A stress-based topology optimization method for heterogeneous structures

  • Cian Conlan-SmithEmail author
  • Kai A. James
Research Paper


In this work, we introduce a method to incorporate stress considerations in the topology optimization of heterogeneous structures. More specifically, we focus on using functionally graded materials (FGMs) to produce compliant mechanism designs that are not susceptible to failure. Local material properties are achieved through interpolating between material properties of two or more base materials. Taking advantage of this method, we develop relationships between local Young’s modulus and local yield stress, and apply stress criterion within the optimization problem. A solid isotropic material with penalization (SIMP)–based method is applied where topology and local element material properties are optimized simultaneously. Sensitivities are calculated using an adjoint method and derived in detail. Stress formulations implement the von Mises stress criterion, are relaxed in void regions, and are aggregated into a global form using a p-norm function to represent the maximum stress in the structure. For stress-constrained problems, we maintain local stress control by imposing m p-norm constraints on m regions rather than a global constraint. Our method is first verified by solving the stress minimization of an L-bracket problem, and then multiple stress-constrained compliant mechanism problems are presented. Results suggest that good designs can be produced with the proposed method and that heterogeneous designs can outperform their homogeneous counterparts with respect to both mechanical advantage and reduced stress concentrations.


Topology optimization Functionally graded materials Stress-based design Compliant mechanism Heterogeneous structures 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringTechnical University of DenmarkLyngbyDenmark
  2. 2.Department of Aerospace EngineeringUniversity of Illinois Urbana-ChampaignUrbanaUSA

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