructures Using Strain Energy-based Method , 2007 .

[96]  Bingqing Chen,et al.  Additive manufacturing of functionally graded materials: A review , 2019, Materials Science and Engineering: A.

[97]  Y. Xie,et al.  Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method , 2007 .

[98]  Oded Amir,et al.  Topology optimization for additive manufacturing: Accounting for overhang limitations using a virtual skeleton , 2017 .

[99]  Shuo Yin,et al.  Data for: Microstructure and mechanical anisotropy of additively manufactured cold spray copper deposits , 2018 .

[100]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[101]  Bin Xu,et al.  Topology optimization of continuum structures under hybrid additive-subtractive manufacturing constraints , 2019, Structural and Multidisciplinary Optimization.

[102]  G. Allaire,et al.  Shape optimization of a layer by layer mechanical constraint for additive manufacturing , 2017 .

[103]  Martin Leary,et al.  Deformation and failure behaviour of Ti-6Al-4V lattice structures manufactured by selective laser melting (SLM) , 2015 .

[104]  Weihong Zhang,et al.  Scale‐related topology optimization of cellular materials and structures , 2006 .

[105]  G. Cheng,et al.  An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures , 2015 .

[106]  Gengdong Cheng,et al.  Multi-objective concurrent topology optimization of thermoelastic structures composed of homogeneous porous material , 2013 .

[107]  O. Sigmund,et al.  Topology optimization approaches , 2013, Structural and Multidisciplinary Optimization.

[108]  Tielin Shi,et al.  Topology optimization of hierarchical lattice structures with substructuring , 2019, Computer Methods in Applied Mechanics and Engineering.

[109]  Yaoyao Fiona Zhao,et al.  Lattice Structure Design and Optimization With Additive Manufacturing Constraints , 2018, IEEE Transactions on Automation Science and Engineering.

[110]  Stephen J. Ludwick,et al.  Natural Frequency Optimization of Variable-Density Additive Manufactured Lattice Structure: Theory and Experimental Validation , 2018, Journal of Manufacturing Science and Engineering.

[111]  Kepeng Qiu,et al.  Bi-Directional Evolutionary Topology Optimization Using Element Replaceable Method , 2007 .

[112]  Shutian Liu,et al.  Topology optimization for minimizing the maximum temperature of transient heat conduction structure , 2019, Structural and Multidisciplinary Optimization.

[113]  Yaoyao Fiona Zhao,et al.  Bidirectional Evolutionary Structural Optimization (BESO) based design method for lattice structure to be fabricated by additive manufacturing , 2015, Comput. Aided Des..

[114]  Dongkyu Lee,et al.  Multi-material topology optimization design for continuum structures with crack patterns , 2018 .

[115]  Boyan Stefanov Lazarov,et al.  Topology optimization using PETSc: An easy-to-use, fully parallel, open source topology optimization framework , 2015 .

[116]  Jian Zhang,et al.  Minimum length scale control in structural topology optimization based on the Moving Morphable Components (MMC) approach , 2016 .

[117]  Alaa Elwany,et al.  Effects of building orientation and heat treatment on fatigue behavior of selective laser melted 17-4 PH stainless steel , 2017 .

[118]  M. Smith,et al.  Finite element modelling of the compressive response of lattice structures manufactured using the selective laser melting technique , 2013 .

[119]  Jiayue Xu,et al.  Flexible n-Type Tungsten Carbide/Polylactic Acid Thermoelectric Composites Fabricated by Additive Manufacturing , 2018 .

[120]  E. A. de Souza Neto,et al.  Topological derivative for multi‐scale linear elasticity models applied to the synthesis of microstructures , 2010 .

[121]  Shutian Liu,et al.  Concurrent topology design of structure and material using a two-scale topology optimization , 2017 .

[122]  Jihong Zhu,et al.  A superelement formulation for the efficient layout design of complex multi-component system , 2012 .

[123]  Xiaoming Wang,et al.  A level set method for structural topology optimization , 2003 .

[124]  Guozhong Zhao,et al.  Multiscale eigenfrequency optimization of multimaterial lattice structures based on the asymptotic homogenization method , 2020 .

[125]  Yingjie Xu,et al.  Thermal conductivities of plain woven C/SiC composite: Micromechanical model considering PyC interphase thermal conductance and manufacture-induced voids , 2018, Composite Structures.

[126]  Yu Sun,et al.  Hybrid analysis and optimization of hierarchical stiffened plates based on asymptotic homogenization method , 2015 .

[127]  Nima Shamsaei,et al.  Fatigue behavior and failure mechanisms of direct laser deposited Ti–6Al–4V , 2016 .

[128]  Jun Yan,et al.  Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency , 2009 .

[129]  M. Bendsøe,et al.  Material interpolation schemes in topology optimization , 1999 .

[130]  Jihong Zhu,et al.  Optimal Packing Configuration Design with Finite-Circle Method , 2012, J. Intell. Robotic Syst..

[131]  Matthijs Langelaar,et al.  An additive manufacturing filter for topology optimization of print-ready designs , 2016, Structural and Multidisciplinary Optimization.

[132]  Shutian Liu,et al.  Finite-Element-Mesh Based Method for Modeling and Optimization of Lattice Structures for Additive Manufacturing , 2018, Materials.

[133]  Johann Sienz,et al.  Part orientation optimisation for the additive layer manufacture of metal components , 2016 .

[134]  James Butler.  Using selective laser sintering for manufacturing , 2011 .

[135]  Weihong Zhang,et al.  Concurrent topology optimization design of structures and non-uniform parameterized lattice microstructures , 2018, Structural and Multidisciplinary Optimization.

[136]  Dirk Mohr,et al.  Large deformation response of additively-manufactured FCC metamaterials: From octet truss lattices towards continuous shell mesostructures , 2017 .

[137]  Shaoying Li,et al.  Concurrent design of hierarchical structures with three-dimensional parameterized lattice microstructures for additive manufacturing , 2020 .

[138]  Gengdong Cheng,et al.  Optimum structure with homogeneous optimum truss-like material , 2008 .

[139]  O. Sigmund.  Tailoring materials with prescribed elastic properties , 1995 .

[140]  Marc A. Meyers,et al.  Functional gradients and heterogeneities in biological materials: Design principles, functions, and bioinspired applications , 2017 .

[141]  N. Shamsaei,et al.  Additive manufacturing of fatigue resistant materials: Challenges and opportunities , 2017 .

[142]  Erik Lund,et al.  Topology optimization with finite-life fatigue constraints , 2017 .

[143]  T. Shi,et al.  Constraints of distance from boundary to skeleton: For the control of length scale in level set based structural topology optimization , 2015 .

[144]  Matthijs Langelaar,et al.  Topology optimization of 3D self-supporting structures for additive manufacturing , 2016 .

[145]  Shutian Liu,et al.  Structural topology optimization considering connectivity constraint , 2016, Structural and Multidisciplinary Optimization.

[146]  Thomas Vietor,et al.  A new methodological framework for design for additive manufacturing , 2016 .

[147]  Yi Min Xie,et al.  A new approach to eliminating enclosed voids in topology optimization for additive manufacturing , 2020 .

[148]  Lu Zhou,et al.  Topology optimization method with elimination of enclosed voids , 2019, Structural and Multidisciplinary Optimization.

[149]  Guoying Dong,et al.  Design and optimization of solid lattice hybrid structures fabricated by additive manufacturing , 2020, Additive Manufacturing.

[150]  Bo Wang,et al.  Efficient Optimization of Cylindrical Stiffened Shells with Reinforced Cutouts by Curvilinear Stiffeners , 2016 .

[151]  Eftychios Sifakis,et al.  Narrow-band topology optimization on a sparsely populated grid , 2018, ACM Trans. Graph..

[152]  P. Breitkopf,et al.  Multiscale structural topology optimization with an approximate constitutive model for local material microstructure , 2015 .

[153]  Bin Xu,et al.  Structural topological optimization with dynamic fatigue constraints subject to dynamic random loads , 2020 .

[154]  O. Sigmund.  Morphology-based black and white filters for topology optimization , 2007 .

[155]  L. Froyen,et al.  Selective laser melting of iron-based powder , 2004 .

[156]  Han Lu,et al.  Generation of a tree-like support structure for fused deposition modelling based on the L-system and an octree , 2019, Graph. Model..

[157]  Kai Tang,et al.  Optimized sequence planning for multi-axis hybrid machining of complex geometries , 2018, Comput. Graph..

[158]  Liang Hao,et al.  Microstructure and mechanical properties of aluminium alloy cellular lattice structures manufactured by direct metal laser sintering , 2015 .

[159]  Erik Holmberg,et al.  Fatigue constrained topology optimization , 2014 .