Modeling of Thermoelastic Asymmetric State of a Transversely Isotropic Body of Revolution

The paper proposes a technique for constructing the stress-strain state of transversely isotropic bodies of revolution under the action of a given temperature field changing in a cylindrical coordinate system according to a cyclic law. The temperature field is assumed to be steady and known throughout the body; there are no heat sources inside the body. The task at hand requires the use of definitions of the boundary state method. The method is based on the space of internal states., which includes displacements of internal points of the region, deformations, stresses, and temperature functions. The integral superposition method is used to establish a relationship between the spatial stress-strain state of an elastic transversely isotropic body of revolution and some auxiliary two-dimensional states whose components depend on two coordinates. The general solution of the plane thermoelastostatic problem for a transversely isotropic material is used as such auxiliary states. A set of plane auxiliary states is formed, and a set of spatial states is constructed using the transition formulas. The set of such states forms a finite-dimensional basis of internal states, according to which, after orthogonalization, the sought state is expanded into Fourier series with identical coefficients. The search for an elastic state is reduced to solving quadratures. The problem of thermoelasticity theory for a transversely isotropic circular cylinder is solved from the action of a temperature field specified by various cyclic laws (sine and cosine). An analysis of the convergence of the series and an estimate of the accuracy of the solution in graphical form are presented.