The writer’s general equations for the mechanics of continua under initial stress are applied to the formulation of a rigorous theory of stability of multilayered elastic media in a state of finite initial strain. The medium is assumed incompressible. It is either isotropic or anisotropic. The problem is analyzed in the context of the writer’s earlier discussions showing the existence of intern...

The paper deals with the two-dimensional exterior boundary value problems of the steady-state oscillation theory for anisotropic elastic bodies. By means of the limiting absorption principle the fundamental matrix of the oscillation equations is constructed and the generalized radiation conditions of Sommerfeld–Kupradze type are established. Uniqueness theorems of the basic and mixed type bound...

Influence of isotropic and anisotropic properties of membrane constituents (nanodomains) on formation of tubular membrane structures in two-component vesicle is numerically investigated by minimization of the free energy functional based on the deviatoric-elasticity model of the membrane. It is shown that the lateral redistribution and segregation of membrane components may induce substantial c...

We study thickness-shear and thickness-twist vibrations of a finite, monolithic, AT-cut quartz plate crystal filter with two pairs of electrodes. The equations of anisotropic elasticity are used with the omission of the small elastic constant c(56). An analytical solution is obtained using Fourier series from which the resonant frequencies, mode shapes, and the vibration confinement due to the ...

This paper is concerned with a problem in the theory of elasticity for a thin composite plate. The principal terms are constructed for the asymptotics of the solution, with only local periodicity of the elastic moduli of the material and the shape of the plate assumed. The asymptotic expression is justified with the help of a weighted anisotropic Korn’s inequality, which is proved by means of t...

Three-dimensional mathematical problems of the elasticity theory of anisotropic piecewise homogeneous bodies are discussed. A mixed type boundary contact problem is considered where on one part of the interface, rigid contact conditions are given (jumps of the displacement and the stress vectors are known), while on the remaining part screen or crack type boundary conditions are imposed. The in...

A. The three-dimensional spectral elasticity problem is studied in an anisotropic and inhomogeneous solid with small defects, i.e., inclusions, voids, and microcracks. Asymptotics of eigenfrequencies and the corresponding elastic eigenmodes are constructed and justified. New technicalities of the asymptotic analysis are related to variable coefficients of differential operators, vectoria...

Smectics in strained aerogel exhibit two new glassy phases. The strain both ensures the stability of these phases and determines their nature. One type of strain induces an “XY Bragg glass,” while the other creates a novel, triaxially anisotropic “m � 1 Bragg glass.” The latter exhibits anomalous elasticity, characterized by exponents that we calculate to high precision. We predict the phase di...

Boundary contact problems of statics of the moment (couplestress) theory of elasticity are studied in the case of a unilateral contact of two elastic anisotropic nonhomogeneous media. A problem, in which during deformation the contact zone lies within the boundaries of some domain, and a problem, in which the contact zone can extend, are given a separate treatment. Concrete problems suitable fo...

An atomic model of dislocations in face centered cubic crystals with a twoatom basis is proposed. This model has the standard cubic anisotropic elasticity as its continuum limit, and its main ingredients are the elastic stiffness constants and a dimensionless periodic function that restores the translation invariance of the crystal and influences the dislocation size. Possible applications incl...