On basic problems for elastic prismatic shells with microtemperatures

Abstract

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.

An a priori error analysis of a Lord–Shulman poro-thermoelastic problem with microtemperatures

“…Remark 1 We note that additional conditions (17) are introduced to simplify the calculations in the following proof. It could be adapted to use conditions (1).…”

“…One possible effect for the microstructure is the so-called microtemperatures [5][6][7][8]. In fact, many studies have been developed to understand the qualitative behavior of this kind of materials [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. However, almost whenever microtemperatures effects we find again a parabolic system and therefore these effects also propagate with unbounded speed and we have another model where the causality principle is violated.…”

Analyticity of solutions to thermo‐elastic‐plastic flow problem with microtemperatures

“…Clearly, neither so called microtemperature vector nor its components are temperatures, they represent the variation of the temperature within a microelement ω [22].…”

“…The vectors (Θ 1 , Θ 2 , Θ 3 ) and (𝑇 1 , 𝑇 2 , 𝑇 3 ) are called the microtemperature vectors by Riha [32] and Ieşan and Quintanilla [19,20], respectively. Clearly, neither so called microtemperature vector nor its components are temperatures, they represent the variation of the temperature within a microelement 𝜔 [23]. The effect of microtemperature has been studied first on thermoelastic continua [6,8,9,12,[19][20][21][22]27].…”

Explicit solutions of the BVPs of the theory of thermoelasticity for an elastic circle with voids and microtemperatures

“…Many problems are investigated for elastic materials with microstructures by several researchers (see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] and references given there).…”