三维高阶数值流形方法研究  

Study of three-dimensional high-order numerical manifold method

作　　者：姜清辉[1] 邓书申[1] 周创兵[1] 

机构地区：[1]水资源与水电工程科学国家重点实验室武汉大学

出　　处：《岩土力学》2006年第9期1471-1474,共4页Rock and Soil Mechanics

基　　金：国家自然科学基金(No.50309010);国家自然科学基金重点项目(No.50239070);水资源与水电工程科学国家重点实验室开放基金(No.2003C004);中科院岩土力学重点实验室开放基金(No.206152152)资助。

摘　　要：将三维流形单元的位移函数从一阶拓展为二阶,基于最小势能原理建立了有限单元覆盖的高阶流形方法分析格式,详细推导了三维流形单元的刚度矩阵、等效节点荷载列阵以及位移约束矩阵。计算结果表明,提高物理覆盖函数的阶次可有效提高流形方法的计算精度。The three-dimensional numerical manifold with high-order displacement functions has been developed based on the tetrahedron element meshes. The global equilibrium equations of high-order manifold method are established by minimizing the total potential energy. The stiffness matrix, the loading matrix and displacement resistance matrix are derived and added to the global equations. The example of the cantilever bending under the area loading is calculated by the high-order manifold method and the numerical results agree well with theoretical solutions.

关 键 词：数值流形方法 高阶位移函数 有限覆盖 

分 类 号：TB115[理学—数学]