Shape and Topology Optimization for Elliptic Boundery Value Problems using a Piecewise Constant Level Set Method

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hadadi, Alireza | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46014 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Fotouhi Firouzabad, Morteza
Abstract:
The aim of this thesis is describes the method 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 the present algorithm
Keywords:
Shape Optimization ; Topology Optimization ; Piecewise Constant Level Set Method ; Projection Lagrangian Method

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