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In this study, nonlinear bending analysis of ring-stiffened annular laminated composite plates is studied. A discretely stiffened plate theory for elastic large deflection analysis of uniformly distributed loaded is introduced. The governing equations are derived based on a first-order shear deformation plate theory (FSDT) and large deflection von Karman equations. The numerical results are obtained using the dynamic relaxation (DR) method combined with the central finite difference discretization technique. For this purpose, a FORTRAN computer program is developed to generate the numerical results. In order to verify the accuracy of the present method the results are compared with those available in the literatures and ABAQUS finite element package as well. The computer code can handle symmetric, unsymmetrical and general theta-ply schemes. The effects of the plate thicknesses, different ratio of outer to inner radius, depth of stiffener, boundary condition and laminates lay-up are studied in detail.

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In this study, the non-linear bending analysis of isotropic and orthotropic rectangular plates is performed by Dynamic Relaxation (DR) method. In order to model the plate, the four-variable refined plate theory, which is a new and simple higher-order shear deformation theory and has a good capability in analysis of thick plates, is adopted. Despite the first-order shear deformation plate theory; this theory does not need the shear correction factor, predicts shear strains and stress parabolically across the plate thickness and satisfies the zero stress conditions on free surfaces. The governing equations are obtained using virtual work principle and the Von-Karman nonlinear terms are considered in strain-displacement equations. The non-linear coupled governing equations are solved by DR method combined with finite difference technique, and for this purpose a computer code is provided in MATLAB software. In order to demonstrate the accuracy of present method, the numerical results are compared with the existing ones and very good agreement is observed. Also the effects of side-to-thickness ratio and boundary conditions on the results are examined. Finally, the variations of shear effects by changing the plate thickness and also changing the orthotropy ratio in orthotropic plates are investigated.

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A finite element formulation for bending analysis of isotropic and orthotropic plates based on two-variable refined plate theory is developed in this paper. The two-variable refined plate theory which can be used for both thin and thick plates predicts parabolic variation of transverse shear stresses across the plate thickness and therefore, it does not need shear correction factor in the formulation and the zero stress conditions are satisfied on free surfaces. The von-Karman nonlinear terms are considered in strain-displacement equations and governing equations are derived using the Hamilton's principle. After constructing weak form equations, a new 4-node rectangular plate element with six degrees of freedom at each node is used for discretization of the domain. The non-linear coupled governing equations are solved by Newton–Raphson method. The finite element code is written in MATLAB which can be used for analysis of thin and thick, isotropic and orthotropic plates with various boundary conditions. Some benchmark problems are solved by the developed code and the obtained displacements and stresses are compared with the existing results in the literature which show the accuracy and efficiency of presented finite element formulation.