The approximate reanalysis method for topology optimization under harmonic force excitations with multiple frequencies

In mode acceleration method for topology optimization related harmonic response with multiple frequencies, most of the computation effort is invested in the solution of the eigen-problem. This paper is focused on reduction of the computational effort in repeated solution of the eigen-problem involved in mode acceleration method. The block combined approximation with shifting method is adopted for eigen-problem reanalysis, which simultaneously calculates some eigenpairs of modified structures. The triangular factorizations of shifted stiffness matrices generated within a certain number of design iterations are utilized to calculate the modes. For improving computational efficiency, Basic Linear Algebra Subprograms (BLAS) are utilized. The reanalysis method is based on matrix-matrix operations with Level-3 BLAS and can provide very fast development of approximate solutions of high quality for frequencies and associated mode shapes of the modified structure. Numerical examples are given to demonstrate the efficiency of the proposed topology optimization procedure and the accuracy of the approximate solutions.