A level set‐based parameterization method for structural shape and topology optimization

TLDR

The study proposes a parametric level‑set method that employs compactly supported radial basis functions and optimality‑criteria techniques for structural shape and topology optimization. The method represents the design boundary as the zero level set of a level‑set function interpolated with smooth radial basis functions, treats the expansion coefficients as design variables, and iteratively updates them using an optimality‑criteria velocity field to drive the boundary toward optimality. This approach eliminates the need for upwind schemes, velocity extension, and reinitialization, simultaneously preserves shape fidelity and topology change, maintains smooth boundaries, and improves convergence. © 2007 John Wiley & Sons, Ltd.

Abstract

Abstract This paper presents an effective parametric approach by extending the conventional level set method to structural shape and topology optimization using the compactly supported radial basis functions (RBFs) and the optimality criteria (OC) method. The structural design boundary is first represented implicitly by embedding into a higher‐dimensional level set function as its zero level set, and the RBFs of a favorable smoothness are then applied to interpolate the level set function. The original initial value problem is thus converted to a parametric optimization, with the expansion coefficients of the interplant posed as the design variables. The OC method is then applied to advance the structure boundary in terms of the velocity field derived from the parametric optimization. Hence, the structural shape and topology optimization is now transformed into a process of iteratively finding coefficients to update the level set function to achieve an optimal configuration. The numerical considerations of the conventional level set method, including upwind schemes, velocity extension, and reinitialization, are eliminated. The proposed scheme is capable of addressing structural shape fidelity and topology change simultaneously and of keeping the boundary smooth during the optimization process. Furthermore, numerical convergence is expected to be improved. A widely investigated example, in the framework of structural stiffness designs, is applied to demonstrate the efficiency and accuracy of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.