Thermoelastic Analysis Of FG Beams Based On A Refined Third-order Shear Deformable Beam Theory

Functionally graded materials(FGMs)are a special type of composite materials.Compared to conventional composite materials,FGMs possess various advantages,such as,the minimization or elimination of stress concentration,high temperature resistance and excellent designability,and they are now developed as very useful and efficient structural members.Consequently,the static and dynamic analyses of FG structures are identified as an interesting and important field of advanced material study in recent years.Based on the refined third-order shear deformation beam theory proposed by Shi and Voyiadjis,the bending,free vibration and buckling of FG beam composed of metal and ceramic are studied in this thesis.The objectives of this thesis are two-folded.(1)Based on the refined third-order shear deformation beam theory proposed by Shi and Voyiadjis and the variational principle,the governing equations of FG beams with thermoelastic coupling are deduced.The resulting governing equations are a system of the eighth-order differential equations in terms of displacement variables.The analytical solutions of the plane bending problems of FG beams are presented to verify the accuracy of the present theoretical model of FG beams.(2)An accurate and reliable two-noded FG beam element is developed for the bending,free vibration and buckling analysis of FG beams by employing the refined third-order shear deformation beam theory and the quasi-conforming element technique.Several typical examples of FG beams are solved using the present FG beam element to study the effects of the material distribution and thermal loading on the defections,stresses and natural frequencies of FG beams.The accuracy of both analytical solutions and numerical results given by the proposed models are validated against the results reported in the literature or the 2D finite element results solved by the author.The following conclusions can be drew form the studies presented in this thesis.(1)The result comparison shows that the present models are capable of yielding not only accurate displacements but also accurate stresses and higher-order frequencies of free vibration for the FG beams with thermoelastic coupling.(2)The present two-noded FG beam element based on the refined third-order shear deformation beam theory proposed by Shi and Voyiadjis and the quasi-conforming element technique are not only free from locking problems as well as free from the time consuming numerical integration,but also very accurate in the static and dynamic analysis of FG beams.The present governing equations of FG beams and the two-noded FG beam element provide an accurate theoretical model and a simple,accurate and efficient computational model for the analysis of FG beams with thermoelastic coupling used in various engineering applications.