The problem of a point dislocation interacting with an elliptical hole located on a bimaterial interface is examined. Analytical solution is obtained by employing the techniques of complex variables and conformal mapping. A rational mapping function is used to map a half-plane with a semielliptical notch onto a unit circle. In the first part of this paper, complex potentials for the bimaterial system with an elliptical hole on the interface is derived when a point dislocation is present in the upper half-plane without loss of generality. The solution derived can be used as Green’s function to study internal cracks interacting with an elliptical interfacial cavity.

This paper discusses the interaction of an interfacial cavity/crack with an internal crack in a bimaterial plane under uniform loading at infinity. The point dislocation solution is used to simulate internal crack by using the distributed dislocation technique. The resulting singular integral equation is solved numerically and the stress intensity factor variations are plotted for some cases of internal crack interacting with interfacial cavity/crack.

A finite element method, which is based on the variational inequality approach, is introduced to calculate the oil film pressure distribution of a journal bearing. The cavitation zone is found by solving a linear complementary problem. By means of this approach a perturbation can be performed directly on the finite element equation and, consequently, the Jacobian matrices of the oil film forces are obtained concisely. The equilibrium position of the bearing at a given static load is found by the Newton-Raphson method and, as byproducts, dynamic coefficients are obtained simultaneously without any extra computing time. Numerical examples show that the method works satisfactorily. [S0742-4787(00)02302-X]

An exact elasticity solution is developed for a radially nonhomogeneous hollow circular cylinder of exponential Young’s modulus and constant Poisson’s ratio. In the solution, the cylinder is first approximated by a piecewise homogeneous one, of the same overall dimension and composed of perfectly bonded constituent homogeneous hollow circular cylinders. For each of the constituent cylinders, the solution can be obtained from the theory of homogeneous elasticity in terms of several constants. In the limit case when the number of the constituent cylinders becomes unboundedly large and their thickness tends to infinitesimally small, the piecewise homogeneous hollow circular cylinder reverts to the original nonhomogeneous one, and the constants contained in the solutions for the constituent cylinders turn into continuous functions. These functions, governed by some systems of first-order ordinary differential equations with variable coefficients, stand for the exact elasticity solution of the nonhomogeneous cylinder. Rigorous and explicit solutions are worked out for the ordinary differential equation systems, and used to generate a number of numerical results. It is indicated in the discussion that the developed method can also be applied to hollow circular cylinders with arbitrary, continuous radial nonhomogeneity.

This paper deals with dynamical systems including spatially localized nonlinear substructures. In these cases, the differential equations of motion consist of the coupled linear and nonlinear subsets. According to the feature of such systems, a modal transformation is used, by means which the number of degrees of freedom of the linear subset is reduced significantly and the localized feature of the nonlinear subset still remains. In accordance with this reduced model, a modified Newmark method that is unconditionally stable is proposed to integrate the responses of the reduced system. The advantage of this method is that the nonlinear iterations only need to be executed on localized nonlinear parts of the system equations. The numerical schemes of this study are applied to a large-order flexible rotor with two elliptical bearing supports. The periodic solutions and long term behaviors of the system are investigated numerically, which reveals many interesting phenomena.

Harmonic and transient torsional responses of a laminated circular disc (or a laminated circular cylinder), caused by torques applied on both ends of the disc, is investigated with use of a continuous analysis. By the analysis, the difficulty brought about by multitudinous reflections and transmissions, taking place at the interfaces of the laminated medium, can be bypassed. The continuous analysis is based on the recognition that stresses at periodic locations in a periodic structure must vary smoothly; therefore these discrete values as a whole approximately form a continuous function, which can be treated analytically. Via the analysis, it is concluded that the real, heterogeneous laminated disc can be modelled into a homogeneous, effective one. The corresponding effective solution provides accurate or exact values of displacements and stresses at the periodic locations of the laminated disc. The density of the effective disc is not a geometric-material constant; it depends on, among others, the frequency and other vibration parameters in the problem. Numerical results are given to validate the analysis.

A circular rigid punch with friction is assumed to contact with a half-plane with one end sliding on the half-plane and another end with a sharp corner. The contact length is determined by satisfying the finite stress condition at the sliding end of the punch. The crack is initiated near the end with a sharp corner where infinite stresses exist. Coulomb’s frictional force is supposed to act on the contact region. The cracked half-plane is mapped into a unit circle by using a rational mapping function, and the problem is transformed into a standard Riemann-Hilbert problem, which is solved by introducing a Plemelj function. The contact length, the stress intensity factors of the crack, and the resultant moment about the origin of the coordinates on the contact region are calculated for different frictional coefficients, Poisson’s ratios of the half-plane, crack lengths, and distances from the crack to the punch, respectively. The stress distributions on the contact region are also shown.

The problem of thin plate bending of two bonded half-planes with an elliptical hole on the interface and interface cracks on its both sides is presented. A uniformly distributed bending moment applied at the remote ends of the interface is considered. The complex stress functions approach together with the rational mapping function technique are used in the analysis. The solution is obtained in closed form. Distributions of bending and torsional moments, the stress concentration factor as well as the stress intensity factor, are given for all possible dimensions of the elliptical hole, various material constants, and rigidity ratios.

In this paper the properties of the eigenfunction expansion form in the interface crack problem of plane elasticity are discussed in detail. After using the Betti’s reciprocal theorem to the cracked dissimilar bonded body, several path-independent integrals are obtained. All the coefficients in the eigenfunction expansion form, including the K 1 and K 2 values, and the J-integral can be related to corresponding path independent integrals. Possibility for formulating the weight function is also suggested.

The second mixed boundary value problem is solved by the classical theory of thin plate bending. The mixed boundary consists of a boundary ( M ) on which one respective component of external force and deflective angle are given, and on the remaining boundary the external forces are given. The boundary ( M ) is straight and the remaining boundary is arbitrary configuration. A closed solution is obtained. Complex stress functions and a rational mapping function are used. A half-plane with a crack is analyzed under a concentrated torsional moment. Stress distributions before and after the crack initiation, and stress intensity factors are obtained for from short to long cracks and for some Poisson’s ratio.

A problem of two bonded, dissimilar half-planes containing an elliptical hole on the interface is solved. The external load is uniform tension parallel to the interface. A rational mapping function and complex stress functions are used and an analytical solution is obtained. Stress distributions are shown. Stress concentration factors are also obtained for arbitrary lengths of debonding and for several material constants. In addition, an approximate expression of the stress concentration factor is given for elliptical holes and the accuracy is investigated.

A general solution of the mixed boundary value problem with displacements and external forces given on the boundary is obtained for an infinite plate with a hole subjected to uniform heat flux. Complex stress functions, a rational mapping function, and the dislocation method are used for the analysis. The stress function is obtained in a closed form and the first derivative is given by such a form that does not contain the integral term. The mapping function is represented in the form of a sum of fractional expressions. A problem is solved for a crack initiating from a point of a circular hole on which the displacement is rigidly stiffened. Stress distributions and stress intensity factors are calculated.