基于哈密顿解法的矩形厚板分析  

RECTANGULAR THICK PLATE ANALYSIS BASED ON HAMILTONIAN APPROACH

作　　者：鞠伟[1] 岑松[2] 龙驭球[1] 

机构地区：[1]清华大学土木工程系,北京100084 [2]清华大学航天航空学院

出　　处：《工程力学》2008年第1期1-7,33,共8页Engineering Mechanics

基　　金：国家自然科学基金(10502028);高等学校全国优秀博士论文作者专项基金(200242);教育部新世纪优秀人才支持计划项目(NCET-07-0477)

摘　　要：建立了分析Reissner-Mindlin厚板问题的哈密顿解法。首先,以x坐标模拟时间坐标,选用互为对偶的混合变量作为基本变量,建立哈密顿正则微分方程组。然后,采用分离变量法和特征函数展开法在相应的边界条件下求出级数解。最后,给出矩形厚板典型例题的解答,分析了级数解的收敛性质。与常用的半逆解法相比,Hamilton解法有其优点:一是求解方法严密合理、有规可循;二是应用范围广,可用于求解系列问题。The Hamilton solution system for Reissner-Mindlin thick plate analysis is established, Firstly, the x coordinate is treated as the time coordinate. The dual mixed variables are taken as the fundamental variables. The Hamiltonian canonical equations are derived. Secondly, the method of separation of variables and the eigensolution expansion method are used to obtain the analytical solutions of thick plates under corresponding boundary conditions. Lastly, the analytical solutions for typical rectangular thick plate problem are carried out. The convergence of the series solution is demonstrated. Compared with the semi-inverse approach, the Hamiltonian approach has some strong points： the solution is carried out more rationally, and the field of application is much wider.

关 键 词：Reissner-Mindlin厚板理论 哈密顿解法 对偶混合变量 正则微分方程 特征函数展开法 

分 类 号：TU318[建筑科学—结构工程]