Structural optimization of mechanical structures targeting vibration characteristics based on the level set method

Abstract

Vibration characteristics such as eigenfrequencies and eigenmodes are crucial factors that determine the dynamic performance of mechanical structures, and high performance structures that function dynamically can be designed by appropriately specifying such vibration characteristics. This paper proposes a structural optimization method for obtaining mechanical structures having specified vibration characteristics, based on the level set method. First, the basic details of a structural optimization method using the level set method, which can be applied to dynamic problems, are briefly discussed. Next, optimization problems that address the maximum eigenfrequencies, and the matching of eigenfrequencies with target values, are formulated. A new optimization algorithm based on the level set method is constructed, where a newly improved geometric reinitialization scheme is used for re-initializing a level set function, based on a zero level set surface. Using the proposed optimization algorithm, both the solving of the eigenvalue problem and the updating of the level set function are performed using the FEM, where non-structural meshes can easily be configured. Finally, several design examples are provided to confirm the usefulness of the proposed structural optimization method.