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Study on Hybrid Meshless Methods and Its Application

Author: HuangZheCong
Tutor: ZhengHong
School: Wuhan Institute of Rock and Soil Mechanics
Course: Geotechnical Engineering
Keywords: Finite element method Meshless method Cell - free Galerkin method Generalized Finite Difference Method Finite volume method Limited ball method Meshless Finite Volume Method Least squares method Moving Least Squares Shepard interpolation Hybrid Local Galerkin meshless method Elastic-plastic Elastic - Viscoplastic
CLC: TP391.7
Type: PhD thesis
Year: 2008
Downloads: 264
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Abstract

The meshless methods, which a good many different ones have been proposed, were developed rapidly in current years. However, the complicated shape functions and their derivatives make the meshless methods difficult in computation and low in efficiency. Moreover, the use of large numbers of integral points increases the calculating burden ulteriorly. This paper puts research emphases on how to improve the calculating efficiency on the premise of good or better precision. How to applying the new methods on practice of engineering is another task of this paper.Firstly, the Element-free Galerkin Finite Difference Method ( EFGFDM), which combined EFGM with generalized finite difference method, is proposed in this paper. The EFGFDM can speed up the calculation rapidly.Secondly, in order to improve the precision and the stability of the meshfree methods, the "hybrid" technique is adopted to interpolate stress as well as displacement indispendently. Based such a technique, a few noval meshless methods are proposed as follows: 1. the hybrid meshless finite volume method(HMFVM); 2. the hybrid meshless finite volume difference method(HMFVDM); 3. the hybrid meshless finite volume least square method(HMFVLSM); 4. the hybrid Element-free Galerkin method(HEFGM); 5. the hybrid meshless local Galerkin method(HMLGM).Finally, the hybrid meshless methods are applied in the fields as follows: 1. solving the elastic problems on condition that the materials are incompressible; 2. solving the elas-plastic problems; 3. solving the elas-viscoplastic problems; 4. stimulating the progresses of cavity excavating; 5. analyzing the problems of slope stabilization.The structure of this paper is as follows:Chapter 1 introduces the classes and developing course of meshless methods. The advantages and defects of many meshless methods are appraised in this chapter.In chapter2, the approximation functions and discrete methods of traditional meshless methods are summarized. Many kinds of meshless methods are compared in detail.Chapter3 presents the Element-free Galerkin finite difference method (EFGFDM) combined with the generalized finite difference method. The proposed EFGFDM is applied to solve anchored problems in this chapter.Chapter 4 proposes the ideal of hybrid meshless methods which are applied in solving the elastic incompressible problems.In Chapter 5, the hybrid meshless methods are used to solve the problems of elas-plasticity and elas-viscoplasticity. The problems of cavity excavating and slope stabilization are also researched in Chapter 5 with the hybrid meshless methods. A new-style MLPG is also presented for solving anchored problems.Combined with the hybrid idea, the EFGFDM is complied to simulate the excavation and anchor of underground powerhouse area of Dagangshan hydropower station.Chapter 7 is conclusions and prospects.

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