A structural optimization method based on the level set method using a new geometry‐based re‐initialization scheme

Abstract

SUMMARYStructural optimization methods based on the level set method are a new type of structural optimization method where the outlines of target structures can be implicitly represented using the level set function, and updated by solving the so-called Hamilton-Jacobi equation based on a Eulerian coordinate system. These new methods can allow topological alterations, such as the number of holes, during the optimization process whereas the boundaries of the target structure are clearly defined. However, the re-initialization scheme used when updating the level set function is a critical problem when seeking to obtain appropriately updated outlines of target structures. In this paper, we propose a new structural optimization method based on the level set method using a new geometry-based re-initialization scheme where both the numerical analysis used when solving the equilibrium equations and the updating process of the level set function are performed using the Finite Element Method. The stiffness maximization, eigenfrequency maximization, and eigenfrequency matching problems are considered as optimization problems. Several design examples are presented to confirm the usefulness of the proposed method.

Coupled aerostructural topology optimization using a level set method for 3D aircraft wings

“…This method is suitable for unstructured meshes as it is FE based. Another method suitable for unstructured meshes is to use a geometry based re-initialization procedure with a FE based solution for the implicit function update (Yamasaki et al 2010). However, both these approaches can be computationally expensive when considering large 3D applications.…”

A boundary element and level set based topology optimisation using sensitivity analysis

“…Ha and Cho [19] utilised an unstructured domain conforming discretisation approach for the optimisation of geometrically nonlinear structures within the LS framework. Yamasaki et al [20] presented a boundary tracking approach for the LS based topology optimisation using a conforming discretisation approach and geometry based re-initialisation scheme [21].…”

Recent development in structural design and optimization

“…The study of the level set method has received considerable interest since its birth. Recently, numerous extensions have been made for this method to solve various types of topology optimization problems [30][31][32][33][34][35][36]. Further explorations of this method are necessary for solving large-scale real-world topology optimization problems.…”