Thermal Responses Of Functionally Graded Plates Under Temperature Fields

Functionally gradient materials(FGM)is a new kind of inhomogeneous composite materials that the composition and structure of materials have a continuous gradient.By controlling its components,it can work normally under various special conditions.It has been applied in aerospace,biology,mechanics,photoelectricity,chemistry and other fields,and even has a huge application prospect in many fields of daily life.In the research and development of functionally graded materials,the thermal response of functionally gradient materials under steady state temperature field becomes a hot topic.Within the framework of three-dimensional elasticity theory,this paper investigates the thermal response of FGM plates in which the material can be transversely isotropic and vary along the thickness direction in an arbitrary manner.The generalized Mian and Spencer method is utilized to obtain the thermoelastic solutions of FGM plates under a through-thickness steady temperature field.The work including:(1)Thermoelastic Navier solutions for transversely isotropic functionally graded rectangular plates is obtained.Through numerical examples,the degree of gradient variation,the geometric size of the plate and different temperatures have significant effects on the thermo-elastic response of functionally graded rectangular plates.The change of the in-plane size and the thick-diameter ratio has little effect on the temperature stress.(2)Thermoelastic solutions for functionally graded strips under steady temperature field is derived.The accuracy and validity of this method are checked by comparing with the existing analytical solutions.With the numerical example analysis,the degree of gradient variation,the geometric size of the plate,different temperatures and the boundary conditions have significant effects on the thermo-elastic response of functionally graded strip.There is no difference between the two kinds of clamped boundary on temperature displacement and temperature stress.(3)Thermoelastic solutions for transversely isotropic functionally graded circular plates is obtained.The accuracy and validity of this method are checked by comparing with the existing analytical solutions.With the numerical example analysis,the influences of the degree of gradient variation,the thick-diameter ratio and the boundary conditions have significant effects on the thermo-elastic responses of functionally graded circular plates.There is no difference between the two kinds of clamped boundary on temperature displacement and temperature stress.(4)3D thermoelastic solutions for functionally graded annular plates is obtained.It is found from the parametric study that the distribution pattern of material,the gradient index,boundary conditions,temperatures on the top and bottom surfaces and inner and outer radius ratio have different effects on the FGM annular plates.(5)When the material constant is changed by temperature,the temperature stress and displacement are further affected.Through the study in this paper,the solution range of three-dimensional elastic theory can be expanded from the shape of plate and boundary condition in the thermoelastic problem of functionally graded plates on steady temperature field.It is beneficial to further understand and accurately grasp the mechanical behavior characteristics of these functionally graded plates and provide the best composition and structure gradient distribution for FGM synthesis.Therefore,the present elasticity solutions can also be used a benchmark to access the validity and accuracy of various simplified plate theories or numerical methods which are used in the study of such plates.