A crack problem in the semi-infinite plane

摘要

This paper discusses the crack problem of band width in a semi-infinite plane, we refer to the singular integral equation theory to this problem and transform the boundary conditions into the boundary value problem of analytic function. Thus the problem can be transformed into the singular integral equations of Cauchy problem. Then by a series of operations, the problem becomes a singular integral equations on crack. Afterwards, the singular integral equation is discretized by the Guass-Chebyshev quadrature formula and the numerical solution of the singular integral equations is obtained. Finally, the obtained solution is simulated by MATLAB, and the trend chart of the displacement with the change of crack width and external force is drawn.