Thermoelastic State of a Piecewise Inhomogeneous Orthotropic Thermosensitive Cylinder

Abstract

We determine the thermoelastic state caused by a plane axisymmetric temperature field and surface loads in a multilayer hollow orthotropic cylinder with regard for the dependences of physical and mechanical characteristics on the coordinates and temperature. The thermoelasticity problem is reduced to solving systems of integral-algebraic equations for radial displacements. These systems are obtained from the integral representation of the solution of the corresponding problem for an ordinary differential equation with generalized derivatives. In this case, we use the Green function of the elasticity problem for a multilayered orthotropic cylinder with constant physical and mechanical characteristics of its layers. The solutions of the obtained systems are found by the method of successive approximations (restricted to the first approximation). The numerical investigations performed for a three-layer orthotropic cylinder with temperature-dependent physical and mechanical characteristics of layers reveal high accuracy of evaluation of the displacements and stresses.