In this dissertation, a meshfree method is developed for the bending analysis of thick laminated composite plates with different shapes and various boundary conditions using a higher-order Zig-Zag deformation theory. In the higher-order Zig-Zag theory proposed by Cho and Parmerter, a linear Zig-Zag variation of in-plane displacement is combined with a cubic variation of in-plane displacement field. The Zig-Zag term represents the shear strain discontinuity between layers resulted from the transverse shear stress continuity conditions. Moreover, the cubic part accounts for the overall parabolic transverse shear stress as in Reddy’s third-order shear deformation theory. By satisfying the transverse shear stress continuity as well as the shear free surface conditions, the Zig-Zag unknowns of each layer are derived in terms of the global unknown displacements of the mid-plane; therefore, the number of unknowns does not change as the number of layers increases. Consequently, for the thick laminates with high transverse anisotropy, this theory is suitable and computationally efficient. Furthermore, the details of imposing different boundary conditions including free, simply supported and clamped are given. In order to define the boundary conditions for free and simply supported edges, a variational approach combined with conventional conditions pertaining to displacements is used. However, for clamped edges, we show that satisfying the conventional Dirichlet conditions may lead to disappearance of transverse shear stress at the clamped edges. Therefore, a new set of conditions are proposed to avoid such an unwanted effect. The solution method used in this dissertation is a Trefftz type which falls in the category of meshfree methods. In this method, exponential basis functions (EBFs) with complex-valued exponents are used. The solution is split into homogenous and particular parts. The homogenous part is approximated by a series of EBFs and the unknown coefficients are determined by satisfaction of the boundary conditions through a collocation method using a discrete transformation technique. The way that one can generally evaluate the EBFs for a laminated plate using a Zig-Zag theory is demonstrated. Apart from giving explicit form of EBFs for single layer isotropic plates, useful for solution on relatively thick plates, we present similar explicit relations for three-layer sandwich plates with in-plane isotropy, having wide applications in structural/mechanical engineering. In addition, two different methods are proposed for approximating the particular solution including a method using another series of EBFs by means of the transformation used in the homogenous solution and the Fourier series solution. In this study, the first method is employed due to its great convergency in bending analysis of plates with uniform loadings. Moreover, the results of our numerical experiments including the bending analysis of composites with different boundary conditions and different configurations are provided and compared with those available in the literature to validate the results. It has been observed that the present method can perform excellently in a wide range of problems defined for the bending analysis of laminated plates. In addition, some results for a sandwich composite plate as a new benchmark using the Zig-Zag theory are presented for further sudies. Key words : Laminated composite plates, Exponential basis functions, Higher-order Zig-Zag deformation theory.
