In this study, a shear-deformable finite element model is developed for static, free vibration and buckling analyses of laminated beams. In order to demonstrate the accuracy of the developed model, (a) layered composite beams and (b) functionally graded sandwich beams are selected for application. In addition to the finite element solution, the analytical solutions of the problems have been made by the Navier method.
In the first chapter, the basic equations of elasticity for anisotropic media and brief information about functionally graded materials are given. Also, a detailed literature survey is presented. In the second chapter, the finite element formulation as well as the analytical solution method for static, free vibration and buckling analyzes of layered composite and functionally graded beams are presented. In the third chapter, the numerical results for displacements and stresses under static loading, natural frequencies and buckling loads for laminated and sandwiched beams are presented in graphs and tables. Based on the comparisons with the analytical solutions made and those available in the literature, accuracy of the proposed finite element model is discussed. In the fourth section, conclusions drawn from the study and some proposals for future work are presented. In the following chapters, the references cited and appendices are given respectively.
Key Words: Finite element method, Navier method, Laminated beams, Composite materials, Functionally graded materials, Bending, Free vibration, Buckling