|
|||||
|
|
| Euler型梁-柱结构的非线性稳定性和后屈曲分析 | |
| 引用本文： | 朱媛媛,胡育佳,程昌钧.Euler型梁-柱结构的非线性稳定性和后屈曲分析[J].应用数学和力学,2011,32(6). |
| 作者姓名： | 朱媛媛 胡育佳 程昌钧 |
| 作者单位： | 1. 上海师范大学 计算机科学与技术系,上海,200234 2. 上海理工大学 机械工程学院,上海,200093 3. 上海大学 理学院 力学系,上海,200072 |
| 基金项目： | 国家自然科学青年基金资助项目(11002084); 上海市浦江人才计划资助项目(07pj14073) |
| 摘 要： | 在有限变形的假设下,建立了位于非线性弹性基础上非线性弹性Euler型梁-柱结构的广义Hamilton变分原理,并由此导出了任意变截面Euler型梁-柱结构的3维非线性数学模型,其中考虑了转动惯性、几何非线性、材料非线性等因素的影响.作为模型的应用,分析了弹性基础上一端完全固支另一端部分固支,并受轴力作用的均质等截面线性弹性Euler型梁的非线性稳定性和后屈曲;结合打靶法和Newton法,给出了一种计算平凡解(前屈曲状态)、分叉点(临界载荷)和分叉解(后屈曲状态)的数值方法,对前两个分支点和相应分支解,成功地实现了数值计算,并考虑了基础反力和惯性矩对分支点的影响. |
| 关 键 词： | 梁-柱结构 广义Hamilton原理 非线性稳定性 打靶法和Newton法 后屈曲分析 |
Analysis of Non-Linear Stability and Post-Buckling for the Euler-Type Beam-Column Structure |
|
| ZHU Yuan-yuan,HU Yu-jia,CHENG Chang-jun.Analysis of Non-Linear Stability and Post-Buckling for the Euler-Type Beam-Column Structure[J].Applied Mathematics and Mechanics,2011,32(6). | |
| Authors: | ZHU Yuan-yuan HU Yu-jia CHENG Chang-jun |
| Institution: | ZHU Yuan-yuan1,HU Yu-jia2,CHENG Chang-jun3 (1.Department of Computer Science and Technology,Shanghai Normal University,Shanghai 200234,P.R.China,2.School of Mechanical Engineering,University of Shanghai for Science and Technology,Shanghai 200093,3.Department of Mechanics,School of Science,Shanghai University,Shanghai 200072,P.R.China) |
| Abstract: | Based on the assumption of finite deformation,the Hamilton variational principle was extended to a nonlinear elastic Euler-type beam-column structure located on a nonlinear elastic foundation,and the corresponding 3-dimension mathematical model for analyzing the non-linear mechanical behaviors of structures was established,in which the effects of rotation inertia,non-linearity of material and geometry were considered.As application,the non-linear stability and the post-buckling for a linear elastic beam wit... |
| Keywords: | beam-column structure Hamilton variational principle nonlinear stability shooting method and Newton-Raphson interactive method post-bulking |
| 本文献已被 CNKI 万方数据 等数据库收录！ | |