Shape and topology optimization based on the phase feld method and sensitivity analysis

Takezawa Akihiro

Nishiwaki Shinji

Kitamura Mitsuru

Journal of Computational Physics

This paper discusses a structural optimization method that optimizes shape and topology based on the phase field method. The proposed method has the same functional capabilities as a structural optimization method based on thelevel set method incorporating perimeter control functions. The advantage of the method is the simplicity of computation, since extra operations such as reinitialization of functions are not required. Structural shapes are represented by the phase field function defined in the design domain, and optimization of this function is performed by solving a time-dependent reaction diffusion equation. The artificial double-well potential function used in the equation is derived from sensitivity analysis. The proposed method is applied to twodimensional linear elastic and vibration optimization problems such as the minimum compliance problem, a compliant mechanism design problem and the eigenfrequency maximization problem. The numerical examples provided illustrate the convergence of the various objective functions and the effect that perimeter control has on the optimal configurations.

shape optimization

topology optimization

phase field method

sensitivity analysis

level set method

eng

Elsevier Inc

Copyright (c) 2009 Elsevier Inc.

[ISSN] 0021-9991

[DOI] 10.1016/j.jcp.2009.12.017

[NCID] AA00696013

[DOI] http://dx.doi.org/10.1016/j.jcp.2009.12.017