A method using successive iteration of analysis and design for large-scale topology optimization considering eigenfrequencies

Repeatedly solving the generalized eigenvalue problems by far dominates the computational cost in large-scale topology optimization involving natural frequency constraints. This study proposes a method for dynamic topology optimization problems considering natural frequencies using successively executed iterations for the structural analysis and design. By using the Rayleigh quotients as approximations of the natural frequencies and achieving sequential approximation of the eigenpairs through inverse iteration-like procedures to improve the eigenvectors along with the topological evolution of the structure, the method avoids solving the time-consuming eigenvalue problem in each design iteration. This makes the method particularly suitable for large-scale frequency-constrained topology optimization problems. The convergence property of the method is analyzed under the assumption of sufficiently small design changes between two successive design iterations. Numerical examples regarding frequency and frequency gap constraints show that this method is able to realize concurrent convergence of the eigenvalue analysis and design optimization, and is more efficient than the conventional double-loop approach.