TRUSS TOPOLOGY OPTIMIZATION WITH FUNDAMENTAL FREQUENCY CONSTRAINTS VIA SEMI-DEFINITE PROGRAMMING

It is difficult to calculate the sensitivity coefficients of multiple eigenvalues for large complex structures due to lack of usual differentiability with respect to a design variable, and the equilibrium equation constraints if exists in the model will lead to nonconvex programming. Consequently the global optimum is difficult to find. To avoid this intractable issue, this paper presents a new optimization model for truss structures. The optimized problem is formulated as compliance minimization with volume and fundamental frequency constraints via semidefinite programming (SDP), and the compliance and fundamental frequency in traditional models are casted as semidefinite matrix constraints, both the cross section and compliance are viewed as variables. In this way, the sensitivity coefficients of multiple eigenvalues are circumvented. The SDP model is applicable both to single and multiple eigenvalues. The theoretical results and the practical use of this model are illustrated by examples at the end of the paper.