Further Study Of The Mechanical Behavior Of Rectangular Plates Of Functionally Graded Materials

Functionally graded materials are new composite materials that have been widely used and have a promising application.How to improve its mechanical response prediction accuracy and further simplify the analytical calculation process has become the focus of research in this field.In this paper,based on the existing shear deformation plate theories,the plate theory S-RPT,which is applicable to the static analysis of functionally graded material plates,and the generalized single-variable plate theory GSSDPT,which is applicable to the free vibration analysis of functionally graded material plates,are proposed.both plate theories are based on the already widely used refined plate theory and are derived by introducing three-dimensional elasticity relations.The advantages of S-RPT and GSSDPT are that their accuracy is comparable to that of the plate theories that contain more unknown functions,but greatly simplify the computational process.What is more,it is worth pointing out that the displacement patterns of the proposed plate theory in this paper show the interrelationship between the grade material properties and the displacement distribution forms,which reveals to a certain extent the intrinsic mechanism of the nonlinear distribution forms of displacements influenced by the grade material properties.Therefore,this paper addresses to a certain extent the problem that the existing plate theories are not suitable or cannot accurately analyze the mechanical response of the functionally graded structures.This dissertation also further investigates the mechanical behavior of the functionally graded material plate in bending,buckling and free vibration by combining the proposed plate theory,or accounting for the effect of thickness stretching.The main aspects of this paper include the following.Chapter 1 introduces the background of the study of functionally graded materials and plate theories.The current plate theories used for the study of the functionally graded materials are described in detail.The development of two-dimensional plate theories and quasi-3D plate theories and the advantages and disadvantages of each are reviewed.Chapter 2 details the simple refined plate theory S-RPT proposed in this paper for the static analysis of functionally graded materials.the derivation process of the S-RPT theory and the derivation of the governing equations are described in detail.In addition,the calculation results in isotropic and functionally graded plates verify the accuracy and simplicity of S-RPT.Finally,based on the S-RPT,the bending and buckling behaviors of graphene-enhanced functionally graded porous plates are analyzed.Chapter 3 details the generalized single-variable plate theory GSSDPT proposed in this paper for the free vibration analysis of functionally graded materials.the derivation process of the GSSDPT theory and the derivation of the governing equations are described in detail.In addition,the calculation results in the functionally graded plate and functionally graded porous plate verify the accuracy and simplicity of GSSDPT.Finally,based on GSSDPT,the free vibration behavior of the functionally graded porous plate is analyzed.Chapter 4 analyzes the bending and free vibration behavior of graphene enhanced functionally graded plates based on the quasi-3D plate theory IRPT considering thickness stretching.By comparing with the two-dimensional plate theory RPT,the effect of thickness stretching on the calculated results is derived.Chapter 5 summarizes the research results and presents new perspectives for future work.