中文摘要：

岩土工程中经常会遇到无穷域问题,而采用无限单元可以实现对其有效地模拟。弱形式求积元法是一个有效的数值工具,它常通过提高积分阶次来提高计算精度。建立了无限弱形式求积单元并被应用于求解岩土工程中的无穷域问题,该单元基于坐标映射,将无穷域变换到标准域,在标准域上进行数值积分和数值微分,保留了传统弱形式求积元的积分点坐标和权系数。求解了瞬态渗流、固结和静力分析等数值算例,并与解析解或截断方法进行了对比。结果表明：基于坐标映射的无限弱形式求积单元使用简单,可以模拟各种类型的无穷域问题,仅需要将感兴趣的范围进行有限域划分并通过提高积分阶次来减小对极点位置的依赖,极大地节省了计算资源,提高了计算精度。

英文摘要：

Unbounded domain problems are frequently encountered in geotechnical engineering and infinite elements are often used effectively for simulation. The weak form quadrature element method is an effective numerical tool in which the computational accuracy is often improved through increasing the order of integration. An infinite weak form quadrature element is developed and applied to the analysis of unbounded domain problems in geotechnical engineering. Based on coordinate transformation, an unbounded domain is mapped onto a standard region where numerical integration and numerical differentiation are conducted and the conventional numerical integration points and weights in the weak form quadrature element method are retained. Numerical examples in the areas of transient seepage, consolidation and elastostatic analysis are given and the results are compared with analytical solutions or those of other numerical methods. It is shown that the infinite weak form quadrature element is simple and applicable to solution of various unbounded domain problems, while conventional elements are used during discretization of the domain of interest. In addition, the dependence on the pole of coordinate transformation can be alleviated considerably with the increase of the integration order of the element. Consequently, computational resources are reduced significantly and accuracy of results is enhanced.