| Meshless method is a numerical analysis method developped rapidly over the past decade, for it can construct shape function without grid, so it can ensure the higher accuracy as well as the lower computational difficulty, the grid reconstructions could be completely put aside when dealing with large deformation, moving boundaries and other issues. The main non-grid methods based on moving-least-square approximation (MLS) are: Element-Free Galerkin method (EFG), Finite-Point Method (FPM), diffusion-element method (DEM), local-boundary integral method (LBIE), local-Peterlove Galerkin meshless method (MLPG), least-square-collocation meshless method (LSC) , the weighted-least-square meshless method and so on. The selection of weight functions in MLS approximation is important as the calculation results may be influenced greatly, It should satisfy four conditions: non-negative, compact support, monotone decreasing and smoothness. The common weight functions are: Gaussian, exponential, spline, and compactly supported radial basis function (CSRBF) and so on. As an exponential function, normal distribution functions satisfy the normalization while others can not. Known by the error theory, the normal distribution of data, least- square estimates consistent with the best unbiased and minimum variance properties, but whether normal distribution functions can achieve the above characteristics and improve the accuracy is the right thing explored in this paper. Name the normal distribution function based on the weight function as normal weight function here, it's feasibility in several meshless methods were inspected and verified first, then it's used to solve the generalized linear, non- linear Poisson equations and the flat piezoelectric cantilever-structure problem. The optimal values of the support radius factor scale were discussed, the shape parameter of normal weight functionσ, the shape parameters of the exponential and the Gaussian weight functions were also given.
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