Analysis of bonded anisotropic wedges with interface crack under anti-plane shear loading.pdf

Appl. Math. Mech. -Engl. Ed., 35(5), 637–654 (2014) Applied Mathematics DOI 10.1007/s10483-014-1818-6 and Mechanics c Shanghai University and Springer-Verlag Berlin Heidelberg 2014 (English Edition) Analysis of bonded anisotropic wedges with interface crack under anti-plane shear loading∗ M. GHADIRI1, A. R. SHAHANI2 (1. Faculty of Engineering, Department of Mechanics, Imam Khomeini International University, Qazvin 34149-16818, Iran; 2. Department of Applied Mechanics, Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Tehran 19697-64499, Iran) Abstract The antiplane stress analysis of two anisotropic finite wedges with arbitrary radii and apex angles that are bonded together along a common edge is investigated. The wedge radial boundaries can be subjected to displacement-displacement boundary condi- tions, and the circular boundary of the wedge is free from any traction. The new finite complex transforms are employed to solve the problem. These finite complex transforms have complex analogies to both kinds of standard finite Mellin transforms. The traction free condition on the crack faces is expressed as a singular integral equation by using the exact analytical method. The explicit terms for the strength of singularity are extracted, showing the dependence of the order of the stress singularity on the wedge angle, material constants, and boundary conditions. A numerical method is used for solving the resul- tant singular integral equations. The displacement boundary conditi