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Barycentric Rational Interpolation Iteration For Solving Irregular Thin Plate Bending Problems

Posted on:2017-05-25Degree:MasterType:Thesis
Country:ChinaCandidate:M L ZhuangFull Text:PDF
GTID:2180330482490627Subject:Engineering Mechanics
Abstract/Summary:PDF Full Text Request
Structural members, common in engineering practice, consist of plates with shapes other than rectangular, such as circular plates, annular plates, polygon plates and arbitrarily complex shape plate. Therefor the more general forms with complex shapes are discussed in this paper:irregular thin plate bending problems in rectangular coordinate system and polar coordinates. The numerical model of plate bending problem is boundary value problems of biharmonic equation. We consider possible solutions, which can be obtained analytically with relative ease for some geometrical forms of plates different from rectangular and circular. Linear elastic bending problems of plates involving complex geometries, loading and boundary conditions have been extensively studied. Therefore, how to precisely solve potential problems in complex regions is an important issue in the field of numerical calculation. In this paper,we put up an effective and convenient and high precision numerical calculation method of barycentric rational interpolation collocation method for solving the bending problems of irregular thin plates.This paper describes a regular domain collocation method based on the barycentric rational interpolation for solving the bending problems of irregular thin plates. Embedded the irregular domain into a regular domain, the barycentric rational interpolation in tensor form is used to approximate unknown function. The governing equation of bending plate in a regular domain is discretized by the differentiation matrix derived from barycentric rational interpolation to form a system of algebraic equations. The constraint algebraic equation of boundary condition can come from the unknown function value of interpolation nodes of the barycentric interpolation of the regular domain by taking a number of nodes on the boundary of the irregular thin plate. Combine discrete equation of the governing equation of the irregular plate and the constraint algebraic equation of boundary condition into newconstraint algebraic equations. Using the least square method to solve the equations and get the node displacement value in the regular domain. Using interpolation of the barycentric interpolation can get function values of any node in the irregular plate.When axisymmetric thin plates are analyzed, it is convenient to express the governing differential equation of biharmonic equation in polar coordinates. Simplify the governing differential equation of biharmonic equation in polar coordinates according the axisymmetric character of thin plates, and apply the boundary conditions to solve the governing differential equation. The irregular thin plates without axisymmetric bending in rectangular coordinate systems and in polar coordinates can be analyzed by a regular domain collocation method based on the barycentric rational interpolation.In this paper,8 numerical experiments for irregular thin plats bending problems in rectangular coordinate system and polar coordinates are shown. Numerical experiments of the irregular plate bending are carried out to demonstrate the flexibility, high efficiency and accuracy of the method. By comparing the numerical solutions with the analytical solutions, we can conclude that the method is a new high and efficiency method for solving irregular thin plate bending problems. The calculation formula of the method is simple and program of it is convenient, the calculation precision is very high.
Keywords/Search Tags:irregular thin plates, barycentric rational interpolation, collocation method, a regular domain collocation method, differential matrix
PDF Full Text Request
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