辛几何
数学
叠加原理
屈曲
欧几里得空间
边值问题
偏微分方程
抓住
哈密顿系统
数学分析
计算机科学
结构工程
工程类
程序设计语言
作者
Rui Li,Haiyang Wang,Xinran Zheng,Sijun Xiong,Zhe Hu,Xiaoye Yan,Zhe Xiao,Houlin Xu,Peng Li
标识
DOI:10.1016/j.euromechsol.2019.04.014
摘要
This paper deals with a classic but very difficult type of problems, i.e., pursuing analytic buckling solutions of biaxially loaded rectangular thin plates with two free adjacent edges that are characterized by having both the free edges and a free corner. The primary challenge is to find the solutions satisfying both the governing high-order partial differential equations (PDEs) and non-Lévy-type boundary constraints. Here, an up-to-date symplectic superposition method is developed for the issues, which yields the analytic solutions by converting the problems to be solved into the superposition of two elaborated subproblems that are solved by the symplectic elasticity approach. The distinctive merit of the method is that a direct rigorous derivation helps to access the analytic solutions without any assumptions/prior knowledge of the solution forms, which is attributed to the implementation in the symplectic space-based Hamiltonian system rather than in the classic Euclidean space-based Lagrangian system. As the important outputs, comprehensive new analytic results are obtained, with 1200 critical buckling loads and 100 buckling mode shapes presented, which are all well validated by the refined finite element analysis. The rapid convergence and favorable accuracy of the present method make it competent as a benchmark one for similar problems.
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