在工程中有很多弹性力学问题是在无界区域上给出的，例如：坝体的弹性地基问题。利用经典的有限元方法去寻找这些问题的数值解是很困难的。在工程中常用的方法是：引入人工边界把无界城分为有界子域和无界子域，在人工边界上加上边界条件，考虑有界子域上的边值问题。人工边界的法向应力常常取为零。这种人工边界条件只是真实边界条件的粗糙的近似。当需要较高的精度时，有界子域必须取得很大，计算数值解仍然比较困难。　　在本文中，我们把线弹性力学方程组在无界子域上离散化。通过解决离散化后的问题，我们得到了人工边界上法向应力同位移的关系。这个关系可以做为离散的人工边界条件。这样，我们把原来无界区域上的问题转化为有界子域上的边值问题，并利用有取元方法解这个有界子域上的边值问题。计算实例说明我们采用的这种方法非常有效。

In engineering many problems of elasticity are given on unbounded domains, such as the problem of the elastic foundation of a dam. Using classic finite element method to find the numerical solutions of these problems is very difficult. The usual method in engineering is to introduce an artificial boundary and divide the unbounded domain into two parts, one bounded subdomain and one unbounded subdomain, and to set the boundary condition on the artificial boundary and consider the boundary value problem on the bounded subdomain. On the artificial boundary the normal stress is always set to be yero. This kind of artificial boundary condition is only a rougy approximation of the enact boundary condition on the artificial boundary. When a high accuracy is required, the bounded subdomain must be very large and it is difficult to get the numerical solution.　　In this paper, we discretige the linear elastic equations on the unbounded subclomain. By solving the discretiyed problem we get the relation between the normal stress and the displace mant on the artificial boundary. This relation can be used as a discrete artificial boundary condition. Hence, we reduce the original problem on the unbounded domain to an appronimate boundary problem on the bounded subdomaind and we can solve this problem by using the finite element method. A numerical example shows that this method we use is very effective.