Abstract:
This paper presents a method for determining the stress-strain state of transversally isotropic bodies of rotation in a steady temperature field varying according to the cyclic law of cosine and sine in a cylindrical coordinate system.
The problem is solved in terms of the definitions of the boundary conditions method. This method is based on the space of internal states, which includes displacements, deformations, stresses, and temperature functions. Using the method of integral superpositions, the relation between the spatial stress-strain state of an elastic transversally isotropic body of rotation and some auxiliary two-dimensional states is determined. The auxiliary states are presented as a general solution to the plane thermoelastostatic problem for a transversely isotropic material. This general solution is used to construct the basis of internal states. After orthogonalization of the basis, the desired state is expanded into a Fourier series with identical coefficients in the form of quadratures. The problem of the theory of thermoelasticity for a transversally isotropic circular cylinder in a temperature field specified according to a harmonic law is solved.
Keywords:thermoelasticity, transversely isotropic materials, state space, non-axisymmetric deformation.
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