Topology optimization by a time-dependent diffusion equation

A. Kawamoto*, T. Matsumori, T. Nomura, T. Kondoh, S. Yamasaki, S. Nishiwaki


研究成果: Article査読

9 被引用数 (Scopus)


Most topology optimization problems are formulated as constrained optimization problems; thus, mathematical programming has been the mainstream. On the other hand, solving topology optimization problems using time evolution equations, seen in the level set-based and the phase field-based methods, is yet another approach. One issue is the treatment of multiple constraints, which is difficult to incorporate within time evolution equations. Another issue is the extra re-initialization steps that interrupt the time integration from time to time. This paper proposes a way to describe, using a Heaviside projection-based representation, a time-dependent diffusion equation that addresses these two issues. The constraints are treated using a modified augmented Lagrangian approach in which the Lagrange multipliers are updated by simple ordinary differential equations. The proposed method is easy to implement using a high-level finite element code. Also, it is very practical in the sense that one can fully utilize the existing framework of the code: GUI, parallelized solvers, animations, data imports/exports, and so on. The effectiveness of the proposed method is demonstrated through numerical examples in both the planar and spatial cases.

ジャーナルInternational Journal for Numerical Methods in Engineering
出版ステータスPublished - 2013 2月 24

ASJC Scopus subject areas

  • 数値解析
  • 工学(全般)
  • 応用数学


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