Stability Analysis Of Functionally Graded Material Circular Plates/Beams Considering Pre-buckling Coupling Deformation

Due to the inhomogeneity of FGM Structure,there will be the stretch-bending coupling effect.This effect will lead to pre-buckling coupling deformation under certain conditions,that is,deflection will occur as long as in-plane loads is applied.In this paper,the nonlinear deformation of functionally graded circular plates and beams under mechanical loads and thermal loads is studied,as well as the stability considering the pre-buckling coupling deformation.Firstly,assuming that the material properties only change with the thickness location,based on the classical plate/beam theory,the equilibrium equations and the buckling control equations including the effect of the pre-buckling coupling deformation,of functionally graded circular plates and beams,are derived by using the energy principle.Finally,shooting method is used to solve the equations.The main contents of this paper include the following aspects:1.Nonlinear deformation of FGM circular plates.Based on the classical plate theory,the governing equations of FGM circular plate under mechanical loads and thermal loads are derived.The shooting method is used to solve the problem.The loads deflection relations under different temperature ratios are obtained,the deformation of simply supported FGM circular plates with and without temperature dependence of material properties is compared,the influence of temperature dependence of material properties on the nonlinear deformation of FGM circular plates is analyzed.2.Buckling of FGM circular plates.Due to the stretch-bending coupling effect,there exists the pre-buckling coupling deformation of FGM simply supported circular plates.According to the coupled pre-buckling theory,the governing equations including the pre-buckling coupling deformation of FGM simply supported circular plate under mechanical loads and thermal loads are derived respectively.The relationship between the critical loads and the gradient exponent under mechanical loads and thermal loads is given.The critical buckling loads are compared when considering pre-buckling coupling deformation and without considering the pre-buckling coupling deformation,considering temperature dependence of material properties and not considering temperature dependence of material properties.The effects of the pre-buckling coupling deformation and the temperature dependence of material properties on the stability of FGM circular plate are analyzed.3.The nonlinear deformation of FGM simply supported beams under thermal loads.Based on the classical beams theory and the concept of physical neutral surface,the basic equations of the problem are derived.The relationships between loads and deflection under different temperature ratios are obtained.The effects of temperature dependence of material properties and temperature ratio on the nonlinear deformation of FGM simply supported beams are analyzed.4.Buckling of simply supported FGM beams under thermal loads.The buckling governing equation including the effect of the pre-buckling coupling deformation is derived,and the temperature dependence of material properties is considered.The effects of gradient exponent,temperature ratio and temperature dependence of material properties on the buckling of FGM simply supported beams are analyzed.