Eigenvalue topology optimization of structures by using MMA

This paper presents a new optimization algorithm for topology optimization of freely vibrating continuum structures for optimal simple and repeated natural eigenfrequencies. Finite element method (FEM) is used to formulate the topology optimization. The modified solid isotropic material with penalization (SIMP) model is used to avoid artificial modes in low density areas. During the optimization process a simple frequency may become multiple. However, the sensitivity of repeated eigenfrequencies is not unique. To capture this behavior, sensitivity of them are calculated by the mathematical perturbation analysis. The eigenvalue topology optimization is considered as a max-min formulation. In order to solve the problem, the method of moving asymptotes (MMA) is used.Two dimensional, plane elasticity problems with different sets of boundary condition and attachment of a concentrated non-structural mass are considered. Numerical results show the validity and supremacy of the proposed approach

Keywords:

Topology optimization , Eigenfrequency design , SIMP , Multiple eigenvalues , MMA