The Study Of Choosing The Reproducing Kernel Particle Shape Function

Meshless method is a new numerical analysis method developed rapidly in recent years mainly by virtue of node and shape function in local support area to realize the numerical value of calculation in the whole field, which can thoroughly or partly eliminate mesh influence, therefore avoid remeshing completely, compared with the finite element method it not only has more flexibility and validity but also can keep the exactness of computing.Reproducing kernel particle (RKP) method whose shape function is based on the kernel approximation is a new meshless method. Its shape function has the advantages of both Finite Element Method and Meshless Method: partition of unity, translation invariant and the property of Kronecker delta function, so it is easy to accord with the basic boundary condition accurately.This paper is based on the research production of I.Babuska and begins with both reasoning mathematics and practical application. Firstly, this paper introduces systematically the history of messhless development at home and abroad and the general approximate meshless method. Secondly, it gives the basic RKP Meshless method knowledge of the Functional Analysis and Sobolev Space. Based on this knowledge, we construct the uniformly distributed particle shape function about RKP Meshless method in local area, then extend the uniformly distributed particle shape function to the general distributed particle shape function. Thirdly, it introduces the property and interpolation of the reproducing shape function and gives the proof of feasibility from academic aspect. Finally, it gives the example of linear distributes loads bar of one dimensional and cantilever beam, applying the RKP Meshless method to the numerical calculation and analyses. It is aimed to interpret the feasibility and validity of this method. In order to prove the feasibility of RKP Meshless method in solving the problem of elasticity mechanics, this paper compares the numerical solution with the exact solution and the ANSYS solution, from the two perspectives of theory and application we know that the RKP Meshless method is of high practicability and good application prospect in engineering domain.