Analysis of the Identical (in Form) Equations for Some Versions of the Theory of Plates in Polar Coordinates

Abstract

We construct equations of thermoelasticity for transversely isotropic thin plates of constant thickness, i.e., identical (in form) equations for some versions of the theory of plates in polar coordinates. By using these equations, it is possible to deduce equations of some refined theories of elasticity or thermoelasticity for isotropic or transversely isotropic plates, as well as the equations of the classical theory of thermoelasticity of isotropic plates. As an example of application of the constructed equations, we consider a symmetric problem of deformation of the annular plate. For some characteristic types of symmetric mechanical or thermal loads, we present the values of the stress and moment concentration factors near the hole.