Study Of Meshless Method Based On B-spline Wavelet Function

At present, the finite-element method is always the effective way to solve complex project analyses problem. But in practical application, it is of a few limitationss to deal with large deformation and arbitrary and complex paths of the crack angle. In this case, mesh fininite element method will become extremely complex, and sometimes re-meshing, the presence of the grid will lead to the failure of the results. So people need a new method to solve these problems.With its distinctive characteristics, meshless or meshfree methods has been one of the hottest topics in numerical analysis. In meshless methods, since the discretization is only based on a set of nodes and does not require a mesh, there is a method of fitting the shape functions by using the scattered nodes in the problem domain. The nodes can be easily added or removed, so they can naturally handle large deformation and domain discontinuity issues. The element free Galerkin method is the new efficient meshless method, the shape functions are constructed of the the moving least-squares approximation.It is a widely used in the meshless for its high precision,its continuous derivative and move the border with flexible.Wavelet translation is a time-frequency analysis,its basic ideas is mul-scale and refined analys to a signal through the function of expansion and the translation,the original signal is decomposed into the local signal with different time-frequency and direction characteristics,its size of the time or space window can be transformed with high and low frequency. Because the wavelet transform have the ability to characterize local signal characteristics and multi-resolution analysis characteristics in time and frequency domain, it is known as "mathematical microscope". It has achieved very good application in the physical exploration, image processing, fault diagnosis, signal analysis and so on. So it is a milestone in the development history of signal analysis progress. In the theoretical framework of multi-scale analysis, the B spline wavelet function is constructed by B spline functions, is more suitable for the multi-scale analysis and processing of image curves or surfaces.How to combine the two organic, give full play to both applications in the mechanical advantage of good academic research has been a new field of force.This paper attempts to apply the B-spline wavelet function in Galerkin mesh-free method meshless method for constructing weight functions and basis functions of the shape functionsin by using Using the b-spline wavelet good properties that other wavelet not possess, such as display expressions, orthogonality, approximation order. Construct the corresponding B spline wavelet function by adjusting its translation and scaling variables. It used in the analysis of stress calculation of one and two dimensional structures. Repeatly, did a large amount of numerical simulation example ,repectively in different weight function support radius, different numerical integal plan. Through the comparison analysis with Gauss weight function, spline weight function,verify the b-spline wavelet as weight function has obvious advantages and as base function can also be achieved good effect. And its used in crack factor calculation through numerical analysis of rule node distribution and irregular node distribution in 2d board. Trought did a lot of numerical simulation experiment, respectively in different scales and different weight functions, different translation and scaling variables, the results were analyzed and compared. Eventually come to a conclusion, through a large number of experiments show that using good nature of the B spline wavelet and using meshless method to solve the cracks and mutation of mechanics problems have certain advantagesespecially less affected by support radius。By using B spline wavelet function as weight function can improve the calculation accuracy and improve the computational efficiency. In some extent could alleviate the defects of meshless that computation is big. For using meshless to solve mechanical problems provides a new way and for the development of meshless method develop some new development space.