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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。
Geotechnical engineering often encounters the problem of infinite fields, and the use of infinite elements can be effectively simulated. Weak form quadrature method is an effective numerical tool, it often improves the accuracy of the calculation by increasing the integral order. The infinitesimal weak form quadrature unit is established and applied to solve the infinite region problem in geotechnical engineering. Based on the coordinate mapping, the unit transforms the infinity into the standard domain and performs numerical integration and numerical differentiation on the standard domain, Integral Point Coordinates and Weighting Coefficients of Weakly Typed Quadrature. The numerical examples of transient seepage, consolidation and static analysis are solved and compared with analytical solutions or truncation methods. The results show that the infinitesimal weak form quadrature unit based on coordinate mapping is easy to use and can simulate various types of infinite fields, only need to divide the region of interest into finite fields and increase the integral order to reduce the position of the pole Dependent, which greatly saves the computing resources and improves the calculation accuracy.