用无单元伽辽金法求解几何非线性问题

用无单元伽辽金法(EFGM)求解了几何非线性问题。无单元伽辽金法采用移动最小二乘函数近似试函数,并用罚函数法施加本质(位移)边界条件,是一种与单元划分无关的无网格方法。在求解几何非线性问题时,采用了增量和修正的Newton-Raphson迭代分析的方法,并在整个分析过程中所有变量的表达格式都采用全拉格朗日格式。算例表明:EFGM在求解几何非线性问题时仍具有很好的精度。

THE ELEMENT-FREE GALERKIN METHOD FOR THE GEOMETRICALLY NONLINEAR PROBLEM

The element-free Galerkin (EFGM) method is extended to solving the geometrically nonlinear problem. The EFG method is based on moving least square (MLS) approximations and the essential boundary conditions are imposed by the penalty factor method. Only nodal data are necessary and there is no need to make elements with nodes in this method. An incremental and iterative solution procedure using modified Newton-Raphson iterations is used to solve the geometrically nonlinear problem, and measurements of strain and stress are related back to the original configuration, namely, the total Lagrangian method is used. Examples show that in solving the geometrically nonlinear problem the element-free Galerkin method achieves results of good accuracy.