Quick and Highly Efficient Modal Analysis Method Based on the Reanalysis Technique for Large Complex Structure and Topology Optimization

Abstract

Modal analysis is widely used to investigate the dynamic characteristics of large and complex structures. For finite element models, iterative solvers are needed to precisely calculate eigenpairs or frequency and vibration mode. However, in cases such as large-scale analysis or reanalysis studies, or optimization design of a huge structure, computational cost may become too time consuming. This paper focuses on the quick structural modal analysis based on the reanalysis technique for large complex structures. Based on the stiffness and mass matrix of the analytical structures, a high precision and efficiency eigensolution is generated by the proposed modal analysis method (the Pseudo Random Independent and Coupling Inverse Iteration (PRICII) method), which combines the pseudo random number initialization, ICII (Independent and Coupling Inverse Iteration) strategy with the double Rayleigh–Ritz analysis. By comparing with the Subspace iteration method, Lanczos method, etc. the large-scale numerical examples show that the actual computational savings of the proposed method are usually higher than 75% with sufficient precision. Also, its applications in topology optimization are greatly effective.