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HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 684Barycentric Interpolation Newton-Raphson Iterative...

Barycentric Interpolation Newton-Raphson Iterative Method for Solving Nonlinear Beam Equations

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Abstract:

A barycentric interpolation Newton-Raphson iterative method for solving nonlinear beam bending problems is presented in this article. The nonlinear governing differential equation of beam bending problem is discretized by barycentric interpolation collocation method to form a system of nonlinear algebraic equations. Newton-Raphson iterative method is applied to solve the system of nonlinear algebraic equations. The Jacobian derivative matrix in Newton-Raphson iterative method is formulated by the Hadamard product of vectors. Some numerical examples are given to demonstrate the validity and accuracy of proposed method.

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Proceedings of 2014 International Conference on Mechanics and Mechanical Engineering

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Periodical:

Applied Mechanics and Materials (Volume 684)

Pages:

41-48

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.684.41

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Online since:

October 2014

Authors:

Zhao Qing Wang, Jian Jiang, Bing Tao Tang*, Wei Zheng

Keywords:

Barycentric Interpolation, Beam Equation, Collocation Method, Newton-Raphson Iterative Method, Nonlinear Bending Problem

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© 2014 Trans Tech Publications Ltd. All Rights Reserved

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