A Level Set Method in Shape and Topology Optimization for Variational Inequalities
نویسندگان
چکیده
منابع مشابه
A Level Set Method in Shape and Topology Optimization for Variational Inequalities
The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an ...
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This paper proposes an effective algorithm based on the level set method (LSM) to solve shape and topology optimization problems. Since the conventional LSM has several limitations, a binary level set method (BLSM) is used instead. In the BLSM, the level set function can only take 1 and -1 values at convergence. Thus, it is related to phase-field methods. We don’t need to solve the Hamilton-Jac...
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The classical level set method, which represents the boundary of the unknown geometry as the zero-level set of a function, has been shown to be very effective in solving shape optimization problems. The present work addresses the issue of using a level set representation when there are simple geometrical and topological constraints. We propose a logarithmic barrier penalty which acts to enforce...
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Numerical methods of shape and topology optimization based on the level set representation and on shape di erentiation make possible topology changes during the optimization process. But they do not solve the inherent problem of illposedness of shape optimization which manifests itself in the existence of many local minima, usually having di erent topologies. The reason is that the level set me...
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ژورنال
عنوان ژورنال: International Journal of Applied Mathematics and Computer Science
سال: 2007
ISSN: 1641-876X
DOI: 10.2478/v10006-007-0034-z