Improving accuracy of opening-mode stress intensity factor in two-dimensional media using fundamental solution based finite element model

Abstract

A hybrid finite element method (FEM) is developed for determining stress intensity factor of opening-mode cracks. The model is based on fundamental solutions and higherorder displacement extrapolation. In the present formulation, linear combination of fundamental solutions and shape functions are respectively used to approximate the element interior and frame fields. The equality of the two approximations is enforced through a hybrid functional and element boundary integrals are involved only. Numerical examples are considered to investigate effects of element size, number of elements and crack length on crack tip singularity. Results show that the proposed approach can achieve better numerical accuracy than conventional FEM.

Keywords:

• Stress intensity factor
• crack opening displacement
• displacement extrapolation
• fundamental solutions
• hybrid finite element

Additional information

Notes on contributors

H Wang

Hui Wang received his Bachelor degree in Theoretical and Applied Mechanics from Lanzhou University, China, in 1999. Subsequently he joined the College of Science as an assistant lecturer at Zhongyuan University of Technology, where he spent two years teaching. He earned his Master degree from Dalian University of Technology in 2004 and Doctoral degree from Tianjin University in 2007, both of which in Solid Mechanics. In 2007, he joined the College of Civil Engineering and Architecture, Henan University of Technology, as a lecturer. He was promoted to Associate Professor in 2009. His main research interest is in computational mechanics, and so far he has published more than 20 scientific papers and three books. In 2010, he was awarded the Australia Endeavour Award.

Q H Qin

Qing-Hua Qin received his Bachelor of Engineering degree in mechanical engineering from Chang An University, China, in 1982, and his Master of Science and PhD degrees from Huazhong University of Science and Technology (HUST), China, in 1984 and 1990, respectively. Both MS and PhD degrees are in applied mechanics. He joined the HUST Department of Mechanics as an associate lecturer in 1984, and was promoted to lecturer of mechanics in 1987 during his PhD candidature period. After spending 10 years lecturing at HUST, he was awarded a DAAD/K.C. Wong research fellowship in 1994, which enabled him to work at the University of Stuttgart in Germany for nine months. In 1995 he left HUST to take up a postdoctoral research fellowship at Tsinghua University, China, where he worked until 1997. He was awarded a Queen Elizabeth II fellowship in 1997 and a Professorial fellowship in 2002 at University of Sydney and stayed there till December 2003, both by the Australian Research Council. He is currently a Professor in the Research School of Engineering at the Australian National University, Australia. He has published over 200 journal papers and five monographs.

W Yao

Wei-an Yao received his Bachelor of Science degree in Computational Mathematics from Liaoning University in 1985. He was conferred a Master of Engineering degree in Computational Mechanics from Dalian University of Technology in 1988 for his research in shape optimisation of annular fins. From 1985 to 1996, he made researches on optimisation and boundary element method in Dalian University as a lecturer or assistant professor. In 1996, he moved to Dalian University of Technology. He was promoted to professor in 2002 and earned his Doctoral degree in Solid Mechanics from Dalian University of Technology in 2004 for research in further application of symplectic dual solution system in elasticity. He has published more than 80 scientific papers and one book titled Symplectic elasticity by World Scientific Publishing Company in 2009. In the year of 2010, he was a recipient of the Second National Natural Science Award of China.