In this dissertation, the bending and free vibration problems of thick laminated composite plates based on In static problems the governing differential equations are satisfied over the problem domain directly in a global or local form. In this method, the solution is first split into homogenous and particular parts and then the homogenous part is approximated by the summation of an appropriately selected set of exponential basis functions (EBFs) that are restricted to satisfy the governing differential equation. The process of finding the EBFs for CLPT, FSDT and TSDT are described and the explicit expressions are given for special cases of laminated plates. Two different methods are also proposed for approximating the particular solution including the Fourier series solution and a method using another series of EBFs with a similar transformation technique to the homogenous solution. Comparison of the results of these two methods reveals significant supremacy of the latter over the former in many problems regarding the computational costs. The boundary conditions are enforced through a collocation approach on a set of boundary points. In this sense, the method may be Contrary to the adopted approach for static problems, a variational form of the differential equations is satisfied in an iterative way for the case of free vibration problems. In this method the basis functions for approximating the unknown variables are selected by enforcing the boundary conditions on a set of boundary points directly. The frequency parameters are obtained by solving the eigenvalue problem of the weak or strong form of the differential equations. The solutions of several bending and free vibration laminated plate problems with various geometries, boundary conditions and plate lamination schemes are presented to validate the accuracy, efficiency and applicability of the proposed methods. It has been observed that the presented methods can perform excellently in a wide range of problems defined for the bending and free vibration analysis of laminated plates based on various plate theories. Key words : Laminated composite plates, Exponential basis functions, Shear deformation theorie
