Solution of the axisymmetric problem of thermoelasticity for a circular plate with due consideration for the connectivity of thermoelastic fields

Abstract

A new closed solution of the coupled axisymmetric problem of thermoelasticity is constructed for a rigidly fixed circular isotropic plate in the case temperature variations on its front surfaces. It is known that any change in volume of the body affects the temperature field of the structure. Taking this fact into account causes serious mathematical difficulties, and ignoring this leads to significant errors in calculating the stress-strain state of the structure. Most of the previously considered works were solved in such a formulation that the physicomechanical characteristics of the material were considered independent of temperature. However, for a comprehensive analysis of the strength characteristics, it is necessary to take connectivity of thermoelastic fields into account. In this work, the proposed calculation method assumes physical and mechanical characteristics depending on temperature and makes it possible to analyze the effect of temperature load on the temperature field and the stress-strain state of the structure. On the basis of the constructed solution algorithm, specific software has been developed that allows one to analyze the influence of the coupling of thermoelastic fields. The calculated ratios were obtained using the method of finite biorthogonal transformations and are valid for an external temperature effect that is arbitrary in time (boundary conditions for thermal conductivity of the 1st kind). Numerical analysis of the calculation results shows that for a given external temperature effect, the stiffness of an elastic system has a significant effect on its thermoelastic field. At the same time, proper consideration of the rate of volume change of the plate leads to decrease in temperature and mechanical stresses during heating of the plate. In the future, at a constant temperature regime, the connectivity of the fields is not observed. The developed calculation algorithm finds its application in the design of enclosing structures in the form of single-layer and multi-layer plates.