A THEORETICAL SOLUTION OF CYLINDRICALLY ISOTROPIC CYLINDRICAL TUBE FOR AXISYMMETRIC PLANE STRAIN DYNAMIC THERMOELASTIC PROBLEM

A dynamic thermoelastic solution of a cylindrically isotropic cylindrical tube or solid cylinderwith axisymmetric plane deformations is developed.Since there exist thermal boundary conditions and trac-tions on the two surfaces of a cylindrical tube,the problem under consideration is with inhomogeneous bound-ary conditions.Therefore we introduce a special function to transform the inhomogeneous boundary conditionsto homogeneous ones for an unknown function.Then by using the method of separation of variables,the un-known function can be expressed as the multiplication series of Bessel functions and unknown time functions.Thirdly,by virtue of the orthogonal properties of Bessel functions,the equations about these unknown timefunctions are derived and the solutions are obtained.Finally,the displacement is obtained by adding the twoparts mentioned above.By means of the present method,integral transform can be avoided.It is suitable forarbitrary thermal loads and mechanical loads.Numerical results are also presented for thermal shocked,cy-lindrically isotropic cylindrical tube and solid cylinder.