流形元法及其在工程中的应用

MANIFOLD METHOD AND ITS APPLICATION TO ENGINEERING PROBLEMS

叙述了流形元法的原理和应用，依据林德璋和莫海鸿的工作，参照ＥＦＧ法（无单元伽辽金法）作了理论的协调，介绍了所形成的计算方法。这一方法特别适合于裂纹扩展、应力集中、渗流集中等问题，可以将连续介质及非连续介质结合起来。文中给出了工程实例。

Manifold method which is applicable to arbitrary shapes but requires only nodal data is applied to solve mechanics problems. It is used to slove partial differential equations with moving least squares interpolants. This method requires only nodal data and no element connectivity is needed. Lagrange multipliers are used to ensure the essential boundary conditions. Weighted orthogonal basis functions are constructed, so the need for solving equations at each quadrature point is eliminated. Using covers in manifold is effective in obtaining its solution of the domain. It is much simplier than FEM.