Semi-Definite Programming for Topology Optimization of Trusses under Multiple Eigenvalue Constraints

Topology optimization problem of trusses for specified eigenvalue of vibration is formulated as Semi-Definite Programming (SDP), and an algorithm is presented based on the Semi-Definite Programming Algorithm (SDPA) which utilizes extensively the sparseness of the matrices. Since the sensitivity coe#cients of the eigenvalues with respect to the design variables are not needed, the SDPA is especially useful for the case where the optimal design has multiple fundamental eigenvalue. Global and local modes are defined and a procedure is presented for generating optimal topology from the practical point of view. It is shown in the examples, that SDPA has advantage over existing methods in view of computational e#ciency and accuracy of the solutions, and an optimal topology with five-fold fundamental eigenvalue is found without any di#culty. 1 Introduction The eigenvalues of free vibration as well as the linear buckling load factor are important performance measures of the structures. Theref..