Finite Element Solution Algorithm for Nonlinear Elasticity Problems by Domain Decomposition Method

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UMBC Mathematics and Statistics Department

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https://orcid.org/0000-0002-8053-8956

Date

2005-06-06

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conference papers and proceedings
preprints
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Bedřich Sousedík: Finite element solution algorithm for nonlinear elasticity problems by domain decomposition method, Proceedings of the 13th Conference of mathematics students of VSTEZ schools, Černice, Czech Republic, June 6-8, 2005

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Abstract

The purpose of the present work is to give a brief description of the finite elasticity and of its approximation via finite element method. We formulate the problem for the case of compressible elasticity. Weak formulation allows to use any isotropic hyperelastic material model that satisfies polyconvexity assumptions. Discretization using FEM leads to systems of non-linear equations. Such systems of equations can be solved by Newton’s method and its modifications. In each iteration of Newton’s method a linearized system of equations has to be solved. We propose to use BDDC preconditioning iterative method for the solution of linear system of equations.