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Voigt–Reuss topology optimization for structures with nonlinear material behaviors
Author(s) -
Swan Colby C.,
Kosaka Iku
Publication year - 1997
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19971030)40:20<3785::aid-nme240>3.0.co;2-v
Subject(s) - topology optimization , topology (electrical circuits) , consistency (knowledge bases) , sensitivity (control systems) , mathematics , domain (mathematical analysis) , mathematical optimization , nonlinear system , finite element method , structural engineering , engineering , mathematical analysis , geometry , physics , combinatorics , quantum mechanics , electronic engineering
This work is directed toward optimizing concept designs of structures featuring inelastic material behaviours by using topology optimization. In the proposed framework, alternative structural designs are described with the aid of spatial distributions of volume fraction design variables throughout a prescribed design domain. Since two or more materials are permitted to simultaneously occupy local regions of the design domain, small‐strain integration algorithms for general two‐material mixtures of solids are developed for the Voigt (isostrain) and Reuss (isostress) assumptions, and hybrid combinations thereof. Structural topology optimization problems involving non‐linear material behaviours are formulated and algorithms for incremental topology design sensitivity analysis (DSA) of energy type functionals are presented. The consistency between the structural topology design formulation and the developed sensitivity analysis algorithms is established on three small structural topology problems separately involving linear elastic materials, elastoplastic materials, and viscoelastic materials. The good performance of the proposed framework is demonstrated by solving two topology optimization problems to maximize the limit strength of elastoplastic structures. It is demonstrated through the second example that structures optimized for maximal strength can be significantly different than those optimized for minimal elastic compliance. © 1997 John Wiley & Sons, Ltd.