Structural Optimization of Mechanical Structures Based on the Level Set Method (Construction of a New Re-initialization Method and Its Application to the Stiffness Maximization Problem)

Abstract

This paper proposes a structural optimization method for obtaining mechanical structures that maximize structural stiffness, based on the level set method. First, the basic details of a structural optimization method using the level set method are briefly explained, and an optimization problem that addresses the minimum mean compliance problem is formulated. Next, an optimization algorithm is constructed based on this formulation. In this optimization scheme, a new re-initialization method is proposed, in which a level set function is re-initialized, based on a zero level set surface. This re-initialization method can easily deal with level set function singularities, and can be applied to non-structural meshes. A second new method is also proposed in which the level set function is modified to satisfy a volume constraint while preserving topology of the structure being optimized. By using these two new methods, structural optimization problems can be solved using the finite element method rather than the finite difference method. Finally, several examples are provided to confirm the usefulness of the proposed structural optimization method.