Topology Optimization of Trusses for Specified Multiple Eigenvalue by using Semidefinite Programming

Abstract

Algorithms based on Semi-Definite Programming (SDP) are proposed for the truss topology optimization problems for specified fundamental eigenvalue of free vibration and linear buckling load factor, and optimal topologies of trusses are computed by using the Semi-Definite Programming Algorithm (SDPA). It is well known that optimizing structures for specified minimum eigenvalue is difficult because of non-differentiability of the minimum eigenvalue for the cases of multimodal solutions. It is shown, in the examples, that the proposed algorithms are applicable to multimodal cases.