A Short Survey: Topological Shape Optimization of Structures Using Level Set Methods

Zhen Luo

doi:10.4172/2168-9873.1000123

Abstract

This paper will give a short survey about topology optimization of structures. It is particularly focused on topological shape optimization of structures using level-set methods, including the level-set based standard methods and the level-set based alternative methods. The former often directly solve the Hamilton-Jacobi partial differential equation (H-J PDE) to obtain the boundary velocity field using Finite Differential Methods (FDM), and the later commonly employ parametric or equivalent methods to evaluate the velocity field without directly solving the H-J PDE. The unique characteristics of the level-set based topology optimization methods are discussed, and a future perspective and prospects in this research area is also included. A benchmark numerical example is used to showcase the effectiveness of the level-set based methods.

Highlights

This paper will give a short survey about topology optimization of structures
In contrast to the detailed designs of a structure, topology optimization [1] is highly challenging at the conceptual design stage, because it requires automatic determination of an optimal material layout of a structure in conjunction with an optimal shape of the boundary, to make cost-efficient use of a given amount of material for improving the concerned structural performance
Several typical methods have been developed for topology optimization of structures, including the homogenization method [2], the SIMP (Solid Isotropic Material with Penalization) approach [3,4] and the level set-based method [5,6,7,8]

Summary

Structural Optimization Using Level Set Methods

Over the past two decades, a relatively new field known as topology optimization is rapidly expanding in computational design research. The velocity field is incorporated into the H-J PDE to enable the update of the discrete level set function values, and the evolution of the design boundary. To overcome the shortcomings in the first category of the level set methods, the level set model is better when transformed into a parametric or equivalent one to avoid drawbacks of its classic discrete forms, while retain the topological shape benefits of the level set boundary representation In this way, the level set method will be naturally connected with the more powerful optimization algorithms in the field. The second category is the development of alternative level set methods [25,26,27,28,29,30,31] for shape and topology optimization of structures, without directly solving the H-J PDE. The topology optimization design of level sets is free of checkerboards that make a design practically manufacturable

Numerical Example

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Conclusions and Perspectives

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