__.________________.______ Introduction _ _ _ ___ _ _ .. Principal features of the theory of elasticity Stress __________._____.__.___ ___ Types of stress. ______________.__.. Variation with orientation of stress at a point Stresses in static equilibrium _ Strain . ... _.... _........ . _...._.. ......... Definitions and notation .. . Stress-strain relations in the elastic state. Condition of c...

Monge-Ampère equations of the form, uxxuyy − u 2 xy = F (u, ux, uy) arise in many areas of fluid and solid mechanics. Here it is shown that in the special case F = u y f(u, ux/uy), where f denotes an arbitrary function, the Monge-Ampère equation can be linearized by using a sequence of Ampère, point, Legendre and rotation transformations. This linearization is a generalization of three examples...

The theory of Cosserat elasticity (also known as micropolar or asymmetric elasticity) was introduced by Cosserat brothers [1] and further developed by Eringen [2] to model the mechanical behavior of materials for which the microstructure is significant (see [3] for a review of works in this area and an extensive bibliography). The theory was intended to eliminate discrepancies between the class...

In this paper, we are interested with the spectral study of an operator given by an elastic topographical waveguide, a deformed half-space, of which the cross-section is a local perturbation of a homogeneous half-plane. We look for guided waves propagating more rapidly than Rayleigh waves (which mathematically would correspond to embedded eigenvalues) and prove that there are no guided waves pr...

The contact problem of elastic bodies, each consisting of a finite layer of uniform thickness rigidly adhering to a half-plane, is investigated on the basis of the two-dimensional theory of elasticity. The materials of the layer and the half-plane in the contact body are isotropic and homogeneous, yet each of them may have distinct elastic properties. The mixed boundary value problem is reduced...

For the Generalized Plane Stress (GPS) problem in linear elasticity, we obtain an optimal stability estimate of logarithmic type for inverse determining smooth cavities inside a thin isotropic cylinder from single boundary measurement traction and displacement. The result is obtained by reformulating GPS as Kirchhoff–Love plate-like terms Airy function, using strong unique continuation at plate...