带有小剪切的弹性板有限变形边值问题  

Boundary Value Problems of Finite Deformation of Elastic Plates with Small Shear

作　　者：胡成栋[1] 刘纬 

机构地区：[1]吉林大学数学系

出　　处：《吉林大学自然科学学报》1995年第2期1-16,共16页Acta Scientiarum Naturalium Universitatis Jilinensis

摘　　要：对非线性板采用与传统的ｖｏｎＫａｒｍｄｎ板不同的变形假设，应用连续介质力学方法精确推证带有小剪切的弹性板有限变形边值问题的基本方程及边界条件。并对应变能函数作分解假设，使得有限变形边值问题与小转动边值问题解耦。由于此结果更具一般性，可由此得到弹性板边值问题的各种提法及对已有非线性板解的边界效应加以修正。In this paper,a hypothesis regarding deformation of nonlinear plates,which is differentfrom classical von. Kdrmdn plate,s,is made. Basic equations and boundary conditions on boundaryvalue problems of finite deformation of elastic plates with small shear were exactly derived,by apply-ing continuum mechanics method. And a resolution assumption is made for strain energy function,sothat coupling between finite deformation and small rotation is dissolved.Because the resuIt of this pa- per is more general,from the result various propositions on boundary value problems of elastic platesmay be obtained.The boundary effect of nonlinear plates solutions obtained can be corrected,by uti- lizing this result.

关 键 词：弹性板 小剪切 变形 边值问题 

分 类 号：O343[理学—固体力学]