First -order orthotropic shear deformation equations for the nonlinearly elastic bending response of rectangular plates are introduced. Their solution using a computer program based on finite differences implementation of the Dynamic Relaxation (DR) method is outlined. The convergence and accuracy of the DR solutions for elastic large deflection response of isotropic, orthotropic, and laminated plates are established by comparison with various exact and approximate solutions. The present Dynamic Relaxation method (DR) coupled with finite differences method shows a fairly good agreement with other analytical and numerical methods used in the verification scheme. It was found that: The convergence and accuracy of the DR solution are dependent on several factors including boundary conditions, mesh size and type, fictitious densities, damping coefficients, time increment and applied load. Also, the DR large deflection program using uniform finite differences meshes can be employed in the analysis of different thicknesses for isotropic, orthotropic or laminated plates under uniform loads. All the comparison results for simply supported (SS4) edge conditions showed that deflection is almost dependent on the direction of the applied load or the arrangement of the layers. Keywords DeflectionIn plane, out of plane and rotational fictitious densities.Curvature and twist components of plate mid -plane IntroductionComposites were first considered as structural materials a little more than half a century ago. From that time to now, they have received increasing attention in all aspects of material science, manufacturing technology, and theoretical analysis.The term composite could mean almost any thing if taken at face value, since all materials are composites of dissimilar subunits if examined at close enough details. But in modern engineering materials, the term usually refers to a matrix material that is reinforced with fibers. For instance, the term "FRP" which refers to Fiber Reinforced plastic, usually indicates a thermosetting polyester matrix containing glass fibers, and this particular composite has the lion's share of today commercial market.In the present work, a numerical method known as Dynamic Relaxation (DR) coupled with finite differences is used. The DR method was first proposed in 1960s and then passed through a series of studies to verify its validity by Turvey and Osman Refs. . In this method, the equations of equilibrium are converted to dynamic equations by adding damping and inertia terms. These are then expressed in finite difference form and the solution is obtained through iterations. The optimum damping coefficient and time increment used to stabilize the solution depend on a number of factors including the matrix properties of the structure, the applied load, the boundary conditions and the size of the mesh used.Numerical techniques other than the DR include finite element method, which widely used in the present studies i.e. of Damodar R. Ambur et al [12], Ying Qing Huang et al [...

It was found that symmetric laminates are stiffer than the anti – symmetric one due to coupling between bending and stretching which decreases the buckling loads of symmetric laminates. The buckling load increases with increasing aspect ratio, and decreases with increase in modulus ratio. The buckling load will remain the same even when the lamination order is reversed. The buckling load increases with the mode number but at different rates depending on the type of end support. It is also observed that as the mode number increases, the plate needs additional support.

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The motivation that led to the carrying out of the present study has come from many years of studying classical laminated plate theory (CLPT) and its analysis by the finite element (FE) method, and also from the fact that there does not exist a publication that contains a detailed coverage of classical laminated plate theory and finite element method in one volume. The present study is an attempt to fulfill the need for a complete treatment of classical laminated theory of plates and its solution by a numerical solution.The material presented is intended to serve as a basis for a critical study of the fundamentals of elasticity and several branches of solid mechanics including advanced mechanics of materials, theories of plates, composite materials and numerical methods.The problem of critical buckling loads of laminated composite plates is analyzed and solved using the energy method which is formulated by a finite element model. In that model, four nodded rectangular elements of a plate is considered. Each element has three degrees of freedom at each node. The degrees of freedom are the lateral displacement w, and the rotations ϕ and ψ about the y and x axes respectively.The effects of lamination scheme on the non -dimensional critical buckling loads of laminated composite plates are investigated.The material chosen has the following properties: 1 2 12 13 23 2 12

New numerical results are generated for in-plane compressive biaxial buckling which serves to quantify the effect of material anisotropy on buckling loading. The coupling effect on buckling loads is more pronounced with the increasing degree of anisotropy. It is observed that the variation of buckling load becomes almost constant for higher values of elastic modulus ratio. Keywords---biaxial buckling, classical laminated plate theory, composite laminated decks plates, finite element, fortran program, material anisotropy.