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The Computational Method Based on Singularity Theory and Its Applications

Author: LiuDongZuo
Tutor: WangXuYue
School: Harbin Institute of Technology
Course: General and Fundamental Mechanics
Keywords: Stress intensity factor Continuous dislocation model Finite Element Singular integral equation
CLC: O346.1
Type: Master's thesis
Year: 2008
Downloads: 56
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Abstract

Unlimited area of ??fracture problem by means of classical fracture theory analytical solution for a limited area containing crack geometries, due to the complexity of the situation of the border, is generally difficult to obtain analytical solutions only by the finite element or boundary element method numerical solution. Application of traditional finite element solution fracture problem, you need a very fine mesh division in the region near the crack tip, so that the calculation of the large increase, and the calculation accuracy depends on the type of unit and grid program. Based on the infinite regional dislocation elastic solution of the continuous dislocation model is very effective in dealing with cracked infinite regional fracture problem, with a simple, convenient, and high accuracy, but can not be directly applied to the case of a limited area. This project developed a set of coupled continuous dislocation model and finite element fracture analysis of semi-analytical method, the continuous dislocation model characteristics of crack problems and finite element for the perfect combination of good adaptability of the complex boundary, can be widely used analysis of various types of limited regional configuration of linear elastic fracture problems, especially for small-size structural problems is very effective. The main content of this paper as follows: First, the application of the principle of linear superposition, the limited area of ??the fracture problem into unlimited regional faults and limited non-singular issues, continuous dislocation model and finite element method were used for these two issues processed by the dislocation density function to the solution of two problems are coupled, the use of force of the crack surface boundary conditions and displacement single-valued conditions corresponding with Cauchy kernel singular integral equations by means of the development of Erdogan discrete numerical methods, unknown dislocation density function for transformation and Chebyshev polynomial asymptotic expansions of the main part, the singular integral equations into the dislocation density function expansion coefficients of linear algebraic equations obtained by solving the algebraic equations corresponding bit dislocation density function and the stress field. Secondly, coupling continuous fracture dislocation model and finite element analysis method to establish the appropriate fracture problem solving equations of a rectangular plate with a central crack, crack intensity factor of the crack tip under the special form of load solution, the calculation results with the stress intensity factor manual and Wang Zhuo finite difference method calculation results were analyzed and compared to prove that the coupling continuous dislocation model and finite element method for calculation of fracture effectiveness in dealing with the rules of regional fracture problem, accuracy and excellence. Finally, the coupling of consecutive bits the fracture dislocation model and finite element analysis method to establish the corresponding trapezoidal plate with eccentric crack fracture problem solving equations, solving the crack tip loading of the special form of crack intensity factor, the calculation results with Wang Zhuo Finite Difference Method of calculation results were analyzed and compared, indicating the validity of the model and finite element method for calculation of fracture, accuracy coupled continuous dislocation. The conclusion of this topic show that the coupling continuous dislocation model and the finite element method for calculation of fracture fracture issues with high accuracy, and precision control, calculation accuracy is not dependent on the cell type, the grid program and stress interpolation scheme for solving high efficiency, without area border restrictions, the solution is simple and easy.

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CLC: > Mathematical sciences and chemical > Mechanics > Solid Mechanics > Strength theory > Fracture theory
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