Topology optimization of three-dimensional linear elastic structures with a constraint on 'perimeter'

摘要

This work presents a computational model for the topology optimization of a three-dimensional linear elastic structure. The model uses a 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 an additional constraint on perimeter and a penalty on intermediate volume fraction are considered. 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 optimization problem augmented Lagrangian. The computational model is tested in several numerical applications.