Font Size: a A A

The Application Of Point Interpolation Method In 2-D Solid

Posted on:2004-05-17Degree:MasterType:Thesis
Country:ChinaCandidate:W T MaFull Text:PDF
GTID:2120360095956398Subject:Solid mechanics
Abstract/Summary:PDF Full Text Request
A point interpolation method developed in recent years is one of the new kind of mesh-less method. In the PIM, the problem domain is represented by properly scattered points. The displacement at a point is interpolated by the displacements in the influence domain of this point. The interpolation function has the Delta function property, so the essential boundary conditions can be simply imposed. In this paper, the principal and method of PIM is deeply studied. The most difficulty in the PIM is how to avoid the singularity of matrix. Changing basis function is an effective method .So, fixed nodes method which needs same numbers of points in every sub-domain is advanced. This method not only can deal with the problem of singularity, but can simplify the numerical process of interpolation function, Based on the principle of minimum total potential energy, The formulas of PIM are arrived. Numerical examples show this mesh-less method is simple and effective.Then, The presented method is used for calculation of elastic plane-plate. The governing equation of PIM is obtained on the basis of variational principle. Numerical examples show that the method is applicable widely, considerably precious, and can be used for the calculation of both thin an thick plate.Lastly, using the compactly supported radial functional to take the place of the polynomial function, local radial point interpolation method, is presented in this paper. It is a new truly mesh-less method, because the background cells for integration are not needed. It uses the weighted function of Gaussian or of Spline as a test function of the weighted residual method. It involves only integrations over a regular local sub-domain in and on a local sub-boundary centered at the node in question. The numerical solutions show that this method which can give quit accurate and effective numerical can offer tremendous potential in engneering applications.
Keywords/Search Tags:Mesh-less Method, Point Interpolation Method, Elastic Plane-plate, Compactly Radial Basis Function, the Local Radial Point Interpolation Method
PDF Full Text Request
Related items