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A Lie-Group Shooting Method for Post Buckling Calculations of Elastica

Chein-Shan Liu1
Department of Mechanical and Mechatronic Engineering, Department of Harbor and River Engineering, Taiwan Ocean University, Keelung, Taiwan E-mail: csliu@mail.ntou.edu.tw

Computer Modeling in Engineering & Sciences 2008, 30(1), 1-16. https://doi.org/10.3970/cmes.2008.030.001

Abstract

In this paper we propose a new numerical integration method of second-order boundary value problems (BVPs) resulting from the elastica of slender rods under different loading conditions and boundary conditions. We construct a compact space shooting method for finding unknown initial conditions. The key point is based on the construction of a one-step Lie group element G(T) and the establishment of a generalized mid-point Lie group element G(r) by using the mean value theorem. Then, by imposing G(T) = G(r) we can search the missing initial condition through a closed-form solution in terms of the weighting factor r ∈ (0,1). The Lie-group shooting method is very effective for large deflection problems of elastica even exhibiting multiple solutions.

Keywords

Elastica, Post-Buckling, Multiple solutions, Lie-Group shooting method

Cite This Article

Liu, C. (2008). A Lie-Group Shooting Method for Post Buckling Calculations of Elastica. CMES-Computer Modeling in Engineering & Sciences, 30(1), 1–16.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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