Thermo-elastic Analysis Of Functionally Graded Hollow Cylinders Based On State Space Theory

In this paper,the steady and transient thermo-elastic problems are studied for functionally graded hollow cylinders,with material properties varying arbitrarily in the radial direction,subjected to both axisymmetric mechanical and thermal loads.By the equations of heat conductivity,thermo-elasticity,and mechanical equilibrium,together with the heat flux introduced,the state space theory is established for the thermo-elastic analysis of hollow cylinders under the condition of axisymmetric plane strain state.In the steady state,by dividing the hollow cylinder in a series of subshells and discretizing material properties as piece-wise constant functions,the state space solution is derived for the steady thermo-elastic problem of graded hollow cylinders.In the transient state,using division within the space domain and applying difference scheme within the time domain,the governing equations are discretized and the state equations of the system are constituted.The state space solution is obtained for transient thermo-elastic problems of functionally graded hollow cylinders..By using the state space solution for steady state analysis,the distributions of the temperature,radial displacement,radial stress and circumferential stress of a concrete filled steel tube and a functionally graded composite cylinder are presented under steady state condition,respectively.The state space solution is compared to the finite element results.In addition,the effects of material parameters and surface convection coefficient on the temperature field and elastic field of the cylinder are further discussed.With the state space solution for transient state analysis,the distributions of the temperature,radial displacement and radial stress of functionally graded cylinders,functionally graded composite cylinders and composite concrete-filled steel tubular columns are given under transient state condition.The state space solution of the functionally graded hollow cylinder is compared to with the solution in the existing literature.The numerical examples show that the present method is not only correct,but also efficient computationally,which is suitable for hollow cylinders with material properties varying arbitrarily in the radial direction.The distribution of temperature field,displacement field and stress field in cylinder is related to the variation of material parameters along the radial direction and the convection coefficient inside and outside the cylinder.