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Level set shape and topology optimization of finite strain bilateral contact problems
Author(s) -
Lawry Matthew,
Maute Kurt
Publication year - 2017
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/nme.5582
Subject(s) - finite element method , shape optimization , topology optimization , level set (data structures) , level set method , discretization , nonlinear system , parametric statistics , compliant mechanism , topology (electrical circuits) , representation (politics) , computer science , mathematics , mathematical optimization , mathematical analysis , structural engineering , engineering , physics , statistics , segmentation , quantum mechanics , artificial intelligence , combinatorics , politics , law , political science , image segmentation
Summary This paper presents a method for the optimization of multicomponent structures comprised of 2 and 3 materials considering large motion sliding contact and separation along interfaces. The structural geometry is defined by an explicit level set method, which allows for both shape and topology changes. The mechanical model assumes finite strains, a nonlinear elastic material behavior, and a quasi‐static response. Identification of overlapping surface position is handled by a coupled parametric representation of contact surfaces. A stabilized Lagrange method and an active set strategy are used to model frictionless contact and separation. The mechanical model is discretized by the extended FEM, which maintains a clear definition of geometry. Face‐oriented ghost penalization and dynamic relaxation are implemented to improve the stability of the physical response prediction. A nonlinear programming scheme is used to solve the optimization problem, which is regularized by introducing a perimeter penalty into the objective function. Design sensitivities are determined by the adjoint method. The main characteristics of the proposed method are studied by numerical examples in 2 dimensions. The numerical results demonstrate improved design performance when compared to models optimized with a small strain assumption. Additionally, examples with load path dependent objectives display nonintuitive designs.