An Efficient Reanalysis Method for Topological Optimization of Vibrating Continuum Structures for Simple and Multiple Eigenfrequencies

Abstract

This paper shows how the reanalysis method can be utilized for speeding up the optimized process in topology optimization related to vibrating structures for simple and multiple eigenfrequencies. The block combined approximation with shifting (BCAS) method is used for reducing the computational effort included in repeated solution of eigenvalue problem, which will dominate a lot of the CPU time, especially for large problems. By utilizing Level 3 Basic Linear Algebra Subprograms (BLAS), the computation efficiency of the BCAS method is improved. For achieving an accurate optimal result, two indicators are presented to control the approximate reanalysis procedure. The effectiveness of the proposed method is demonstrated by three numerical examples.

On-the-fly model reduction for large-scale structural topology optimization using principal components analysis

“…Gogu (2015) extended the approach of Kirsch and Papalambros (2001) and used Gram-Schmidt orthonormalization to construct a reduced basis on-the-fly based on the violation of an error residual. A survey of the available literature reveals a recent resurgence of interest in reanalysis in topology optimization (Zheng et al 2017;Sun et al 2018;Senne et al 2019).…”