Generalized Thermoelastic Analysis Of Functionally Graded Cylinders Under Thermal Shock Based On L-S Theory

The Fourier law can satisfy the accuracy requirements for the thermoelastic problems of conventional heat conduction.With the development of science and technology,some unconventional heat conduction problems,such as ultrashort pulse laser heating,rapid cooling,and rapid solidification of metals,have gradually appeared in engineering applications.In such cases,the classical thermoelastic theory will not describe the thermoelastic response of this kind of unconventional heat conduction accurately.Thus,it is necessary to develop the generalized thermoelastic theory based on the non-Fourier law to study the generalized thermoelastic problems.In the present work,the thermoelastic analysis of the functionally graded cylinder with material parameters varying arbitrarily in the radial direction is carried out.The difference between the generalized thermoelastic theory and the classical thermoelastic theory is considered.The main contents include:1)Based on the Fourier law,the energy conservation equation,the thermoelastic equation,and the equilibrium equation under the condition of the axisymmetric plane-strain state,the semi-analytical solution to the classical thermoelastic problem of functionally graded cylinders is obtained by discretizing the governing equations with the division of the cylinder into sub-shells in space domain and the finite difference scheme in time domain.2)Based on the Fourier law,the modified energy conservation equation,the thermoelastic equation,and the equation of motion under the axisymmetric plane-strain state,the semi-analytical solution to the coupled thermoelastic problem of arbitrarily graded cylinders is presented by considering the coupling effect in the energy conservation equation.The influences of the inertia term in the equation of motion,the coupling term in the energy conservation equation,and the distribution of material parameters on the temperature,the radial displacement,and the radial tress of cylinders are analyzed and discussed by applying different temperature boundary conditions,.3)Based on the L-S generalized thermoelasticity theory under the axisymmetric plane-strain state,the semi-analytical solution to the generalized thermoelastic problem of arbitrarily graded cylinders is performed by introducing the thermal relaxation time into the heat conduction equation and considering the coupling effect,together with the thermoelastic equation and the motion equation.The influences ofthe delay and coupling effects on the temperature and the radial stress of cylinders are analyzed and discussed subsequently.In this paper,by combining the state space technique with the finite difference scheme,the solving process seems simple and the computational efficiency is very high in the thermoelastic analysis of cylinders with arbitrarily graded material properties in the radial direction.The obtained solution may be readily applied to several kinds of boundary conditions,and also suitable for some complex nonlinear problems.