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Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Problems in Elasticity
Joint Authors
Source
Mathematical Problems in Engineering
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-05-31
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Cheng, Pan& Zhang, Ling. 2018. Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Problems in Elasticity. Mathematical Problems in Engineering،Vol. 2018, no. 2018, pp.1-8.
https://search.emarefa.net/detail/BIM-1208616
Modern Language Association (MLA)
Cheng, Pan& Zhang, Ling. Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Problems in Elasticity. Mathematical Problems in Engineering No. 2018 (2018), pp.1-8.
https://search.emarefa.net/detail/BIM-1208616
American Medical Association (AMA)
Cheng, Pan& Zhang, Ling. Mechanical Quadrature Methods and Extrapolation for Solving Nonlinear Problems in Elasticity. Mathematical Problems in Engineering. 2018. Vol. 2018, no. 2018, pp.1-8.
https://search.emarefa.net/detail/BIM-1208616
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1208616