Functionally gradient isotropic cylindrical shell locally heated by heat sources

Abstract

The stress-strain state of a functionally gradient isotropic thin circular cylindrical shell under local heating by a flat heat source has been investigated. For this purpose, a mathematical model of the classical theory of inhomogeneous shells has been used. A two-dimensional heat equation is derived under the condition of a linear dependence of the temperature on the transverse coordinate. The solutions of the non-stationary heat conduction problem and the quasi-static thermoelasticity problem for a finite closed cylindrical pivotally supported shell have been obtained by means of methods of Fourier and Laplace integral transforms. Numerical results are presented for the metal-ceramic composite used to restore the integrity of human tooth crowns.

Quasi-static problem of thermoelasticity for layered shallow cylindrical shells of irregular structure

“…To investigate the ther-moelastic state of the shell, a two-dimensional mathematical shear model of the first order (a model of Timoshenko type) is employed. The model is based on the assumption of linear dependence of the tangential components of the displacement vector and temperature on the transverse coordinate [14]. For thermal stress problems, this model consists of two independent systems of equations, i.e.…”

“…A more detailed review of various models and methods is given in [1,2]. In the paper [14], local heating by heat sources of a functionally gradient isotropic cylindrical shell is considered. In the paper [15], the stress-strain state of a layered cylindrical shell under local convective heating is examined.…”

Temperature field of metal structures of transport facilities with a thin protective coating

“…These papers mainly deal with the heating of the solid through the coating, with the issues of head conduction over the coating and exchange of heat with the solid and the ambient environment not being elaborated on. Papers [20][21][22] present temperature distributions in piecewise inhomogeneous solids and estimate their impact on the strength of structural elements. The study of the temperature field in a three-layer model (defective ferroconcrete pipe reinforced with a metal corrugated structure) [20] has established the nonuniformity of temperature distribution across the layers, which leads to a contact effect defined by non-ideal conditions of heat exchange at the junction between the layers.…”

“…Papers [20][21][22] present temperature distributions in piecewise inhomogeneous solids and estimate their impact on the strength of structural elements. The study of the temperature field in a three-layer model (defective ferroconcrete pipe reinforced with a metal corrugated structure) [20] has established the nonuniformity of temperature distribution across the layers, which leads to a contact effect defined by non-ideal conditions of heat exchange at the junction between the layers. Similar calculation outcomes of temperature fields have been achieved in the studies on multilayered bridge structures [21,22].…”

Stressed and strained state of layered cylindrical shell under local convective heating

“…In the literature [1], there are studies of the thermal stressed state of an isotropic cylindrical shell made of a functional-gradient material under local thermal heating. The temperature regime of the dental crown, which is modeled by a cylindrical shell made of isotropic functional-gradient cermets, was also studied in [2]. In addition, layered cylindrical shells are widely used in many branches of modern technology, in particular in aerospace construction, to increase the strength and rigidity of structures, as well as to protect them from low or high temperatures.…”