有限元广义伽略金方程,边界变分方程,边界积分方程
The Generalized Galerkin’s Equations of the Finite Element, the Boundary Variational Equations and the Boundary Integral Equations
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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 Sa or on theboundaries Γa.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 Γa of integration is not accurate along the surface of interior element Sa by J-integral suggested by Rice [2].
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[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). -
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