Static And Dynamic Response Of Functionally Graded Material Plates And Shells With Thermal Loads

Functionally graded material (FGM) is a kind of new functional materials. Through optimal of design of the material, the FGM structures can have better mechanical properties in thermal environment than homogenous material structures. Due to its virtue of physical characteristics, FGM can be used as heat-shielding material for the high-speed spacecraft, nuclear reactor and chemical engineering. The studies of mechani€al behaviors of FGM plates and shells have being become one of the important direction in solid mechanics. The present study is focus on study the static and dynamic responses of FGM circular plates and cylindrical shells subjected to thermal loads. The main research results and conclusion are summarized as follows:1) Forced vibration of FGM circular plate with surface periodic thermal loadsThe material properties of a FGM plate are graded continuously in the direction of thickness. The variation of the properties followed a simple power-law distribution in the term of the volume fraction of the constituents. In the view of the form of surface thermal loads, the through thickness temperature distribution is assumed to be two parts, static and dynamic. The temperature distributions are solved on the bases of one-dimensional unsteady-state heat conduct equation, the static and dynamic thermal membrane forces and bending moments are obtained numerically by shooting method. On the basis of von Karman's plate theory, the non-linear governing equations of thin FGM circular plate are formulated. Assuming that the vibration is harmonic and using Kantorovich time averaging method, the partial differential equations are converted into a system of nonlinear ordinary differential equations. Numerical results of thin FGM circular plates with simply-supported boundary and subjected to surface periodic thermal loads are obtained by using shooting method. The effects of the static and dynamic thermal load parameters on the natural frequencies are examined in details. Especially, the characteristics of resonance phenomenon are also analyzed.2) Geometrical nonlinear theory of thin FGM shellsIn genral, the reduced shell theories of homogenous material structures are not fit for FGM shells. In order to study mechanical behaviors of FGM cylindrical shell, the geometrical nonlinear theory for thin FGM shells is derived based on Kirchhoff-Love assumption by using vector tools. In derivation of the geometrical equations, the variations of deformed curve surface resulting in the direction change of basis vectors are considered, and the elongation ratio of line segment in basis vectors and the nonlinear strain and displacement relations in any point of the shell are obtained. The changes of stress distribution due to deformation are taken into account in constitutive equations. The equilibrium equations are formulated on deformed element. Above mentioned basic equations are applicable to the large deformation problems of shells. The results of degenerative forms of the equations for the thin shell with small deflection are consistent with those in the literature. For the small deflection problem of cylindrical shells, the equations of Flugge's shell theory can be obtain.3) Large deformation and free vibration of FGM cylindrical shell under static temperature rise fieldConsidering the temperature-dependent properties of FGM, the temperature distribution, the thermal membrane forces, thermal bending moments and high-order thermal forces of the FGM cylindrical shell are evaluated under static thermal loads on the surface. Nonlinear governing equations for thin FGM circular cylindrical shell are reduced from the general ones derived in this dissertation. By using the numerical method, response of the static large deformation of a short FGM cylindrical shell with three kinds of symmetry boundary conditions are investigated. and the effects of the geometric and load parameters, the volume fraction of material on the deflection of the cylindrical shell. By using the time-assumed mode of the free vibration and on the basis of Hamilton principle, the governing equations in terms of displacements for free vibration of FGM cylindrical shell subjected to thermal loads are obtained. By numerical method, the relations between the linear frequencies and the geometrical and material parameters of the structure are presented.4) Forced vibration of cylindrical shell under periodic thermal loadsAccording to the numerical results of the static deformation obtained in the former analysis, the fitting functions of the static bending configurations can be obtained by least square method, the space mode shape of dynamic responses are assumed by trigonometric functions. By using Hamilton principle, nonlinear ordinary differential equations in the time domain governing the large amplitude vibration of FGM cylindrical shell are derived. By analyzing the free vibration with small amplitude under static thermal loads, we arrived at the results coincided with those by shooting method, which shows that the method is feasible. The periodic solution of nonlinear forced vibration of FGM cylindrical shell under periodic surface thermal loads is investigated by multi-scale method. Further more, the dynamic stability of nonlinear vibration is examined.The investigation of this dissertation will enrich the research results of mechanical behavior of the functionally graded structures under dynamic thermal loads, which may be helpful and beneficial in better understanding for such advanced composite material structures in the engineering application.