拉格朗日元法中无限域问题的求解  

Solving Infinite Domain Problems in Lagrangian Method

作　　者：戴荣[1] 李仲奎[1] 尹宏磊[1] 

机构地区：[1]清华大学水利水电工程系,北京100084

出　　处：《长江科学院院报》2007年第3期33-36,共4页Journal of Changjiang River Scientific Research Institute

基　　金：国家自然科学基金(50379020);清华大学基础研究基金(JC2003008)

摘　　要：近年来,拉格朗日元法在岩土工程中得到了广泛的应用。但它对岩土工程中大量存在着的无限和半无限域问题并没有进行有针对性的处理,仍然不得不采用截断边界的办法。在对拉格朗日元和无限元的数值格式进行深入研究的基础上,将无限元引入拉格朗日元中,提出了二者的耦合方案:在中心计算区域采用拉格朗日元,而边界则采用无限元来处理;在求解时,对无限元边界也采用显式格式,无需形成整体刚度矩阵;算法的收敛性问题也得到了较好的解决。数值算例表明,所提出的算法能显著地降低截断边界对计算结果的影响。Lagrangian method is applied widely in geotechnical engineering in recent years. However, it doesn＇ t deal with infinite domain problems well, which are frequently encountered in geotechnical engineering. Truncated boundaries must be used to slove such problems in Lagrangian method. Thus the Lagrangian method and infinite element method are investigated carefully first. Based on these, infinite elements are imported to the Lagrangian method and a coupling schema is proposed. In the schema, the center domain is treated with Lagrangian method and the boundary with infinite element. Explicit scheme is adopted for the calculating procedure of infinite element, same as the Lagrangian method, which spares the calculation of global stiffness matrix. Numerical convergence of the method is also disposed successfully. It is evidenced by some numerical examples that the proposed method can reduce errors on the truncated boundary obviously.

关 键 词：拉格朗日元 无限元 耦合算法 

分 类 号：O241.3[理学—计算数学]