An application of Lobatto–Chebyshev method to a nonhomogeneous plane problem with two cracks

Abstract

In this manuscript, Lobatto–Chebyshev method, which is an effective collocation method, is applied to a system of singular integral equations, which leads from a nonhomogeneous plane problem. It is assumed that there are two cracks in a nonhomogeneous medium. The problem is formulated in the view of the basics of the elasticity theory and boundary conditions of the problem. By using the method of singular integral equation, the problem is converted to a system of first kind Cauchy type singular integral equations. It is aimed to determine the stress intensity factors (SIFs) of the crack problem. It is seen that Lobatto–Chebyshev quadrature has many advantages in determining SIFs. To verify the validity of the method, the obtained results corresponding to the one crack case are compared with the results in literature.