A level set topology optimization method using a biharmonic equation based on plate theory

Abstract

This study aims to propose a new level set optimization method capable of adjusting the complexity of resulting structure without loss of its optimality. The key idea is the deformational behavior of plates. We consider the level set function as the deflection of a fictitious plate on an elastic foundation subjected to the accumulative topological derivative load. The governing equation of this plate contains linear and biharmonic operators. The linear operator, arising from elastic foundation, directly connects the topological derivative to the level set function and plays the main role in creating new holes over the working domain based on the value of the topological derivative. While the biharmonic operator, arising from physical behavior of plate, performs as a filter and adjusts complexity of optimized structure. In the present paper, the topological derivative at a certain point is obtained by measuring the influence of removing element on an objective function. To impose a constraint, the classical controllers are added to the procedure. The results of several numerical examples confirm the validity and efficiency of the proposed optimization method.