Research On Thermal Post-buckling Of FGM Beams And Plates Subjected To Transverse Constraints

Functionally graded materials (FGM) are widely applied in modern engineering structures, especially in high temperature environment, because they can eliminate the interfaces exiting in composite materials and reduce the thermal stress concentration in the high temterature gradient enviromemt. The researches on the mechanical behaviors of FGM structures under thermal loadings have been a new research area in solid mechanics. Constrained buckling, which is also called confined buckling, means that the bucking configurations of structures can not evolve freely due to the existence of the constraint. This type of problems also has many applications in the practical engineering and is a classic problem of solid mechanics, In this thesis, thermal post-buckling response of functionally graded beams and plates subjected to transverse constraints is studied including the following parts:1. Thermal post-buckling of FGM circular plates subjected to transverse point-constraint.The FGM circular plates with immovably clamped edges are bilaterally constrained by rigid point-constraints at the center with clearance. It is assumed that material properties and non-uniform temperature rise change only through the thickness direction. The plates will go into thermal post-buckling when the radial pressure caused by temperature rise exceeds the critical value. The focus of this thesis is the changes of thermal post-bucking responses during the contact. Firstly, based on von Karman’s nonlinear thin plate theory, governing equations of axisymmetric thermal post-buckling of constrained FGM circular plates are derived, which including parameter of thermal loading are nonlinear ordinary differential equations in terms of the displacements of the middle plane, with boundary conditions changing when the plates contact the point-constraints. Then, by using the shooting method, thermal post-buckling responses of the FGM circular plates are obtained before and after it contact the point-space constraint. The changes in the characteristics of the deformation and the internal forces of FGM plates are discussed. The effects of gradients of material properties and non-uniform temperature rise parameters on the thermal post-buckling behaviors of the plates are also examined. The equilibrium configurations and equilibrium paths are given. The results according to the linear mixture rule and Mori-Tanaka model are compared. As an example, the behaviors of the circular/annular plates with a centric rigid mass are analyzed. The effect of the size of the centric rigid circular plate on the constrained post-buckling response is studied for the plates with both immovably clamped and simply supported edges. 2. Thermal post-buckling of FGM Timoshenko beams on nonlinear elastic foundations.Based on the accurate geometrically nonlinear theory for Timoshenko beams, thermal post-buckling of FGM Timoshenko beams on nonlinear elastic foundations is studied. Governing equations of this problem consist of a two-point boundary value problem of nonlinear ordinary differential equations including seven basic unknown functions with two types of boundary conditions, namely; immovably clamped and simply supported ends. The numerical solutions are arrived at by the shooting method. The critical buckling temperatures vary with the foundation stiffness and the corresponding critical buckling modes transit with the increasing foundation stiffness. Stability boundaries, or critical load curves, are presented for different values of the power exponent and boundary conditions. Post-buckling equilibrium configurations and equilibrium paths are demonstrated for different values of nonlinear elastic foundation parameters, the power exponent, boundary conditions, non-uniform temperature rise, and slenderness ratio. The results of Timoshenko beams are compared with Euler-Bernoulli beams to examine the effect of the shearing deformation. The results of uniform beams are compared with those in the literature, which show a good agreement.3. Thermal post-buckling of FGM beams subjected to transverse point-constraint.On the basis of the aforementioned study, governing equations for large post-buckling deformation of FGM beams with point-constraint are formulated. One dimensional steady state temperature field is considered. It is assumed that the material properties of the beam vary continuously as a power function of the thickness coordinate and the point-constraint is at the side of the middle point of the beam and the space value is in the range of thermal post-buckling deformation. The derived governing equations are nonlinear ordinary differential equations including seven basic unknown functions, with boundary conditions changing due to the appearance of point constraint force. By using shooting method to solve the nonlinear bounadary value promlem numerically, thermal post-buckling responses of the FGM beam are obtained when it contacts the point constraint. Curves of the point constraint force changing with the thermal load are plotted. The effects of parameters of the gradients of material properties, non-uniform temperature rise, slenderness ratio and the space value on the thermal post-buckling behaviors of FGM beams are also examined.