A New Approach for Solving Singular Systems in Topology Optimization Using Krylov Subspace Methods
For topology optimization practitioners, this work addresses the singularity issue in stiffness matrices, but the results are incremental as they only demonstrate equivalence on a single test problem.
The paper shows that Conjugate Residual and Conjugate Gradient methods can solve singular systems in topology optimization, achieving local optimal solutions. Simulations on a cantilever beam confirm that CGM matches CRM results.
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.