A Refined Theory Of Axisymmetric Piezothermoelastic Circular Cylinder With Transversely Isotropic

The circular cylinder is a fundamental component of engineeringstructure, which has been studied deeply by some scholars. The stress anddeforrmation analysis of the elastic circular cylinder are given by them. With the wideapplication of new material, the axisymmetric deformation of the piezothermoelasticcircular cylinder has also become one of the basic research topics on solid mechanics.In this paper, the axisymmetric deformation of the piezothermoelastic circularcylinder with transversely isotropic is analyzed. Its refined theory is given. Moreover,the accurate boundary conditions of the axisymmetric piezoelectric circular cylinderare given. This paper mainly bases on six aspects. In chapter one, according to somethe domestic and international literatures, the research status of this field is described.In chapter two, chapter three and chapter five, the refined theorys of the thermoelasticcircular cylinder with transversely isotropic, piezoelectric circular cylinder withtransversely isotropic and piezothermoelastic circular cylinder with transverselyisotropic are respectively studied, and the decomposed theorem with cylindricalhomogeneous boundary conditions and the refined theory with nonhomogeneousboundary conditions are also respectively derived. In chapter four, the generalboundary conditions of the axisymmetric piezoelectric circular cylinder are analyzed.In chapter six, conclusions are given and some suggestions for further developmentare bring forward.For the thermoelastic circular cylinder, on the basis of the constitutive equations,balance equations and heat conduction equations, without employing any ad hocassumptions, the refined equation of an axisymmetric thermoelastic circular cylinderwith transversely isotropic is obtained, which yields Bessel’s function and the generalsolutions of the anxisymmetric theromelastic circular cylinder. In case of thehomogenous boundary conditions, the refined equation can be decomposed into threeparts: the1-orders equation, the transcendtal equation and the temperature equation,so the problem on deformation of axisymmetric thermoelastic circular cylinder withtransversely isotropic is decomposed into the axially loading problem, the transcendtalproblem and the thermal-stress coupled problem. And the distribution of thedisplacement fields, the stress fields and the temperature fields of the circular cylinderwith radial direction surface loading, axially direction surface loading and thetemperature effect are obtained.For the piezoelectric circular cylinder, on the basis of the constitutive equations,balance equations and Gauss equations, without employing any ad hoc assumptions,the refined equation of an axisymmetric piezoelectric circular cylinder withtransversely isotropic is obtained, which yields Bessel’s function and the generalsolutions of the axisymmetric piezoelectric circular cylinder. And the distribution of the displacement fields, the electric displacement fields, the stress fields and theelectric potential fields of the circular cylinder with radial direction surface loading,axially direction surface loading and the piezoelectric effect are obtained. By usingthe reciprocal theorem and the general solutions of piezoelectric elastic mechanics,the general boundary conditions of the axisymmetric circular cylinder are derived.Finally, the results of the piezoelectric circular cylinder are simplified to thetransverse isotropic material and isotropic material. Moreover, the mixed boundaryconditions of the axisymmetric elastic circular cylinder with isotropic are provedcorrect.For the piezothermoelastic circular cylinder, on the basis of the constitutiveequations, balance equations, Gauss equations and heat conduction equations, withoutemploying any ad hoc assumptions, the refined equation of an axisymmetricpiezoelectric thermoelastic circular cylinder with transversely isotropic is obtained,which yields Bessel’s function and the general solutions of the axisymmetricpiezoelectric thermoelastic circular cylinder. And the displacement fields, the electricdisplacement fields, the electric potential fields, the stress fields and the temperaturefields of the circular cylinder with temperature effect are obtained.