其他摘要：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.
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