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Topology optimization of three-dimensional linear elastic structures with a constraint on “perimeter”. (English) Zbl 0992.74058

Summary: This work presents a computational model for topology optimization of a three-dimensional linear elastic structure. The model uses the material distribution approach, and the optimization criterion is the structural compliance subjected to an isoperimetric constraint on volume. Usually the obtained topologies using this approach do not characterize a well-defined structure, i.e. it has regions with porous material and/or with checkerboard patterns. To overcome these problems, we introduce an additional constraint on perimeter and a penalty on intermediate volume fraction. The necessary conditions for optimum are derived analytically, approximated numerically through a suitable finite element discretization, and solved by a first-order method based on the augmented Lagrangian. The computational model is tested in several numerical applications.

MSC:

74P15 Topological methods for optimization problems in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
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