In this article, the dispersion of propagation waves in an arbitrary direction in LAMINATED COMPOSITE PLATES is studied in the framework of elasticity. Three-dimensional field equations of elasticity are considered, and the characteristic equation is obtained on employing the continuity of displacements and stresses at the layers' interfaces. Obtained characteristic equation is further simplified by making use of the properties of the block matrices. Some important particular cases such as of free waves on reducing PLATES to single layer and the surface waves when thickness tends to infinity are also discussed. Numerical results are also obtained and represented graphically.

The Levy-type analytical solution is employed for the problem of bending of cross-ply and antisymmetric angle-ply piezoelectric hybrid LAMINATED PLATES with at least two simply supported opposite edges. The governing equations of equilibrium are derived in the framework of the first-order shear deformation plate theory. The equations are classified according to the crystallography type of piezoelectric layers and a comprehensive discussion on limitations of the method for the analysis of this kind of structures is performs. Finally, the governing equations of equilibrium are solved analytically with the aid of the state-space approach. We concluded that during the analysis of piezoelectric hybrid LAMINATED PLATES with Levy-type method, simultaneous applying of all electrical forces and moments is not possible (depending on type of lay-up, crystallography of piezoelectric layers, and expansion of electrical potential, some of electrical forces and moments may not be considered). In order to study the accuracy and several numerical examples are examined. The numerical results are compared with those obtained by the Navier method and those presented in the other published articles. It is found that the present results have very good agreements with those obtained by other methods.

Structural optimization is a process by which the optimum design is aimed while satisfying all the defined constraints. In recent years, using LAMINATED COMPOSITE materials in fabrication of mechanical, airspace, marine and machine industries are of major attention, due to their high strength and light weight. One of the objectives of the present paper is seeking the optimum weight and cost of a LAMINATED COMPOSITE plate, while undergoing the heaviest load prior to a complete failure. Various failure criteria are defined for such structures in the literature. In this work, the Tsai-Hill is used as the failure criterion. The multiobjective function introduced here consists of weight, cost and failure loading. Therefore, one realizes that in this work a minimal-maximal objective function is to be optimized, thus, the weight and the cost will be minimized while the failure load for all the LAMINATED plies is to be maximized. The design variables could be any combination of thickness, orientation of fibers and the material for each layer. The thickness of the layers could be considered continuous whereas the cost and the material for each layer to be discrete. With regard to the problem in hand, a decision was made to employ a newly introduced type of optimization technique called the Genetic Algorithms, based on a new type of selection, to handle the optimization process. The theory of analysis was based on the Classical Lamination Theory (CLT). Therefore, attempts were made to produce software for the analysis and the optimum design of LAMINATED COMPOSITE PLATES under any combination of design parameters. A number of problems were solved under two different models. First, a multi-objective optimization procedure under a new approach was introduced, where the problem is considered unconstrained. The second model, namely the constrained optimization problem, consists of secondary valued terms which were defined as constraints, while the objective function contained only the major term, as selected by the user. The verification of the results was made satisfactorily, as a consequence of which some benchmark examples were also attempted and recorded.

In this paper, a finite element model is presented for the transient analysis of low velocity impact, and the impact induced damage in the COMPOSITE plate subjected to low velocity impact is studied. The failure criteria suggested by Choi and Chang and the Tsai-Hill failure criteria are used for the prediction of the damage in the COMPOSITE plate; then the effect of various parameters on the impact induced damage is investigated. The first order shear deformation plate theory and the Ritz finite element method are employed for modeling the behavior of plate, and the modified Hertz contact low is used for the prediction of the contact force through the impact. In the numerical results, the time history of indentation, contact force and stress during the impact and the impact induced damage is investigated. The matrix cracking and delamination in the plies of the LAMINATED COMPOSITE plate subjected to low velocity impact are studied and the effects of various parameters are investigated.

In this paper, the free vibration response of a LAMINATED COMPOSITE rectangular plate supporting a rotating circular patch mass is studied. The two variables refined plate theory which has the number of unknown functions involved is only four, as against five in case of other simple shear deformation theories, is applied to define the third order displacement field of a COMPOSITE rectangular plate. The plate is considered to have simply supported boundaries. The first variation of the Lagrangian (Hamilton’s principle) is used to obtain the equations of motion for the rectangular plate. Due to the significance of fundamental frequency of the plate, its variation with respect to the non-dimensional geometrical parameters such as aspect ratio of the plate, size, location and angular velocity of the rotating patch mass, is investigated. It will be shown herein that the proposed theory is simple in solving the free vibration problems of PLATES with patch masses.

A modeling technique for simulating the nonlinear post buckling behaviour of LAMINATED COMPOSITE PLATES with cut out and subjected to axial compression is developed. The present progressive damage model capable of predicting the interaction effects between the post-buckling behaviour and the various failure modes of compressively loaded openhole PLATES. Due to the large bending deformation, resulting in buckling caused by transverse loading, the geometric nonlinear analysis becomes important. Various failure modes such as fiber breakage, matrix cracking are modeled by degrading the material properties. The final failure load of the structure is found using the geometric nonlinear progressive analysis based on degenerated shell element, comprising three basic steps, stress analysis, failure analysis and material property degradations rules. The present results are found to compare well with those available in the literature.

It is well known that for LAMINATED COMPOSITE PLATES a Levy-type solution exists only for cross-ply and antisymmetric angle-ply laminates. Numerous investigators have used the Levy method to solve the governing equations of various equivalent single-layer plate theories. It is the intension of the present study to introduce a method for analytical solutions of LAMINATED COMPOSITE PLATES with arbitrary lamination and boundary conditions subjected to transverse loads. The method is based on separation of spatial variables of displacement field components. Within the displacement field of a first-order shear deformation theory (FSDT), a LAMINATED plate theory is developed. Two systems of coupled ordinary differential equations with constant coefficients are obtained by using the principle of minimum total potential energy. Since the procedure used is simple and straightforward it can, therefore, be adopted in developing higher-order shear deformation and layer wise LAMINATED plate theories. The obtained equations are solved analytically using the state-space approach. The results obtained from the present method are compared with the Levy-type solutions of cross-ply and antisymmetric angle-ply laminates with various admissible boundary conditions to verify the validity and accuracy of the present theory. Also for other laminations and boundary conditions that there exist no Levy-type solutions the present results may be compared with those obtained from finite element method. It is seen that the present results have excellent agreements with those obtained by Levy-type method.

In this study, an analysis of fiber reinforced, symmetrically LAMINATED COMPOSITE PLATES containing circular holes has been carried out. First, the stress state of a layer in a LAMINATED plate is studied. After obtaining the stress state for each layer due to the uniaxial loading of a plate, the stress concentrations around a circular hole are studied. A number of diagrams are drawn to show the stress concentrations around a hole for layers having different oriented fibers using different material pairs with different E1/E2 ratios (ratio of elasticity modulus of fiber direction to that of transverse direction). Graphs are given for various E1/E2 values for the circumferential stress values around the hole versus angular location of points for two different fiber orientation angles. Second, the failure of the LAMINATED COMPOSITE plate is studied. To determine the “first–ply failure” of a LAMINATED plate, Tsai-Hill failure criterion is employed to find minimum bearing circumferential stresses and where they occur as a function of the fiber orientation angle.

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