Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Problems in Elasticity

This paper will study the high accuracy numerical solutions for elastic equations with nonlinear boundary value conditions. The equations will be converted into nonlinear boundary integral equations by the potential theory, in which logarithmic singularity and Cauchy singularity are calculated simul...

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Main Authors: Pan Cheng, Ling Zhang
Format: Article
Language:English
Published: Hindawi Limited 2018-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2018/6932164
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spelling doaj-2f51f8dddd0e4b14a794c024bedd5c832020-11-24T22:37:36ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472018-01-01201810.1155/2018/69321646932164Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Problems in ElasticityPan Cheng0Ling Zhang1School of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, ChinaSchool of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing 400074, ChinaThis paper will study the high accuracy numerical solutions for elastic equations with nonlinear boundary value conditions. The equations will be converted into nonlinear boundary integral equations by the potential theory, in which logarithmic singularity and Cauchy singularity are calculated simultaneously. Mechanical quadrature methods (MQMs) are presented to solve the nonlinear equations where the accuracy of the solutions is of three orders. According to the asymptotical compact convergence theory, the errors with odd powers asymptotic expansion are obtained. Following the asymptotic expansion, the accuracy of the solutions can be improved to five orders with the Richardson extrapolation. Some results are shown regarding these approximations for problems by the numerical example.http://dx.doi.org/10.1155/2018/6932164
collection DOAJ
language English
format Article
sources DOAJ
author Pan Cheng
Ling Zhang
spellingShingle Pan Cheng
Ling Zhang
Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Problems in Elasticity
Mathematical Problems in Engineering
author_facet Pan Cheng
Ling Zhang
author_sort Pan Cheng
title Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Problems in Elasticity
title_short Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Problems in Elasticity
title_full Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Problems in Elasticity
title_fullStr Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Problems in Elasticity
title_full_unstemmed Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Problems in Elasticity
title_sort mechanical quadrature methods and extrapolation for solving nonlinear problems in elasticity
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2018-01-01
description This paper will study the high accuracy numerical solutions for elastic equations with nonlinear boundary value conditions. The equations will be converted into nonlinear boundary integral equations by the potential theory, in which logarithmic singularity and Cauchy singularity are calculated simultaneously. Mechanical quadrature methods (MQMs) are presented to solve the nonlinear equations where the accuracy of the solutions is of three orders. According to the asymptotical compact convergence theory, the errors with odd powers asymptotic expansion are obtained. Following the asymptotic expansion, the accuracy of the solutions can be improved to five orders with the Richardson extrapolation. Some results are shown regarding these approximations for problems by the numerical example.
url http://dx.doi.org/10.1155/2018/6932164
work_keys_str_mv AT pancheng mechanicalquadraturemethodsandextrapolationforsolvingnonlinearproblemsinelasticity
AT lingzhang mechanicalquadraturemethodsandextrapolationforsolvingnonlinearproblemsinelasticity
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