Thermal Buckling Analysis Of Thick And Thin Functionally Graded Material Plates Using A Spline Finite Point Method

Functionally Graded Materials(FGMs),a new type of composite material developed in recent years,are obtained by mixing two(such as metal and ceramic)or several materials in a certain volume ratio.Unlike traditional composite materials,the material composition of FGMs changes continuously along one direction without obvious delamination,so the physical properties mutation between different materials can be eliminated easily.They can avoid stress concentration,reduce residual stress and improve bond strength between material layers effectively.Therefore,FGMs are more advantageous than traditional composite materials in practical application with high scientific research value and great potential for development.They have been widely used in many fields nowadays,such as aerospace,medicine,electronic technique,mechanical and construction engineering and so on.Various existing studies showed that in temperature field,the heat conduction phenomenon and temperature dependence of FGMs can significantly affect the bending,buckling and vibration of the plate.The influence of thermal environment on FGM plates which has significant applied value for theory and practical engineering cannot be ignored.The spline finite point method(SFPM),one of a meshless semi analytical solution,has advantages in solving the buckling problem of FGM plates with high accuracy,good convergence and compactness,and simple boundary condition treatment.In addition,the analysis of thin plate based on the first or higher-order plate theory which considers shear deformation,may induce false shear strain and over stiffness,namely shear-locking,while the general theory which takes the in-plane displacements u、v,deflection w and shear strains γxz、γyz as basic unknowns,is simple and suitable for the analysis of both thick and thin FGM plates without shear locking.Moreover,the governing equations and boundary conditions can be simplified and the computational efficiency becomes higher based on physical neutral surface.In this paper,a buckling model based on a SFPM and general theory is presented for the FGM plates resting on the Winkler-Pasternak elastic foundation by using the MATLAB software programming.First,the critical buckling loads of FGM plates at room temperature are calculated,the effects of thickness,volume fraction index,boundary condition and external load on the coupling and uncoupling model which considering and not considering the in-plane displacement are discussed.Second,the thermal buckling behavior of FGM plates in constant temperature field is studied.The change rules of critical buckling temperature and load of FGM plates under different material compositions,volume fraction indexes,thicknesses,temperature variations,foundation stiffnesses and heating-up conditions are discussed.The reasons for the deviation between middle and neutral surface results are analyzed.By controlling relevant factors,the buckling deformation of FGM plate becomes weakened and the buckling resistance is enhanced.The numerical results show that the SFPM and general thick/thin plate theory adopted in this paper are reliable and effective for the study on the buckling problems of FGM plate with good convergence and high computational efficiency.