Papers by Keyword: Dual Integral Equations

Abstract: The moving crack problem in an infinite plate of orthotropic anisotropy functionally graded materials (FGMs) subjected to an anti-plane shear loading is studied by making use of non- local theory. The shear modulus and mass density of FGMs are assumed to be of exponential form. Fourier transform is employed to solve the partial differential equation. The mixed boundary value problem is reduced to a pair dual integral equations which is solved by using Schmidt’s method. The semi-analytic solution of crack-tip stress is obtained, contrary to the classical elasticity solution, the crack-tip stress fields does not retains the stress singularity. The influences of the characteristic length, graded parameter, orthotropic coefficient and crack velocity on the crack-tip stress are analyzed. The numerical results show that the stress at the crack tip decrease as the characteristic length, crack velocity, graded parameter are increased and increase as the orthotropic coefficient is increased.

Abstract: A crack in an infinite plate of functionally graded materials (FGMs) under anti-plane shear impact loading is analyzed by making use of non-local theory. The shear modulus and mass density of FGMs are assumed to be of exponential form and the Poisson’s ratio is assumed to be constant. The mixed boundary value problem is reduced to a pair dual integral equations through the use of Laplace and Fourier integral transform method. In solving the dual integral equations, the crack surface displacement is expanded in a series using Jacobi’s polynomials and Schmidt’s method is used. The numerical results show that no stress singularity is present at the crack tip. The stress near the crack tip tends to increase with time at first and then decreases in amplitude and the peak values of stress decreases with increasing the graded parameters.

Abstract: A moving crack in a laminated structure with free boundary subjected to anti-plane shear loading is investigated in this paper. Using the bonding conditions of the interface between different media, all the quantities in our question have been represented with a single unknown function, and the problem is transformed into a dual integrated equation with the method of Fourier transform. The equation is solved using Schmidt method. Finally the numerical results show the relationships among the dynamic stress intensity factor and crack velocity, the height of different laminated material, shear moduli of different laminated material.

Abstract: In this paper, the behavior of a finite crack in an infinite plate of functionally graded materials (FGM) with free boundary subjected to SH-waves is considered. To make the analysis tractable, it is assumed that the material properties vary exponentially with the thickness direction and the problem is transformed into a dual integrated equation with the method of integral transform. The dynamic stress intensity factor is obtained using Schmidt method. The numerical examples are presented to demonstrate this numerical technique for SH-waves propagating in FGM plate. Finally the number of the waves, the gradient parameter of FGM and the angle of the incidence upon the dynamic stress intensity factor are also given.

Abstract: This article provides a theoretical and numerical treatment of a crack subjected to an anti-plane shear loading in an infinite strip of FGMs. The crack situated in the mid-plane of strip moves at a constant velocity. It is assumed that the shear moduli varies continuously in the thickness direction and is to be of exponential form. The mixed boundary value problem is reduced to a pair dual integral equations by means of nonlocal elasticity theory and integral transform method. The stress field and displacement field for the strip are solved near the tip of the crack by using Schmidt’s method. Then the influences of the characteristic length, graded parameters and crack velocity on the stress at crack tip are studied. Unlike the classical elasticity solution, the magnitude of stress at the crack tip is finite, and it is found that the maximum stress increases with the crack velocity as the strip length is decreased, and the maximum stress decreases with the characteristic length as the graded parameters is increased.

Abstract: A moving crack in an infinite strip of orthotropic anisotropy functionally graded material (FGM) with free boundary subjected to anti-plane shear loading is considered. The shear moduli in two directions of FGM are assumed to be of exponential form. The dynamic stress intensity factor is obtained by utilizing integral transforms and dual-integral equations. The numerical results show the relationships among the dynamic stress intensity factor and crack velocity, the height of the strip, gradient parameters and nonhomogeneous coefficients.