On Smoothing Technology Of Meshless Collocation Method And Its Application

In the use of the meshless method,the derivation or partial derivative in numerical calculation always leads to great error. For example, great error exists in the process of stress. Therefore, researches of how to reduce such errors are of great academic value. There are many methods of processing derivative or partial derivative, such as the finite difference method,using Green formula to divide the area into a line integral method. All these methods can reduce the order of the known derivatives or partial, reducing the error, thus have a great significance in the study of mechanical engineering.Smoothing, based on the collocation method, is a new method. The so-called smoothing is an approach which can achieve the minimum error of the derivation of the meshless method by reducing the order of a derivative or partial derivative of the original shape function. The greatest benefit of the collocation method is no need of mesh, It is equivalently to solve a group of partial differential equations, And a series of equations related to the partial derivative of shape function and shape function could be got after dispersing. By smoothing, the order of derivative in partial differential equation or equation set can be reduced. So does the order of the discrete differential operator matrix. Then a new global stiffness matrix and a more accurate numerical solution can be got.In this paper, studies the smoothing of collocation method based on radial point interpolation shape functions(RPIM) and moving least squares shape functions(MLS) have studied, thus avoiding the great error of derivative or partial derivative of shape functions. Examples include the boundary value, the initial value, dynamic coefficient of heat conduction and Euler-Bernoulli beam in the one-dimensional and equation of poisson, equation of biharmonic and Cantilever beam in the two-dimensional. After comparing the numerical solutions obtained before and after smoothing, it can be concluded that the numerical solutions after smoothing are more close to the exact solutions. The method in this paper is not only simple in calculation but also has a higher accuracy and convergence,and gets a better result, with the promotion of good value.