Multi-objective topology optimization of multi-component continuum structures via a Kriging-interpolated level set approach

This paper explores a framework for topology optimization of multi-component sheet metal structures, such as those often used in the automotive industry. The primary reason for having multiple components in a structure is to reduce the manufacturing cost, which can become prohibitively expensive otherwise. Having a multi-component structure necessitates re-joining, which often comes at sacrifices in the assembly cost, weight and structural performance. The problem of designing a multi-component structure is thus posed in a multi-objective framework. Approaches to solve the problem may be classified into single and two stage approaches. Two-stage approaches start by focusing solely on structural performance in order to obtain optimal monolithic (single piece) designs, and then the decomposition into multiple components is considered without changing the base topology (identical to the monolithic design). Single-stage approaches simultaneously attempt to optimize both the base topology and its decomposition. Decomposition is an inherently discrete problem, and as such, non-gradient methods are needed for single-stage and second stage of two-stage approaches. This paper adopts an implicit formulation (level-sets) of the design variables, which significantly reduces the number of design variables needed in either single or two stage approaches. The number of design variables in the formulation is independent from the meshing size, which enables application of non-gradient methods to realistic designs. Test results of a short cantilever and an L-shaped bracket studies show reasonable success of both single and two stage approaches, with each approach having different merits.

[1]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

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

[3]  M. Bendsøe.  Optimal shape design as a material distribution problem , 1989 .

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

[5]  N. Kikuchi,et al.  Topological design for vibrating structures , 1995 .

[6]  Noboru Kikuchi,et al.  APPLICATION OF TOPOLOGICAL OPTIMIZATION TECHNIQUES TO STRUCTURAL CRASHWORTHINESS , 1996 .

[7]  Tao Jiang,et al.  A Systems Approach to Structural Topology Optimization: Designing Optimal Connections , 1997 .

[8]  Ole Sigmund,et al.  On the Design of Compliant Mechanisms Using Topology Optimization , 1997 .

[9]  Lothar Thiele,et al.  Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach , 1999, IEEE Trans. Evol. Comput..

[10]  B. Bourdin.  Filters in topology optimization , 2001 .

[11]  T. E. Bruns,et al.  Topology optimization of non-linear elastic structures and compliant mechanisms , 2001 .

[12]  G. Rozvany.  Aims, scope, methods, history and unified terminology of computer-aided topology optimization in structural mechanics , 2001 .

[13]  Yi Min Xie,et al.  Evolutionary structural optimization for connection topology design of multi‐component systems , 2001 .

[14]  Ole Sigmund,et al.  A 99 line topology optimization code written in Matlab , 2001 .

[15]  K. Deb,et al.  Design of truss-structures for minimum weight using genetic algorithms , 2001 .

[16]  Thomas A. Poulsen,et al.  Topology optimization in wavelet space , 2002 .

[17]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

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

[19]  Eric V. Denardo,et al.  Dynamic Programming: Models and Applications , 2003 .

[20]  Xiaomin Deng,et al.  An evaluation of simplified finite element models for spot-welded joints , 2004 .

[21]  F. Keulen,et al.  Topology optimization using a Topology Description function , 2004 .

[22]  G. Allaire,et al.  Structural optimization using sensitivity analysis and a level-set method , 2004 .

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

[24]  N. Olhoff,et al.  Reliability-based topology optimization , 2004 .

[25]  Ren-Jye Yang,et al.  Approximation methods in multidisciplinary analysis and optimization: a panel discussion , 2004 .

[26]  Dr. Zbigniew Michalewicz,et al.  How to Solve It: Modern Heuristics , 2004 .

[27]  G. Allaire,et al.  Topology optimization for minimum stress design with the homogenization method , 2004 .

[28]  Panos Y. Papalambros,et al.  Panos Papalambros a Survey of Structural Optimization in Mechanical Product Development , 2022 .

[29]  J. F. Aguilar Madeira,et al.  Multi-objective optimization of structures topology by genetic algorithms , 2005, Adv. Eng. Softw..

[30]  H. Chickermane,et al.  Design of multi-component structural systems for optimal layout topology and joint locations , 1997, Engineering with Computers.

[31]  M. Wang,et al.  Radial basis functions and level set method for structural topology optimization , 2006 .

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

[33]  George I. N. Rozvany,et al.  A critical review of established methods of structural topology optimization , 2009 .

[34]  Sylvia R. Almeida,et al.  A simple and effective inverse projection scheme for void distribution control in topology optimization , 2009 .

[35]  M. Wang,et al.  Piecewise constant level set method for structural topology optimization , 2009 .

[36]  Julián A. Norato,et al.  Stress-based topology optimization for continua , 2010 .

[37]  Takayuki Yamada,et al.  A topology optimization method based on the level set method incorporating a fictitious interface energy , 2010 .

[38]  James K. Guest,et al.  Reducing dimensionality in topology optimization using adaptive design variable fields , 2010 .

[39]  Anders Clausen,et al.  Efficient topology optimization in MATLAB using 88 lines of code , 2011 .

[40]  Ole Sigmund,et al.  On the usefulness of non-gradient approaches in topology optimization , 2011 .

[41]  Hae Chang Gea,et al.  Compliant Mechanism Design Using a Strain Based Topology Optimization Method , 2011, DAC 2011.

[42]  Kazuhiro Saitou,et al.  Topology Synthesis of Multicomponent Structural Assemblies in Continuum Domains , 2011 .

[43]  Decomposition Templates and Joint Morphing Operators for Genetic Algorithm Optimization of Multi-Component Topology , 2011, DAC 2011.

[44]  Kai A. James,et al.  An isoparametric approach to level set topology optimization using a body-fitted finite-element mesh , 2012 .

[45]  M. Wang,et al.  Shape equilibrium constraint: a strategy for stress-constrained structural topology optimization , 2013 .

[46]  Hesham A. Hegazi,et al.  An Explicit Level-Set Approach for Structural Topology Optimization , 2013, DAC 2013.

[47]  Hideyuki Azegami,et al.  Shape optimization of continua using NURBS as basis functions , 2013 .

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

[49]  Hesham A. Hegazi,et al.  A Kriging-Interpolated Level-Set Approach for Structural Topology Optimization , 2014 .

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

[51]  Kazuhiro Saitou,et al.  Decomposition Templates and Joint Morphing Operators for Genetic Algorithm Optimization of Multicomponent Structural Topology , 2014 .

[52]  Hesham A. Hegazi,et al.  Image Matching Assessment of Attainable Topology via Kriging-Interpolated Level-Sets , 2014, DAC 2014.

[53]  Gordon Lewis,et al.  Product Design for Manufacturing and Assembly , 2015 .