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The Finite Cell Method For Three-dimensional Problems Of Solid Mechanics

A. Düster, J. Parvizian, Z. Yang, E. Rank
Published 2008 · Mathematics

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This article presents a generalization of the recently proposed finite cell method to three-dimensional problems of linear elasticity. The finite cell method combines ideas from embedding or fictitious domain methods with the p-version of the finite element method. Besides supporting a fast, simple generation of meshes it also provides high convergence rates. Mesh generation for a boundary representation of solids and for voxel-based data obtained from CT scans is addressed in detail. In addition, the implementation of non-homogeneous Neumann boundary conditions and the computation of cell matrices based on a composed integration is presented. The performance of the proposed method is demonstrated by three numerical examples, including the elastostatic computation of a human bone biopsy.
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