有限元广义伽略金方程,边界变分方程,边界积分方程

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The Generalized Galerkin’s Equations of the Finite Element, the Boundary Variational Equations and the Boundary Integral Equations

摘要: 在[1]的基础上,我们进一步应用可动边界的变分原理于固体体系的离散分析,得到有限元广义伽略金方程,边界变分方程,边界积分方程.这些方程描述了待解函数在元素内部与元素的边界上应满足的方程.当对固体体系进行离散分析时,可以应用这些方程去建立不同情况下的求解待解函数的离散方程.亦可作为相应情况下的简化计算的依据.由本文得到的边界积分方程可知,在[2]中提出的J积分形式,应用于内部元素边界的围道积分计算是不适宜的.

Abstract: Based on [1], we have further applied the variational principle of the variable boundary to investigate the discretization analysis of the solid system and derived the generalized Ga-lerkin's equations of the finite element, the boundary variational equations and the boundary integral equations.These e-quations indicate that the unknown functions of the solid system must satisfy the conditions in the element S_a or on theboundaries Γ_a.These equations are applied to establishing the discretization equations in order to obtain the numerical solution of the unknown functions. At a time these equations can be used as the basis for the simplified calculation in various corresponding cases.In this paper, the results of boundary integral equations show that the calculation Γ_a of integration is not accurate along the surface of interior element S_a by J-integral suggested by Rice [2].

[1]	牛庠均,固体的离散型变分原理(1981),505-520.有限元离散分析的变分原理,应用数学与力学,2,5(1981)505-520
[2]	Rice,J.R.,A path independent integral and the approximate analysis of strain concentration by notches and crack,Journal of Applied Mechanics,35,2 June(1968).