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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2018-01-01
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Series: | Mathematical Problems in Engineering |
Online Access: | http://dx.doi.org/10.1155/2018/6932164 |
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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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1725716301448478720 |