Ostanin I.A.   Zorin D.N.   Mikhalev A.Y.   Oseledets I.V.  

Fast topological shape optimization with boundary elements

Reporter: Ostanin I.A.

Wide class of engineering design tasks can be posed as optimization problems where the shape and topology of an elastic domain are optimized to reduce costs, e.g. global compliance, while satisfying certain constraints, such as volume constraint. We propose an application of a fast 3D boundary element code to the problems of shape and topology optimization. Our algorithm is based on the formalism of topological derivatives. Adaptive tree strategy of sampling of topological derivatives inside the domain, high performance algebraic solver and the analysis of optimization problem in reduced dimensions promise state of the art performance in the problems of engineering optimization. The approach can be applied to various optimization problems, such as minimization of compliance of an elastic structure or minimization of the distance from a current homogenized elasticity tensor of a periodic structure to the desired one. The efficiency of the approach is illustrated with a numerical example.

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