A multi-step relay implementation of the successive iteration of analysis and design method for large-scale natural frequency-related topology optimization.

Large-scale natural frequency-related topology optimization problems pose a great challenge due to the high computational cost required by the iterative computation of the system eigenvalues and their sensitivities in each design iteration. This paper presents a new framework based on a multi-step relay strategy in conjunction with the idea of successive iteration of analysis and design (SIAD), to find high-quality solutions at affordable computational costs. The method starts from a relatively coarse finite element discretization, and then use gradually refined meshes to improve the design resolution. For a given level of mesh resolution, the method interleaves the eigenvalue solution routine with the optimization iterations to achieves sequential approximations of the eigenpairs along with the structural design evolution, thus avoiding the time-consuming eigenpair analysis in each optimization iteration. By sequentially solving the optimization problem and projecting intermediate designs and the corresponding approximate eigenmodes from a coarser mesh onto finer meshes, the proposed multi-step relay method can further substantially alleviate the computational burden and generate high-resolution boundaries in the final design. Numerical examples show that this method can be used to solve natural frequency maximization topology optimization problems with millions of degrees of freedom on a desktop workstation, and is much more efficient than the conventional double-loop method. [ABSTRACT FROM AUTHOR]