Bending,Vibration And Buckling Of Functionally Graded Sandwich Plates In Thermal Environments

Functionally graded(FG)sandwich structures are a class of novel sandwich structures.They are proposed to eliminate mechanically and thermally induced stresses due to the material property mismatch in conventional sandwich structures.The commonly used FG sandwich structures can be divided into two types: type-A,sandwich structures with FG face sheets and homogeneous core;type-B,sandwich structures with homogeneous face sheets and FG core.In literature,most of the investigations into FG sandwich structures focused on the bending and buckling under pure mechanical or pure thermal load,as well as on the vibration neglecting the thermal effect.In this thesis,a four-variable plate theory neglecting the stretching effect is developed to analyze the bending,vibration and buckling behaviors of FG sandwich plates in thermal environments.In addition,a five-variable plate theory considering the stretching effect is presented to investigate the effect of thickness stretching on thermomechanical bending of FG sandwich plates.Both type-A and type-B sandwich plates are considered.The contents of this thesis are as follows.Firstly,the concepts of sandwich structures,functionally graded materials(FGMs)and FG sandwich structures are introduced.Based on the problems that need to be further investigated,the research contents are presented.Then the volume fraction and the effective material properties for two types of FG sandwich plates are given.Based on the four-variable plate theory and the five-variable plate theory separately,the geometric equations are obtained.The quasi-3D and 3D constitutive equations accounting for the thermal effect are given.The governing equations for the bending of FG sandwich plates are derived using the principle of minimum potential energy.Close-form solutions for the displacements and stresses are obtained via Navier approach.Then based on the four-variable plate theory,the von Karman nonlinear geometric equations are given.Using the principle of minimum potential energy and the Hamilton's principle respectively,the governing equations for the buckling and vibration are derived.The results on critical buckling load and temperature change,as well as the natural frequencies of simply supported FG sandwich plates are obtained.Compared with other theories containing more unknowns,the present theory has the same accuracy with fewer unknowns.Since the investigations into the bending,buckling and vibration of FG sandwich plates in thermal environments are rare,some benchmark results are presented.These results include: deflections and stresses of type-B FG sandwich plates;the relationship between the mechanical load and the temperature change in which a FG sandwich plate buckles;and the natural frequencies of FG sandwich plates in thermal environments.The influences of volume fraction distribution,geometrical parameters and thermal load on the bending,buckling and vibration behaviors of FG sandwich plates are discussed in detail.Finally,the research work is briefly summarized.Some conclusions are drawn and the innovations are pointed out.A few research topics for future works are proposed.