Stress constrained topology optimization simultaneously considering the uncertainty of load positions

This study presents a topological optimization method simultaneously considering the stress constraint and the uncertainty of the load positions for practical applications. The phase field design method is used to derive the topologically optimal structure shape. The stress penalization function, which makes intermediate design variable values disproportionately expensive, is employed to ensure numerical stability and avoid the singularity during the optimization process. The adaptive mesh refinement and a modified P-norm stress with correction factor are also employed to reduce the computational cost. As numerical examples, cantilever beam, L-shaped, and MBB-beam are presented to verify the proposed design method. The open-source code FreeFEM++ is used for the finite element analysis and the design process.