This paper deals with the interaction between two inclined cracks in the upper part of bonded dissimilar materials subjected to various stresses which is normal stress (Mode I), shear stress (Mode II), tearing stress (Mode III) and mixed stress. This problem is formulated into hypersingular integral equations (HSIE) by using modified complex potentials (MCP) with the help of continuity conditions of the resultant force and displacement functions where the unknown is the crack opening displacement (COD) function and the tractions along the crack as the right hand terms. Then, the curve length coordinate method and appropriate quadrature formulas are used to solve numerically the obtained HSIE to compute the stress intensity factors (SIF) in order to determine the stability behavior of materials containing cracks. Numerical results showed the behavior of the nondimensionalSIF at the cracks tips. It is observed that the various stresses and the elastic constants ratio are influences to the value of nondimensional SIF at the crack tips. � Published under licence by IOP Publishing Ltd.

Numerical solutions for an elastic half plane with circular arc cracks subjected to uniaxial tension ??x = p is presented. The free traction on the boundary of the half plane is assumed. Based on the modified complex potential and superposition method, the problem is formulated into a singular integral equation with the distribution dislocation function as unknown. Numerical examples exhibit the behavior of the stress intensity factor at the cracks tips for various positions. Our numerical results are in agreement with the existence one. � 2019, Akademi Sains Malaysia.

This paper studied the order and stability of a 2-Point Block Backward Difference method (2PBBD) for solving systems of nonstiff higher order Ordinary Differential Equations (ODEs) directly. The method computes the estimated solutions at two points concurrently within an equidistant block. The integration coefficients that are used in the method are calculated only once at the beginning of the programming. The numerical results obtained compare the stability region and error growth rate of the proposed method with 2-Point Block Divided Difference method (2PBDD) and 1-Point Backward Difference method (1PBD). � 2018 Author(s).

The new hypersingular integral equations (HSIEs) for the multiple cracks problems in both upper and lower parts of the bonded dissimilar materials are formulated using the modified complex potential method, and with the help of the continuity conditions of the resultant force function and displacement. The crack opening displacement is the unknown and the traction along the crack as the right term of the equations. The appropriate quadrature formulas are used in solving the obtained HSIEs for the unknown coefficients. Numerical results for the multiple inclined or circular arc cracks subjected to the remote shear stress are presented.

The new hypersingular integral equations (HSIEs) for the multiple cracks problems in both upper and lower parts of the bonded dissimilar materials are formulated using the modified complex potential method, and with the help of the continuity conditions of the resultant force function and displacement. The crack opening displacement is the unknown and the traction along the crack as the right term of the equations. The appropriate quadrature formulas are used in solving the obtained HSIEs for the unknown coefficients. Numerical results for the multiple inclined or circular arc cracks subjected to the remote shear stress are presented. � 2019 Elsevier Inc.