Numerical solution of a singular integral equation arising in a cruciform crack problem

Abstract

A singular integral equation arising in a cruciform crack problem is investigated in the present paper. Based on the convex technique, the piecewise Taylor-series expansion method is extended by introducing a weight parameter. An approximate solution of the singular integral equation is constructed and its convergence and error estimate are made. The variations of the approximate solutions associating with stress intensity factors are analyzed by considering internal pressures of power and sine functions, respectively. By comparing with the known methods, the observations reveal that a good approximation can be achieved using less derivative times, less discretization points, and a suitable weight parameter. The obtained results show that the crack growth is dependent on applied mechanical loadings.

Keywords:

• Singular integral equation
• cruciform crack
• piecewise Taylor-series expansion method
• approximate solution
• convex technique

AMS Subject Classifications:

• 01A23
• 45B67

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the National Natural Science Foundation of China [grant number 11362002]; Guangxi Natural Science Foundation [grant number 2016GXNSFAA380261]; 2017 Innovation Project of Guangxi Graduate Education and the project of outstanding young teachers’ training in higher education institutions of Guangxi.