A critical comparative assessment of differential equation-driven methods for structural topology optimization

  • Authors:

  • Arun L. Gain;Glaucio H. Paulino

  • Affiliations:

  • Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, USA 61801;Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, USA 61801

  • Venue:
  • Structural and Multidisciplinary Optimization
  • Year:
  • 2013

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Abstract

In recent years, differential equation-driven methods have emerged as an alternate approach for structural topology optimization. In such methods, the design is evolved using special differential equations. Implicit level-set methods are one such set of approaches in which the design domain is represented in terms of implicit functions and generally (but not necessarily) use the Hamilton-Jacobi equation as the evolution equation. Another set of approaches are referred to as phase-field methods; which generally use a reaction-diffusion equation, such as the Allen-Cahn equation, for topology evolution. In this work, we exhaustively analyze four level-set methods and one phase-field method, which are representative of the literature. In order to evaluate performance, all the methods are implemented in MATLAB and studied using two-dimensional compliance minimization problems.