The present paper is devoted to the two-dimensional version of statics of the linear theory of elastic materials with inner structure whose particles, in addition to the classical displacement and temperature fields, possess microtemperatures. Some results of the classical theories of elasticity and thermoelasticity are generalized. The Green's formulas in the case under consideration are obtained, basic boundary value problems are formulated, and uniqueness theorems are proved. The fundamental matrix of solutions for the governing system of the model and the corresponding single and double layer thermoelastopotentials are constructed. Properties of the potentials are studied. Applying the potential method, for the first and second boundary value problems, we construct singular integral equations of the second kind and prove the existence theorems of solutions for the bounded and unbounded domains. This paper describes the use of the L A T E X 2 " mmaauth.cls class file for setting papers for Mathematical Methods in the Applied Sciences.

Our goal was to consider the two-dimensional version of the full coupled linear equilibrium theory of elasticity for materials with double porosity and to construct explicitly the solutions of BVPs, in the form of absolutely and uniformly convergent series that is useful in engineering practice. In this paper, the Neumanntype BVPs of statics for an elastic circle and for a plane with circular hole are considered. The uniqueness theorems of the considered boundary value problems are proved.

This paper is concerned with the linear theory of thermoelasticity with microtemperatures for homogeneous and isotropic solids. We consider the problem of equilibrium of a spherical ring and establish the solution of the Dirichlet boundary value problem (BVP).

The main goal of this paper is to consider the Dirichlet type boundary value problem (BVP) of the fully coupled equilibrium theory of elasticity for solids with double porosity and to construct explicitly the solution of BVP for a spherical layer in the form of absolutely and uniformly convergent series.

In the present paper on the basis of the linear theory of thermoelasticity of homogeneous isotropic bodies with microtemperatures the zeroth order approximation of hierarchical models of elastic prismatic shells with microtemperatures in the case of constant thickness (but, in general, with bent face surfaces) is considered. The existence and uniqueness of solutions of basic boundary value problems when the projections of the bodies under consideration are bounded and unbounded domains with closed contours are established. The ways of solving boundary value problems in explicit forms and of their numerical solution are indicated.