用ψ函数表示伽辽金位移函数  

Expression of GalerKin's Displacement Functions with ψ Function

作　　者：徐汉忠[1] 

机构地区：[1]河海大学工程力学系

出　　处：《河海大学学报（自然科学版）》1990年第5期78-84,共7页Journal of Hohai University(Natural Sciences)

摘　　要：由弹性力学平面问题的艾瑞应力函数求导可得应力,但难以求得位移.由伽辽金位移函数可同时求得应力和位移,但伽辽金位移函数在平面问题中有两个,需满足两个重调和方程,给求解增加了困难.本文证明了两个伽辽金位移函数可用一个重调和函数Ψ表示,从而找到了既能表示应力,又能表示位移的单个函数.这样,在求解无体力的弹性力学平面问题时,只需求解一个重调和方程就可得到Ψ,并可使Ψ导得的应力和位移满足边界条件.It is possible to obtain stresses and difficult to obtain displacements from Airy's stress function in plane elasticity problems. Both stresses and displacements can be derived from GalerKin's displancement functions, but there are two GalerKin's functions which satisfy two biharmonic equations, thus the difficulty in obtainning the solution is increased. This paper proves that the two GalerKin's displacement functions can be expressed by one biharmonic function ψ. Hence one function is found with which both stresses and displacements can be expressed. When solving plane elasticity problems without body force, ψ can be obtained by solving one biharmonic equation, while the stresses and displacements derived from ψ satisfy with boundary conditions.

关 键 词：Ψ函数 伽辽金 位移函数 平面 

分 类 号：O343.1[理学—固体力学]