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A Regular Domain Collocation Method Based On Barycentric Lagrange Interpolation For Solving Elastic Plane Problems In Irregular-region

Posted on:2018-11-09Degree:MasterType:Thesis
Country:ChinaCandidate:S Y JiFull Text:PDF
GTID:2310330515980211Subject:Engineering Mechanics
Abstract/Summary:PDF Full Text Request
The plane elasticity problems have been extensively researched.In engineering practice,the plane elasticity problem is not only applied in the regular domain,but also in the irregular domain,such as arch domain,circular domain,polygonal domain and arbitrary complex plane domain.This thesis employs a numerical method based on collocation method to solve the plane elasticity problems in the irregular domains.The plane elasticity problems can be reduced to the second order boundary value problem of coupling elliptic partial differential equations.The numerical analysis of the elasticity problem is the numerical method to find the boundary value problem of elliptic partial differential equations.For the plane elasticity problem of arbitrary complex shape,it is usually difficult to obtain its analytical solution.The thesis is progressed a method tothe plane elasticity problem with the displacement as unknowns on the irregular domain,which is called regular regional barycentric Lagrange interpolation collocation method.The regular regional barycentric Lagrange interpolation collocation method is adopted to solve the plane elasticity problem on irregular domain in the rectangular coordinate system.By embedding irregular domain into the regular rectangular domain on which the governing equations of plane elasticity problem are discretized through barycentric Lagrange interpolation method,the matrix-vector form of the discreted equations are established directly.In the polar coordinate system,by embedding irregular domain into the regular circular or circumferential domain on which the governing equations are discretized through barycentricLagrange interpolation method,the matrix-vector form of the discreted equations are established as well.The boundary conditions,which are discretized by using the barycentric Lagrange interpolation method on the boundary nodal points,can be imposed in the regular domain.In the irregular domain,boundary conditions are imposed by additional method and an over-constrained linear system of algebra equations is obtained which the least-square method is applied to obtain the numerical solutions of the displacement in the whole regular domain.By the barycentric Lagrange interpolation method,the displacement solutions of arbitrary nodal points in the irregular domain can be obtained.Some numerical examples are given to illuminate the validity,efficiency and computing precision of the proposed method.The numerical examples in this thesis show that the application of barycentric Lagrange interpolation collocation method and regular regional method can effectively solve the irregular plane elasticity problems.Barycentric Lagrange interpolation collocation method has the following advantages: simple program implementation,well node adaptability,meshless and high computing precision.
Keywords/Search Tags:irregular domain, plane elastic problem, barycentric Lagrange interpolation, collocation method, regular domain collocation method, differential matrix
PDF Full Text Request
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