Boundary collocation method for a cracked rectangular plate with double external tension

Abstract

In this article, the boundary collocation method is employed to investigate the problems of a central crack in a rectangular plate which applied double external tension on the outer boundary under the assumption that the dimensions of the plate are much larger than that of the crack. A set of stress functions has also been proposed based on the theoretical analysis which satisfies the condition that there is no external force on the crack surfaces. It is only necessary to consider the condition on the external boundary. Using boundary collocation method, the linear algebra equations at collocation points are obtained. The least squares method is used to obtain the solution of the equations, so that the unknown coefficients can be obtained. According to the expression of the stress intensity factor at crack tip, we can obtain the numerical results of stress intensity factor. Numerical experiments show that the results coincide with the exact solution of the infinite plate. In particular, this case of the double external tension applied on the outer boundary is seldom studied by boundary collocation method.

†Dedicated to Prof. Wei Lin on his 70th bithday.

Keywords:

• Boundary collocation method
• Stress intensity factor
• Crack
• Numerical solution

Keywords:

• 2000 Mathematics Subject Classifications: 45E
• 73C

Acknowledgment

This work is supported through the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, and NNSF(10161009) of P.R. of China.

Notes

†Dedicated to Prof. Wei Lin on his 70th bithday.