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arXiv · 1301.2354

A New Approach for Solving Singular Systems in Topology Optimization Using Krylov Subspace Methods

Teruyoshi Washizawa·Akira Asai·Nobuhiro Yoshikawa
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Abstract

In topology optimization, the design parameter with no contribution to the objective function vanishes. This causes the stiffness matrix to become singular. We show that a local optimal solution is obtained by Conjugate Residual Method and Conjugate Gradient Method even if the stiffness matrix becomes singular. We prove that CGMconverges to a local optimal solution in that case. Computer simulation shows that CGM gives the same solutions obtained by CRM in case of a cantilever beam problem.

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Teruyoshi Washizawa, Akira Asai, Nobuhiro Yoshikawa. 2013-01-10. A New Approach for Solving Singular Systems in Topology Optimization Using Krylov Subspace Methods. https://doi.org/10.1007/s00158-004-0439-3

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