Strong-form framework for solving boundary value problems with geometric nonlinearity

doi:10.1007/s10483-016-2149-8

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (12): 1707-1720.doi: https://doi.org/10.1007/s10483-016-2149-8

Strong-form framework for solving boundary value problems with geometric nonlinearity

J. P. YANG, W. T. SU

Department of Civil Engineering, Chiao Tung University, Hsinchu 30010, Taiwan, China

收稿日期:2015-09-11 修回日期:2016-06-12 出版日期:2016-12-01 发布日期:2016-12-01
通讯作者: J. P. YANG E-mail:jpyang@nctu.edu.tw
基金资助:
Project supported by the Ministry of Science and Technology of Taiwan (No.MOST 104-2221-E-009-193)

Strong-form framework for solving boundary value problems with geometric nonlinearity

J. P. YANG, W. T. SU

Department of Civil Engineering, Chiao Tung University, Hsinchu 30010, Taiwan, China

Received:2015-09-11 Revised:2016-06-12 Online:2016-12-01 Published:2016-12-01
Contact: J. P. YANG E-mail:jpyang@nctu.edu.tw
Supported by:
Project supported by the Ministry of Science and Technology of Taiwan (No.MOST 104-2221-E-009-193)

摘要/Abstract

摘要：

In this paper, we present a strong-form framework for solving the boundary value problems with geometric nonlinearity, in which an incremental theory is developed for the problem based on the Newton-Raphson scheme. Conventionally, the finite element methods (FEMs) or weak-form based meshfree methods have often been adopted to solve geometric nonlinear problems. However, issues, such as the mesh dependency, the numerical integration, and the boundary imposition, make these approaches computationally inefficient. Recently, strong-form collocation methods have been called on to solve the boundary value problems. The feasibility of the collocation method with the nodal discretization such as the radial basis collocation method (RBCM) motivates the present study. Due to the limited application to the nonlinear analysis in a strong form, we formulate the equation of equilibrium, along with the boundary conditions, in an incremental-iterative sense using the RBCM. The efficacy of the proposed framework is numerically demonstrated with the solution of two benchmark problems involving the geometric nonlinearity. Compared with the conventional weak-form formulation, the proposed framework is advantageous as no quadrature rule is needed in constructing the governing equation, and no mesh limitation exists with the deformed geometry in the incremental-iterative process.

关键词: geometric nonlinearity, strong form, radial basis collocation method (RBCM), incremental-iterative algorithm

Abstract:

Key words: incremental-iterative algorithm, geometric nonlinearity, strong form, radial basis collocation method (RBCM)

中图分类号:

74S30

J. P. YANG, W. T. SU. Strong-form framework for solving boundary value problems with geometric nonlinearity[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(12): 1707-1720.

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Strong-form framework for solving boundary value problems with geometric nonlinearity

Strong-form framework for solving boundary value problems with geometric nonlinearity

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