Multiscale optimal design and fabrication of laminated composites

Abstract We present a general framework that digitally integrates the workflow for optimal design and fabrication of novel multiscale laminated fiber-based composites with spatially varying microstructure in each lamina of a flat or curved laminate. Given a design problem, our framework consists of three key components: 1) Design automation, 2) Material compilation, and 3) Digital fabrication. Design automation involves efficient simultaneous synthesis of optimal macroscale topology and spatially varying fibrous microstructure in a laminated composite, whereas digital fabrication comprises manufacture of the optimal structure. Material compilation is an intermediate process that translates the multiscale results of the design automation step to a digitally manufacturable arrangement of matrix and fibers within each layer of a laminate. These components constitute a digital thread and can be initialized by any method or process of choice. In this paper, we develop a multiscale topology optimization approach for design automation, new computational geometry algorithms for material compilation, and voxel-based material jetting for digital fabrication. We demonstrate and experimentally validate the extensive capabilities of our framework with various plate and shell structures that have potential applications in architecture, aerospace and soft robotics.

[1]  Krister Svanberg,et al.  A Class of Globally Convergent Optimization Methods Based on Conservative Convex Separable Approximations , 2002, SIAM J. Optim..

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

[3]  H. Alicia Kim,et al.  New optimization method for steered fiber composites using the level set method , 2015 .

[4]  N. Kikuchi,et al.  General topology optimization method with continuous and discrete orientation design using isoparametric projection , 2015 .

[5]  W. Zhong,et al.  Short fiber reinforced composites for fused deposition modeling , 2001 .

[6]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

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

[8]  Helder C. Rodrigues,et al.  Hierarchical optimization of laminated fiber reinforced composites , 2014 .

[9]  Fionnuala Connolly,et al.  Automatic design of fiber-reinforced soft actuators for trajectory matching , 2016, Proceedings of the National Academy of Sciences.

[10]  Daniel A. Tortorelli,et al.  Nonlinear structural design using multiscale topology optimization. Part I: Static formulation , 2013 .

[11]  Michaël Bruyneel,et al.  SFP—a new parameterization based on shape functions for optimal material selection: application to conventional composite plies , 2011 .

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

[13]  Hongkai Zhao,et al.  A fast sweeping method for Eikonal equations , 2004, Math. Comput..

[14]  Stefanie Reese,et al.  A reduced integration solid‐shell finite element based on the EAS and the ANS concept—Geometrically linear problems , 2009 .

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

[16]  Daniel M. De Leon,et al.  Aeroelastic tailoring using fiber orientation and topology optimization , 2012 .

[17]  R. Ritchie,et al.  Bioinspired structural materials. , 2014, Nature materials.

[18]  Peter D. Dunning,et al.  Simultaneous material and structural optimization by multiscale topology optimization , 2016 .

[19]  Qi Ge,et al.  Active materials by four-dimension printing , 2013 .

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

[21]  J. R. Raney,et al.  Rotational 3D printing of damage-tolerant composites with programmable mechanics , 2018, Proceedings of the National Academy of Sciences.

[22]  Erik Lund,et al.  Discrete material optimization of general composite shell structures , 2005 .

[23]  M. Stingl,et al.  Simultaneous parametric material and topology optimization with constrained material grading , 2016 .

[24]  Y. Benveniste,et al.  A new approach to the application of Mori-Tanaka's theory in composite materials , 1987 .

[25]  J. Lewis,et al.  3D‐Printing of Lightweight Cellular Composites , 2014, Advanced materials.

[26]  Ole Sigmund,et al.  Homogenization-based topology optimization for high-resolution manufacturable micro-structures , 2018 .

[27]  Niels Leergaard Pedersen On topology optimization of plates with prestress , 2001 .

[28]  Erik Lund,et al.  Buckling topology optimization of laminated multi-material composite shell structures , 2009 .

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

[30]  J. A. Sethian,et al.  Fast Marching Methods , 1999, SIAM Rev..

[31]  Charlie C. L. Wang,et al.  Current and future trends in topology optimization for additive manufacturing , 2018 .

[32]  John Rasmussen,et al.  An integrated approach for shape and topology optimization of shell structures , 2002 .

[33]  Daniel M. Vogt,et al.  Embedded 3D Printing of Strain Sensors within Highly Stretchable Elastomers , 2014, Advanced materials.

[34]  G. Allaire,et al.  Stacking sequence and shape optimization of laminated composite plates via a level-set method , 2016 .

[35]  Kurt Maute,et al.  Simultaneous Digital Design and Additive Manufacture of Structures and Materials , 2018, Scientific Reports.

[36]  Damiano Pasini,et al.  Multiscale isogeometric topology optimization for lattice materials , 2017 .

[37]  Bernd Freisleben,et al.  A heuristic and a genetic topology optimization algorithm for weight-minimal laminate structures , 2002 .

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

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

[40]  Helder C. Rodrigues,et al.  Multiscale topology optimization of bi-material laminated composite structures , 2015 .

[41]  Wojciech Matusik,et al.  Two-Scale Topology Optimization with Microstructures , 2017, TOGS.