Quarterly of Applied Mathematics

A method is developed for the solution of problems of uncoupled dynamic thermoelasticity with arbitrarily prescribed spherically symmetric temperature fields. The technique is based on an integration theorem for hyperbolic initial-value problems, together with the construction of image temperature fields in regions outside the actual body so as to satisfy stress or displacement boundary conditions...

A derivation is presented of the equation governing the pressure in a thin, flat film of ideal gas under isothermal conditions, when the surfaces bounding the film are in relative normal and tangential motion. When tangential motion is absent, the pressure equation reduces to a nonlinear heat equation, which admits of very few closed-form solutions. Various approximation methods are discussed, and...

It is known that the time of traverse of a freely falling body through a straight tunnel connecting any two points of the surface of a uniform spherical planet is isochronous. We show here that if the isochronous property is to hold for any planet with a spherical symmetric density, then the density must be constant. Also it is shown that if the isochronous property is to hold for any uniform sphe...

An interface crack in anisotropic dissimilar materials is considered for the general case where all three fracture modes may be coupled. Analytic solutions are obtained for two commonly used models of interface cracks: (1) the fully open crack; and (2) the Comninou model where, even under farfield tension normal to the crack face, the existence of very small contact zones near the crack tips is pe...

When nuclei of strain approach the interface of two materials, the displacement fields may not be unique and may depend on the direction from which the interface is approached. For example, the displacement fields of a center of dilatation at the interface of two materials are not unique and depend on the direction of approach to the interface. To avoid misunderstanding, it can be stressed that ea...

The analogy between potential theory and classical elasticity suggests an extension of the powerful method of integral equations to the boundary value problems of elasticity. A vector boundary formula relating the boundary values of displacement and traction for the general equilibrated stress state is derived. The vector formula itself is shown to generate integral equations for the solution of t...