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

Abstract

a b s t r a c tThis 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 the level set method incorporating perimeter control functions. The advantage of the method is the simplicity of computation, since extra operations such as re-initialization 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 two-dimensional 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.

Molding Direction Constraints in Structural Optimization via a Level-Set Method

“…Among the several methods that appeared in the literature, such as SIMP (Solid Isotropic Material with Penalization) method [14,49,16], the homogenization method [3,13,15], the phase field method [18,41,51,17] or the Soft Kill Option [31,23], the level-set method for shape and topology optimization [10,11,35,38,44] seems to fulfill industrial requirements in a satisfying way. Using a level-set function to describe implicitly the boundary of a shape [36,37] allows topological changes to appear in an easy way, while the geometric nature of the method is a benefit for the study of problems where the position of the interface plays a significant role (stress constraints, thermal problems with flux across the boundary, etc.).…”

Heat Exchanger Design with Topology Optimization

“…This method has been utilized for solid-liquid transitions, diffusion, solidification, crack propagation, multiphase flow and eventually in topology optimization [31]. In the application of these theories, a phase-field function is specified over the design domain that is composed of two phases (e.g.…”

“…In topology optimization utilizing the phase-field method [31][32][33], this interface region defines the structural boundary, thus separating material from void, and is modified via a dynamic evolution of the phase-field function. The primary difference between the level-set and phasefield methods is mainly due to the fact that in the phase-field method, the interface between the boundaries of the two distinct phases is not tracked throughout optimization.…”

“…A MATLAB code for the phase-field method is available for download by visiting the website of Ref. [31].…”

Layout optimization of multi-material continuum structures with the isolines topology design method

“…Hence, there are few approaches in the literature Wang and Zhou (2004), Burger and Stainko (2006), and Takezawa et al (2010). …”