Numerical simulations of fracture problems by coupling the FEM and the direct method of lines

✍ Scribed by Weizhu Bao; Houde Han; Zhongyi Huang

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 182 KB
• Volume: 190
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/s0045-7825(00)00351-0

✦ Synopsis

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 eciency and accuracy of the present method.