Topology optimization: a review for structural designs under vibration problems

Abstract

This article provides a comprehensive review of structural optimization employing topology methods for structures under vibration problems. Topology optimization allows creative and radical design modifications, compared to shape and size optimization techniques. Various works of structural topology optimization, which are subjected to vibration as the response function of the optimization process, are reviewed. Different types of calculus and numerical methods commonly used for solving structural topological optimization problems are briefly discussed. Moreover, different aspects of topology optimization related to vibration problems are explained. The articles reviewed are largely confined to linear systems that concern small vibration amplitudes. Accordingly, the works related to vibration topological optimization are classified according to the method employed (homogenization, evolutionary structural optimization, solid isotropic material with penalization, or level set). The reviewed works are tabulated according to their methodology, year, and the objective functions and applications of each work. Although the homogenization and evolutionary methods were common in the past, the solid isotropic material with penalization (SIMP) method is the most popular method applied in recent years. The advantages of the level set method show promise for future applications.