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Abstract
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The implementation of the spectral element method for the problems of nonlinear
elasticity under finite strains is developed. The analysis is performed for
structures made by junction of preliminarily strained parts. The bending of a
layered beam with a prestressed layer is analyzed as a particular case. It is
assumed that the beam consists of weakly compressible nonlinear-elastic
material.
The theory of superimposed finite strains is used for the problem statement.
The discretization is performed using the Galerkin method. The proposed
approach permits one to vary the order of spectral elements without the mesh
refinement.
The results of analysis are given. The comparison with a known analytical
solution is performed. It is obtained that the results of spectral element analysis are
close to the analytical solution. Substantial nonlinear effects are determined. The
incomplete junction of layers is analyzed.
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Keywords
variable-order spectral element method, superimposed finite
deformations, nonlinear elasticity, layered beam
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Mathematical Subject Classification
Primary: 65N35, 74B20
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Milestones
Received: 15 June 2021
Revised: 21 April 2022
Accepted: 29 May 2022
Published: 20 October 2022
Communicated by Victor A. Eremeyev
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