The Application Of Natural Element Method To Plates And Shells

The Natural Element Method( NEM) is a newly coming numerical method to solve the Partial Differential Equations. NEM shape function on the one hand assumes the characteristics of meshless method and on the other hand possesses the advantages of traditional finite element method. In this work, the basic theory and algorithm of NEM is review, the bending plates theory and the shell theory under orthogonal curvilinear coordinate system, And the natural element method of combining theory with the shell, shell natural element method in the application of a detailed study.Firstly, the paper reviews the history and development trend of the Meshless methods in detail, together with some comments on the advantages and also some existing problems to be further studied. Secondly, the current status of the Natural Element Method (NEM), the construction of the NEM shape function and its properties and advantages and the discrete formulation are discussed in detail. Then the corresponding computer program is developed and several examples are given.Then bending sheet described in detail the basic theory, the natural element method used plate bending on the issue, and through examples were tested natural element method in resolving the issue of board and the feasibility of advantages.Finally acts according to the shell theory under the orthogonal curvilinear coordinates correlation formula, infers the shell the natural element method principle theory of law theory, similarly has confirmed the natural element method through the example on the shell the application superiority.This article studied the natural element method to apply in the board shell question computation, has inferred a spring board shell question natural element method row type, established the related computation analysis program, the example had indicated: The natural element method applies in the board shell question computation is quite successful. The natural element method is a based on the Voronoi diagram and Delaunay geometric structure, adjacent to natural point interpolation function for a new trial numerical method not only has no classic grid method and the finite element method merits, between overcome some shortcomings, is a broad development prospects of solving partial differential equations of numerical methods.