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A polytree‐based adaptive polygonal finite element method for topology optimization
Author(s) -
NguyenXuan H.
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5448
Subject(s) - polygon mesh , volume mesh , topology (electrical circuits) , topology optimization , boundary (topology) , finite element method , computer science , affine transformation , mathematical optimization , mathematics , algorithm , mesh generation , geometry , combinatorics , engineering , computer graphics (images) , mathematical analysis , structural engineering
Summary We propose a highly effective approach using a novel adaptive methodology to perform topology optimization with polygonal meshes, called polytree meshes. Polytree is a hierarchical data structure based on the principle of recursive spatial decomposition of each polygonal element with n nodes into ( n + 1) arbitrary new polygonal elements; enabling more efficient utilization of unstructured meshes and arbitrary design domains in topology optimization. In order to treat hanging nodes after each optimization loop, we define the Wachspress coordinate on a reference element and then utilize an affine map to obtain shape functions and their gradients on arbitrary polygons with n vertices and m hanging nodes, called side‐nodes, as the polygonal element with ( n + m ) vertices. The polytree meshes do not only improve the boundary description quality of the optimal result but also reduce the computational cost of optimization process in comparison with the use of uniformly fine meshes. Several numerical examples are investigated to show the high effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.