Solution Grid Method With The Finite Element Method, Comparative Preliminary Study

In recent decades, the finite element has become a major field of engineering numerical methods, as it is universal and flexible. But defects of the finite element method exist in analyzing large deformation, non-continuity and so on. The meshless method is proposed basing on these defects. The element-free Galerkin method (EFGM) and finite element method (FEM) are adopted to numerically simulate a numerical example basing on the development history and present situation, classification, advantages and disadvantages analysis of the meshless in this text. And comparisons are also made between the results by this two methods basing on the numerical examples in structure discrete, stiffness matrix establishment, application of equivalent node loads and boundary conditions application, etc. And theirs advantages and disadvantages are pointed out.Under the same conditions, the influencing facts of EFGM such as node application program, base function, weight function, shape function and the radius of support domain are analyzed basing on one-dimensional example. All the empirical coefficients of the facts are obtained and it is instructive. Compared to finite element method cell division, the node application is simpler and the post-processing is also more convenient. The selection of weight function is very important. We select the quartic spline-type weight function to be the most accurate results in the several common using weight functions. The shape function established by point interpolation method (PIM) has the character of point interpolation comparing to moving least square method, and it is also more likely to impose boundary conditions. The selection of the support domain radius determines the size of the support domain. It is also the important factor that influences the computational efficiency and accuracy.The article outlines another mature meshless method: the point collocation method. And comparisons are also made between the results by this method and element-free Galerkin method under the same conditions. Compared with element-free Galerkin method, the point collocation method is high efficiency, and easier to impose displacement boundary conditions, but its coefficient matrix is non-symmetric and less stable.This paper briefly describes the Kriging method, and applies it to the shape function establishment of meshless method, building the Kriging element-free Galerkin (KEFG). One-dimensional numerical example is analyzed using KEFG, and comparisons are also made between the results by this method and element-free Galerkin method under the same conditions. The results obtained shows that the method has good stability and point interpolation, and is easier to impose displacement boundary conditions. The error relative to the fixed end in KEFG is smaller, and the calculation quantity is far smaller than the element-free Galerkin method.Finally, the element-free Galerkin method is used to calculate two dimension soil consolidation problems. The comparison is also made between the results by this method and the results by finite element method under same conditions. The good agreement shows that this method can be used to simulate engineering problems efficiently.