A Boundary Element Implementation for Topology Optimization of Elastic Structures

Abstract

The objective of this work is to present the implementation of
topological derivative concepts in a standard BEM code. The
topological derivative is evaluated at internal points, and those
showing the lowest values are used to remove material by opening a
circular cavity. Hence, as the iterative processes evolutes, the
original domain has holes progressively punched out, until a given
stop criteria is achieved. At this point, the optimal topology is
expected. Several benchmarks of two-dimensional elasticity are
presented and analyzed. Because the BEM does not employ domain meshes
in linear cases, the resulting topologies are completely devoid of
intermediary material densities. The obtained results showed good
agreement with previous available solutions, and demanded
comparatively low computational cost. The results prove that the
formulation generates optimal topologies, eliminates some typical
drawbacks of homogenization methods, and has potential to be extended
to other classes of problems. More importantly, it opens an
interesting field of investigation for integral equation methods, so
far accomplished only within the finite element methods context.