期刊
MECHANICS RESEARCH COMMUNICATIONS
卷 83, 期 -, 页码 32-46出版社
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.mechrescom.2017.05.001
关键词
Perturbation; Small-rotation-angle assumption; Large deflection; Circular membrane
类别
资金
- National Natural Science Foundation of China [11572061]
In existing studies, the well-known Hencky problem, i.e. the large deflection problem of axisymmetric deformation of a circular membrane subjected to uniformly distributed loads, has been analyzed generally on small-rotation-angle assumption and solved by using the common power series method. In fact, the problem studied and the method adopted may be effectively expanded to meet the needs of larger deformation. In this study, the classical Hendry problem was extended to the problem without small rotation-angle assumption and resolved by using the perturbation idea combining with power series method. First, the governing differential equations used for the solution of stress and deflection in the perturbed system were established. Taking the load as a perturbation parameter, the stress and deflection were expanded with respect to the parameter. By substituting the expansions into the governing equations and corresponding boundary conditions, the perturbation solution of all levels were obtained, in which the zero-order perturbation solution exactly corresponds to the small-rotation-angle solution, i.e. the solution of the unperturbed system. The results indicate that if the perturbed and unperturbed systems as well as the corresponding differential equations may be distinguished, the perturbation method proposed in this study can be extended to solve other nonlinear differential equations, as long as the differential equation of unperturbed system may be obtained by letting a certain parameter be zero in the corresponding equation of perturbed system. (C) 2017 Elsevier Ltd. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据