High-Order Analytical Solutions and Convergence Discussions of the 2-Step Perturbation Method for Euler-Bernoulli Beams

ZHANG Daguang

doi:10.21656/1000-0887.390272

Volume 40 Issue 6

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ZHANG Daguang. High-Order Analytical Solutions and Convergence Discussions of the 2-Step Perturbation Method for Euler-Bernoulli Beams[J]. Applied Mathematics and Mechanics, 2019, 40(6): 620-629. doi: 10.21656/1000-0887.390272

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High-Order Analytical Solutions and Convergence Discussions of the 2-Step Perturbation Method for Euler-Bernoulli Beams

doi: 10.21656/1000-0887.390272

ZHANG Daguang

School of Architectural and Surveying & Mapping Engineering, Jiangxi University of Science and Technology, Ganzhou, Jiangxi 341000, P.R.China

Received Date: 2018-10-22
Rev Recd Date: 2018-11-14
Publish Date: 2019-06-01

Abstract

Abstract

High-order analytical solutions of the 2-step perturbation method were first obtained for post-buckling and nonlinear bending of Euler-Bernoulli beams. The nonlinear model with centerline inextensibility was derived with the exact curvature expression according to the energy variational principle. Based on the comparison with the exact solutions or high-order perturbation solutions, the asymptotic property and the suitable range of 2-step perturbation solutions were also discussed. The results show that, the lower-order perturbation solutions are suitable for the initial post-buckling stage and the initial nonlinear bending stage, and the higher-order perturbation solutions are necessary for the late post-buckling stage and the highly nonlinear bending stage. Therefore, the reason why some previous perturbation solutions are inaccurate lies in the offside beyond suitable ranges, and the 2-step perturbation method is developed and improved herein.
- 2-step perturbation method,
- high-order analytical solution,
- post-buckling,
- nonlinear bending

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References

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