Numerical Simulations of Fracture Problems by Coupling the Fem and the Direct Method of Lines

Content Provider	Semantic Scholar
Author	Bao, Weizhu Han, Houde Huang, Zhongyi
Copyright Year	2000
Abstract	In this paper, we propose a method for calculating stress intensity factors of plane fracture problems with cracks by coupling the ®nite element method (FEM) and the direct method of lines. We introduce polygonal arti®cial boundaries and divide the physical domain into two parts: a large domain without any crack tips and small polygonal domains surrounding the crack tips. We solve the problem de®ned in the small domains with crack tips by using the direct method of lines and design discrete nonlocal arti®cial boundary conditions on the polygonal arti®cial boundaries by imposing the continuity of displacement and normal stress. Then the original problem is reduced to a boundary value problem de®ned in a domain without any crack tips. The ®nite element approximation of the reduced problem is considered and we can prove that the ®nite element approximation is well posed. Numerical examples and results of a fracture problem with exact solution and two typical fracture problems demonstrate the eciency and accuracy of the present method.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://www.math.nus.edu.sg/~bao/PS/BHH.pdf
Language	English
Access Restriction	Open
Subject Keyword	Acquired deformities of limbs Approximation Computer simulation Direct method in the calculus of variations Displacement mapping Finite element method Inguinal Hernia, Direct Method of lines Nonlocal Lagrangian Numerical analysis Numerical linear algebra Psychologic Displacement Scott continuity
Content Type	Text
Resource Type	Article