Nonlinear Bending And Post-buckling Of Functionally Graded Material Structures

Nonlinear bending and post-buckling problems of functionally graded beams under mechanical load were investigated respectively in this paper.and nonlinear bending and post-buckling of functionally graded circular plates under mechanical and thermal loads.In this paper,The closed form exact solution of functionally graded beam is obtained.For the functionally graded circular plate,The numerical solution is obtained by shooting method.1)The nonlinear mechanical behavior of functionally graded material beams was studied by analytical method.Based on a the shear deformation theory(FBT),And exact solution were obtained.The nonlinear relation between beam deformation and external load is given explicitly.Based on this solution,the nonlinear mechanical behavior of functionally graded materials(FGM)beams is affected by the properties of graded materials,external loads,transverse shear deformation and boundary conditions.In the analysis,it is assumed that the properties of functionally graded materials only change along with the thickness direction of beam.2)Nonlinear mechanical behavior of functionally graded circular plates is investigated numerically.The bending and post-buckling problems of functionally graded circular plates under thermal and mechanical loads are considered.Based on the theory of higher order shear deformation,the equilibrium equation of functionally gradient material circular plate is derived by energy method.The problem is reduced to the classical theory in the analysis.In order to obtain its numerical solution,the shooting method is applied.The effects of material parameters ? boundary conditions and external loads on the bending and post-buckling of the plate are investigated.The results show that both the boundary clamping and the boundary simply supported circular plate will produce branch buckling under in-plane load,but the boundary simply supported circular plate will not produce branch buckling under the thermal load,and the boundary clamped circular plate will produce typical branch buckling.