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

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.

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.

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New numerical results are generated for in-plane compressive biaxial buckling which serves to quantify the effect of reversing lamination scheme on buckling loading. The buckling loads have been determined for two modulus ratios 40 and 5. It is observed that the buckling loads are completely the same for the given first three modes. Therefore, it can be concluded that the buckling load of laminated plates will remain the same even if the lamination order is reversed. The reason behind this is that the transformed elastic coefficients, [ ], are equal for both lamination schemes. . https://doi.org/10.21744/irjeis.v5n3.645 29 framework. The second uses the continuum elements to obtain approximate solutions to heat transfer, fluid mechanics, and solid mechanics problem. The formulation using the discrete element is referred to as matrix analysis of structures and yields results identical with the classical analysis of structural frameworks. The second approach is the true finite element method. It yields approximate values of the desired parameters at specific points called nodes. A general finite element computers program, however, is capable of solving both types of problems and the name" finite element method" is often used to denote both the discrete element and the continuum element formulations.The finite element method combines several mathematical concepts to produce a system of linear and nonlinear equations. The number of equations is usually very large, anywhere from 20 to 20,000 or more and requires the computational power of the digital computer.It is impossible to document the exact origin of the finite element method because the basic concepts have evolved over a period of 150 or more years. The method as we know it today is an outgrowth of several papers published in the 1950 th that extended the matrix analysis of structures to continuum bodies. The space exploration of the 1960 th provided money for basic research, which placed the method of a firm mathematical foundation and stimulated the development of multi-purpose computer programs that implemented the method. The design of airplanes, unmanned drones, missiles, space capsules, and the like, provided application areas.