Support-free robust topology optimization based on pseudo-inverse stiffness matrix and eigenvalue analysis

Current finite element analysis (FEA) and optimizations require boundary conditions, i.e., constrained nodes. These nodes represent structural supports. However, many realistic structures do not have such concrete supports. In a robust optimization, i.e., optimization for uncertain load inputs, it is desirable to involve support uncertainty. However, such a robust optimization has not been available since constrained nodes are required to convert the stiffness matrix to an invertible matrix. This paper demonstrates a quite simple robust optimization based on a pseudo-inverse stiffness matrix and eigenvalue analysis that successfully creates optimal design without constrained nodes. The optimization strategy is to minimize the largest eigenvalue of the pseudo-inverse matrix. It was found that optimization for multiple eigenvalues, i.e., multiple load inputs, is required as the nature of the minimax problem. The created structures are capable of carrying multiple load inputs—bending, torsion, and more complex loads. Configurations created in rectangular design domains exhibited hollow monocoque structures.