Shape and topology optimization for elliptic boundary value problems using a piecewise constant level set method

• Autores: Zhu Shengfeng, Wu Qingbiao, Chunxiao Liu
• Localización: Applied numerical mathematics, ISSN-e 0168-9274, Vol. 61, Nº. 6, 2011, págs. 752-767
• Idioma: inglés
• DOI: 10.1016/j.apnum.2011.01.005
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• Resumen

  • The aim of this paper is to propose a variational piecewise constant level set method for solving elliptic shape and topology optimization problems. The original model is approximated by a two-phase optimal shape design problem by the ersatz material approach. Under the piecewise constant level set framework, we first reformulate the two-phase design problem to be a new constrained optimization problem with respect to the piecewise constant level set function. Then we solve it by the projection Lagrangian method. A gradient-type iterative algorithm is presented. Comparisons between our numerical results and those obtained by level set approaches show the effectiveness, accuracy and efficiency of our algorithm.