The present thesis investigates bending, free vibration an‎d buckling behavior of thin to moderately thick laminated composite plates, using the method of meshless local exponential basis functions (MLEBFs), based on a non-polynomial Zig-Zag theory. Although equivalent single layer theories are widely in use, they do not provide sufficiently accurate predictions of the in-plane an‎d interlaminar behavior of the laminated plates. On the other han‎d, layerwise theories, despite their high accuracy, involve a large number of unknowns depending on the number of layers. To address certain issues related to the laminated composite plates, this research employs a non-polynomial Zig-Zag theory, developed by Sarangan an‎d Singh (2016), as a suitable alternative to the classical plate theory, first-order an‎d third order shear deformation theories, which were used in the previous studies on MLEBFs. The intended Zig-Zag theory was developed using hyperbolic, trigonometric, an‎d inverse trigonometric transverse shear strain functions, in order to preserve the inter-layer continuity in-plane displacement an‎d transvers shear stress. Notably, the number of unknowns in the implemented Zig-Zag theory equals that of the first order shear deformation theory. Additionally, the theory satisfies the zero transverse shear stress on the top an‎d bottom surfaces of the plate, thus eliminating the need for a shear correction factor. The proposed meshless method is developed based on Trefftz’s attitude, in which separation of the solution function into homogeneous an‎d particular parts allows for exactly satisfying the governing equation, thereby eliminating the numerical integration throughout the process. The local form of the method employed here relies on discretizing the solution domain an‎d its boundaries using a set of nodal points, being correlated within overlapped clouds of nodes. This leads to desirable convergence rate an‎d continuity in the stress an‎d deformation components. Straightforward satisfaction of the boundary conditions at discrete points, without requiring boundary elements, is another advantage. In conclusion, integration of the highly accurate Zig-Zag theory with reasonable number of unknowns, with a highly accurate meshless method that eliminates meshing an‎d numerical integration, offers a simple an‎d realistic analysis of laminated composite plates. To assess the accuracy of the proposed approach, various problems with different boundary conditions, ratios of elastic moduli, dimensional ratios, side to thickness ratios an‎d lamination schemes have been presented, compared with analytical an‎d numerical results available in the literature based on various theories.

بيژن برومند قهنويه , نيما نورمحمدي

سعيد صرامي , حسين عموشاهي