關(guān)于二維無網(wǎng)格法研究及其應(yīng)用.pdf

1、三峽大學(xué)碩士學(xué)位論文關(guān)于二維無網(wǎng)格法研究及其應(yīng)用姓名：黃哲聰申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：巖土工程指導(dǎo)教師：鄭宏20050401Abstract Most practical engineering problems related to solids and structures are currently solved using a large number of well-developed FEM software packages

2、. Although the generation of an FEM mesh for many common problems in computational mechanics (e.g. a 2D small displacement elastic problem) is quite trivial and cheap, FEM has inherent shortcomings of numerical methods w

3、hich rely on meshes or elements that are connected to each other by nodes. The meshing and re-meshing are burdensome tasks in FEM, and they also lead to difficulties when FEM is used to deal with some complex problems of

4、 solids (e.g. large deformation problems and dynamic crack problems, etc.). In addition, it is very difficult to practise the adaptive analysis in FEM because of the use of meshes. To overcome drawbacks of the conversion

5、al numerical methods (e.g. FEM), A new class of meshfree methods has been proposed and it has achieved remarkable progress over the past few years. Examples of these methods include the diffuse element method (DEM), the

6、element free Galerkin (EFG) method, the meshless local Petrov–Galerkin (MLPG) method, the finite point method (FPM), the boundary node method (BNM), and so on. Detailed descriptions of many meshfree methods can be found

7、in the recent monograph by Liu. These methods do not require a mesh to discretize the problem domain. The approximation functions are constructed entirely in terms of a set of nodes, and no element or connectivity of nod

8、es is needed for the approximation functions. The meshfree methods overcome the shortcomings of numerical methods which rely on a mesh or elements, such as FEM. Adaptive analyses and simulations using meshfree methods be

9、come efficient and easy to implement, even for problems which pose difficulties for the traditional FEM. Meshfree methods have very good potential to become powerful new generation numerical methods in this century. The

10、moving least-squares (MLS) approximation is currently widely used in meshfree methods to construct shape functions. However, there exist some disadvantages in using MLS. Firstly, the MLS shape functions lack Kronecker de

11、lta function properties. Secondly, the MLS approximation is computationally expensive because of the complexity in algorithms for computing shape functions and its derivatives. Although several strategies have been devel

12、oped for alleviating the above problems, the mentioned disadvantages of using the MLS approximation have not been completely overcome. Two meshfree point interpolation techniques, point interpolation methods (PIMs) that