Papers by Author: Cheng Jin

Abstract: By application of the theory of complex functions, the problem for mode Ⅲ dynamic crack under concentrated force were researched. The Riemann-Hilbert problem is formulated according to relationships of self-similar functions. Analytical solutions of stresses, displacements and dynamic stress intensity factors were obtained by the measures of self-similar functions and corresponding differential and integral operation.

Abstract: Dynamic propagation of mode Ⅲ crack under variable moving loads on the crack surface is investigated using the theory of complex functions. Using the approaches of self-similar functions, the problems are readily transformed into Riemann-Hilbert problems. The paper presents a new mechanical model for dynamic crack propagation, in which the crack is under the conditions that the variable concentrated loads Pt³/x² and Px/t move along x-axial with velocity β. At last, analytical solutions of stress, displacement and stress intensity factor are attained, respectively.

Abstract: Asymmetric dynamic propagation of mode III: crack under variable moving loads on the crack surface is investigated using the theory of complex functions. Using the approach of self-similar function, the problems are readily transformed into Riemann-Hilbert problems. The paper presents a new mechanical model for dynamic crack propagation, in which the crack is under the conditions that the variable concentrated loads Pt3/x2 and Pt/x move along x-axial with velocity β. And then, analytical solutions of stress, displacement and stress intensity factors are attained, respectively. These solutions are utilizable to attain solutions of arbitrarily complex problems, using the superposition theorem

Abstract: By the approaches of the theory of complex functions, propagation problems concerning mode Ⅲ asymmetrical dynamic interface crack were studied. The problems can be transformed into Riemann-Hilbert problem easily by the measures of self-similar functions, and the universal expressions of analytical solutions of the edges of mode Ⅲ asymmetrical dynamics interface crack subjected to variable loads and respectively, were attained.

Abstract: By the approaches of the theory of complex functions, dynamic propagation problems on the surfaces of mode I crack subjected to unit-step loads and instantaneous impulse loads located at the origin of the coordinates were studied for Aluminum alloys, respectively. Analytical solutions to stresses, displacements, dynamic stress intensity factors and dislocation distribution functions are gained by the methods of self-similar functions. The problems considered can be very facilely transformed into Riemann-Hilbert problem and their closed solutions are obtained rather straightforward by Muskhelishvili’s measure.

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: A fatigue crack growth model under constant amplitude loading based on the total plastic energy dissipation per cycle ahead of the crack was proposed. With the energy balance concept, the crack growth rate was correlated with the total plastic dissipation per cycle, and the total plastic dissipation per cycle was obtained through 2-D elastic–plastic finite element analysis of a stationary crack under constant amplitude. The predictions of the model were in good with the experimental results.

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.

Abstract: By the theory of complex functions, dislocation distribution function concerning mode
dynamic crack propagation problem under the conditions of unit-step loads and moving increasing loads was studied respectively. Analytical solution representations are attained by the methods of self-similar functions. The problems investigated can be transformed into Riemann-Hilbert problems and their closed solutions are obtained rather simple by this approach.