自然边界元法在弹性圆形薄板弯曲问题中的应用  

Natural boundary element method and its application in the bending problem of the elastic thin circular plate

作　　者：李顺才[1] 刘玉庆[2] 

机构地区：[1]徐州师范大学工学院,江苏徐州221011 [2]中国矿业大学理学院,江苏徐州221008

出　　处：《陕西工学院学报》2002年第3期80-84,共5页Journal of Shaanxi Institute of Technology

摘　　要：我国学者冯康、余德浩等首创自然边界元法 ,并已成功地研究了调和方程及双调和方程边值问题的自然边界归化方法。本文根据双调和方程边值问题的自然边界归化原理 ,得到了圆形薄板弯曲挠度的泊松积分公式及其边界内力的自然积分方程 ,利用强奇异积分的数值计算方法 ,求得了圆形薄板的弯曲解 ,从实践上证实了这种方法的可行性。FENG Kang, YU De-hao and some other scholars of our country are the first ones to create the natural boundary element method (NBEM), and they have successfully studied the natural boundary reduction method for the boundary value problems of harmonic equation and biharmonic equation. Based on the natural boundary reduction for the boundary value problems of biharmonic equation, the Poisson integral formula on the bending deflection of the thin circular plate and its natural integral equations of boundary internal forces are presented. By means of the numerical method of strongly singular integrals, the bending solutions to the thin circular plate are obtained, and the feasibility of this method has been confirmed in practice.

关 键 词：弹性圆形薄板 弯曲问题 自然边界元法 弯曲解 强奇异积分 自然边界归化原理 挠度 

分 类 号：O343[理学—固体力学]