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Application of Meshless Method to Calculation of Plates and Shells

Author: YeXiang
Tutor: DingChengHui；ZhaoXiQian
School: Nanchang University
Course: Engineering Mechanics
Keywords: Moving Least Squares Meshless Galerkin method Penalty function method The Reissner-mindlin plate theory Thin shell theory
CLC: TU399
Type: Master's thesis
Year: 2005
Downloads: 248
Quote: 2
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Abstract


Meshless Galerkin method is a finite element numerical methods developed in recent years . It uses moving least squares method to construct the shape functions , the weak form of the variational energy functional control equation , and the essential boundary conditions imposed penalty function method , to obtain the numerical solution of partial differential equations . This method only the node information , without even the node into a unit : In addition, as well as high precision , post-processing and easy . -Free Galerkin method of mathematics is based on moving least squares method . Moving least squares method to construct the shape function , just arranged a series of nodes in the area of solving . Therefore , non- grid Galerkin method can not need unit . Moving least squares approximation function , however , does not necessarily accurately by calculating the point , unless you use the singular weight function . Therefore , the nature of the boundary conditions applied treatment becomes complex and concentrated loads but with the advantages of this approach compared to negligible . Calculation of plate bending problems , the introduction of the penalty parameter directly on the board of the intrinsic boundary , combined with the Reissner-Mindlin plate theory derivation of the the meshless method governing equations of plate bending problems . The method can also be applicable to the calculation of sheet and plate , high accuracy can be obtained with fewer nodes . Finally, non- grid Galerkin method to promote applied to shell calculations using the theory of orthogonal curvilinear coordinates housing , using the least squares method to construct the shape functions of the shell model using the variational principle discrete equations , differential form of the shell problem is rare newspapers , then the corresponding calculation program is compiled and numerical examples are . Example the results are compared with the result of the ANSYS , two calculation results are very consistent , which validates the reliability of the present theory .

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