Axisymmetric Problem Of Piezothermoelasticy

The research on axisymmetric classical problems for thermoelastic and piezothermoelastic structures not only can provide the analytical solution for engineering applications but also acts as the necessary benchmarks for various theories of thin plates and calculation methods. For this object, A series of axisymmetric classical problems for thermoelastic and piezothermoelastic structures under coupled loadings are studied in this thesis and the corresponding coupled field are obtained.For thermoelastic stucture, the general solution of transversely isotropic thermoelastic materials, which is expressed in three harmonic functions, are rewritten into a non-dimensional form. Based on the non-dimensional general solution, the coupled field in hollow circular plates under uniform axial and radial tension, identical temperature increment and pure bending, simply-supported circular plates subjected to uniformly distributed loads can be obtained by virtue of three constructed harmonic functions. These solutions all can be degenerated to the corresponding ones of solid circular plate. At last, the numerical results of coupled fields in hollow circular plate are presented in details.For piezothermoelasticity, the general solution of transversely isotropic piezothermoelastic materials, which is expressed in four harmonic functions, are rewritten into a non-dimensional form. Based on the non-dimensional general solution, the coupled field in hollow circular plates under uniform axial and radial tension, uniform electric displacements, identical temperature increment, pure bending, simply-supported circular plates subjected to uniformly distributed loads can be obtained by virtue of four constructed harmonic functions. This solution can be degenerated to the corresponding ones of solid circular plate. At last, the numerical results of coupled fields in cadmium selenide hollow circular plate, including displacements, stresses, electric potential and electric displacements, are presented in details. And the displacement, stress and temperature increament induced by thermal-mechanical loadings are compared with those obtained for the same material where the piezoelectric and pyroelectric effects are ignored.