基于哈密顿解法的厚板边界效应典型算例分析  

ANALYSIS OF BOUNDARY EFFECT PHENOMENON IN THICK PLATES USING HAMILTONIAN APPROACH

作　　者：鞠伟[1] 岑松[2] 傅向荣[3] 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 [3]中国农业大学土木工程系,北京100083

出　　处：《工程力学》2008年第2期1-8,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(10502028);高等学校全国优秀博士论文作者专项基金项目(200242);国家科技支撑计划项目(2006BAK04A03);教育部新世纪优秀人才支持计划项目(NCET-07-0477)

摘　　要：在平板弯曲问题中存在边界效应现象。这个现象用Reissner厚板理论可以论证,而经典薄板理论则无法解释。边界效应现象在板的自由边界附近表现最为典型。该文首先选取均载作用下的三边简支,一边自由的矩形厚板作为典型问题,采用哈密顿解法求出解析解。然后结合这个典型问题,对边界效应现象进行分析,对其影响因素和影响范围进行讨论。The boundary effect phenomenon exists in plate bending problems. This phenomenon can be explained and demonstrated on the basis of Reissner theory of thick plates, while the classical theory of thin plates can not give a satisfactory explanation of it. The boundary effect phenomenon in the neighbourhood of free boundary is a typical one. In this paper, the rectangular thick plate with three simply-supported edges and one free edge is taken as a typical problem and is analyzed using Hamiltonian approach. Then, on the basis of this typical problem, the influence factor and influence domain of boundary effect phenomenon are discussed.

关 键 词：厚板弯曲 边界效应 Reissner厚板理论 哈密顿解法 解析解 

分 类 号：TU318[建筑科学—结构工程]