Study On Thermal Buckling Of Shear Deformable Functionally Graded Circular Plates By Tymplectic Method

Functionally graded materials(FGM)are new non-uniform composites,their composition or structure vary continuously along certain directions.They not only avoid or reduce stress concentration,but also have excellent heat and crack resistance in extreme thermal environment,so they have been widely used in various engineering structures in recent yearsThe research on mechanical behaviors of functionally graded materials under external loads is one of the hot spots in the field of solid mechanics.In this thesis,the symplectic method is used to study the axisymmetric thermal buckling behavior of shear deformable FGM circular plate.Based on the first-order shear deformation theory and the concept of physical mid-plane,the basic equations are established.And then,the symplectic method is used to establish the canonical equation of shear deformable FGM circular plate with the fixed boundary condition and simply supported boundary condition in Hamilton system.At the same time,the symplectic eigensolutions and eigenvalues of the canonical equation are corresponding to buckling modes and buckling loads respectively.By analytic solving the canonical equation exactly,the buckling modes of FGM plate are obtained,then the critical buckling loads are obtained.Finally,the critical buckling temperature rise is obtained by inverse solutionIn this study,the solving processes are established in which the symplectic method is used to solve the thermal buckling problem of shear deformable FGM circular plates in Hamilton system,and the complete buckling mode space is given The results show that the critical buckling temperature rise of shear deformable FGM circular plates increases along with the increase of volume fraction index.The diameter-thickness ratio of the structure,boundary condition and the temperature ratio of the two surfaces also have great influence on the critical buckling temperature rise.