关于求解弹性力学平面问题的功的互等定理法
On the Method of Reciprocal Theorem to Find Solutions of the Plane Problems of Elasticity
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摘要: 本文推广功的互等定理法于求解具有复杂边界条件矩形板的弹性力学平面问题.首先,我们给出了作为基本系统的四边固定矩形板平面问题的基本解,然后基于在具有复杂边界条件的实际系统与基本系统之间应用功的互等定理,从而求得实际系统的位移表达式.当只存在位移边界条件时,用功的互等定理法求得的位移表达式就是真实的.但是在另一些情况下,当有静力边界条件或混合边界条件时,所求得的位移是容许的.为求得真实位移.必须应用最小势能原理.一些计算表明.对于求解具有复杂边界条件的矩形板弹性力学平面问题,功的互等定理法是一简便通用的方法.显然,这是一个新方法.Abstract: In this paper the method of reciprocal theorem is extended to find solutions of plane problems of elasticity of the rectangular plates with various edge conditions.First we give the basic solution of the plane problem of the rectangular plate with four edges built-in as the basic system and then find displacement expressions of the actual system by using the reciprocal theorem between the basic system and actual system with various edge conditions.When only displacement edge conditions exist,obtaining displacement expressions by means of the method of reciprocal theorem is actual.But in other conditions,when static force edge conditions or mixed ones exist,the obtained displacements are admissible.In order to find actual displacement,the minimum potential energy theorem must be applied.Calculations show that the method of reciprocal theorem is a simple,convenient and general one for the solution of plane problems of elasticity of the rectangular plates with various edge conditions.Evidently,it is a new method.
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[1] 付宝连,一个求解位移方程的新方法,东北重型机械学院第三届学术报告会,(1981,1). [2] 付宝连,应用功的互等定理求解具有复杂边界矩形板的挠曲面方程,应用数学和力学,3,3(1982),315-325. [3] 付宝连,关于功的互等定理与迭加原理的等价性,应用数学和力学,6,9(1935),813-813. [4] 付宝连,应用功的互等定理计算矩形弹性薄板的自然频率.应用数学和力学,6,11(1985).985-998. [5] 付宝连,矩形弹性薄板固有频率的一个新算法,东北重型机械学院学报,2(1984,6). [6] 付宝连,二对边简支另一边或两边为自由的矩形弹性薄板的固有频率,东北重型机械学院学报,1(1985,3). [7] 付宝连,计算直梁横向振动自然频率的一个新方法,东北重型机械学院学报,3(1983,9). [8] 钱伟长、叶开连《弹性力学》,科学出版社(1950,10). [9] 徐芝纶,《弹性力学》(上册)(1979,1). [10] Timoshenko,S.and S.Woinowsky-Krieger,Theory of Plates and Shells,2nd edition.
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