Axisymmetric thermo-elasticity field in a functionally graded circular plate of transversely isotropic material

Abstract

This paper presents a set of axisymmetric analytical solutions of the thermo-elasticity field induced by the external thermal load, in a heterogeneous circular plate. The plate can be either simply supported or clamped, and the properties of the transversely isotropic material are assumed to be functions of the thickness coordinate. Three typical types of thermal boundary conditions are considered and the corresponding temperature fields are determined. A direct displacement method is used to solve the governing equations for the elastic field in plate. The displacement functions pertinent to the current problem are solved by a step-by-step procedure of integration. The corresponding integral constants are determined by using the cylindrical boundary conditions in the Saint-Venant’s sense. In the present solutions, all of the material coefficients can vary independently and continuously along the thickness direction. Numerical calculations are performed to validate the present solutions and to show their applications to a heterogeneous model. The influence of the material heterogeneity is finally addressed. Since no ad hoc hypotheses on the elastic deformations of the plate are introduced, the present solution can be a nature benchmark to various plate theories and numerical codes.

3D thermo-mechanical bending solution of functionally graded graphene reinforced circular and annular plates

“…Our analytical solutions are compared with those reported by Li et al [36]. The material properties () Pz such as Table 1, and  is the gradient index characterizing the material inhomogeneity.…”

Three-dimensional magneto-elastic analysis of asymmetric variable thickness porous FGM circular plates with non-uniform tractions and Kerr elastic foundations

“…Although present procedure may be used for a general loading condition, the following distributions of the normal ( ) and shear ( ) tractions are adopted: (5) where 0 p and 0 q are values of the normal and shear tractions at the central point of the top surface, and 1 p , 2 p , 1 q , and 2 q parameters describing variations of the normal and shear tractions, respectively. …”

“…Engineering analysis models of many structural elements may be considered directly or through employing some geometric simplifications (e.g., omitting the gear teeth of a flywheel) as homogeneous, heterogeneous [1,2] or even intelligent [3] circular plates. In many applications, these plates may be supported by non-uniform elastic foundations (e.g., in the clutch systems) or subjected to asymmetric normal and shear tractions (e.g., in disc brakes).…”

Thermo-elastic analysis of functionally graded circular plates resting on a gradient hybrid foundation

“…Based on the state-space formalism, Wen et al [24] presented a three dimensional solution for dynamic analysis of orthotropic functionally graded rectangular plate with simply supported edges under static and dynamic loads. Assuming the material properties to vary with an exponential law in transverse direction, Li et al [25] investigated the axisymmetric thermo-elastic field in a FG circular plate under thermal load and they presented an analytical solution to solve the governing equations using direct displacement method. Nie and Zhong [26] analyzed the three-dimensional free and forced vibration of functionally graded circular plate with various boundary conditions based on three dimensional elasticity theory by using semi-analytical method (State space and one dimensional differential quadrature rule).…”