Bending behavior of laminated composite plates using the refined four-variable theory and the finite element method
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The purpose of this work is to analyze the bending behavior of laminated composite plates using the refined four-variable theory and the finite element method approach using an ANSYS 12 computational code. The analytical model is based on the multilayer plate theory of shear deformation of the nth-order proposed by Xiang et al 2011 using the theory principle developed by Shimpi and Patel 2006. Unlike other theories, the number of unknown functions in the present theory is only four, while five or more in the case of other theories of shear deformation. The formulation of the present theory is based on the principle of virtual works, it has a strong similarity with the classical theory of plates in many aspects, it does not require shear correction factor and gives a parabolic description of the shear stress across the thickness while filling the condition of zero shear stress on the free edges. The analysis is validated by comparing results with those in the literature.Keywords:
Plate theory
Virtual work
Order theory
This paper presents a new 4-node finite-element for the analysis of laminated composite plates. The element is based on a first-order shear deformation theory and is obtained through a mixed-enhanced approach. In fact, the adopted variational formulation includes as variables the transverse shear as well as enhanced incompatible modes introduced to improve the in-plane deformation. The problem is then discretized using bubble functions for the rotational degrees of freedom and functions linking the transverse displacement to the rotations. The proposed element is locking free, it does not have zero energy modes and provides accurate in-plane/out-of-plane deformations. Furthermore, a procedure for the computation of the through-the-thickness shear stresses is discussed, together with an iterative algorithm for the evaluation of the shear correction factors. Several applications are investigated to assess the features and the performances of the proposed element. Results are compared with analytical solutions and with other finite-element solutions. Copyright © 1999 John Wiley & Sons, Ltd.
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A third-order shear deformation theory of laminated composite plates and shells is developed, the Navier solutions are derived, and its finite element models are developed. The theory allows parabolic description of the transverse shear stresses, and therefore the shear correction factors of the usual shear deformation theory are not required in the present theory. The theory also accounts for the von Karman nonlinear strains. Closed-form solutions of the theory for rectangular cross-ply and angle-ply plates and cross-ply shells are developed. The finite element model is based on independent approximations of the displacements and bending moments (i.e., mixed finite element model), and therefore, only C sup o -approximation is required. The finite element model is used to analyze cross-ply and angle-ply laminated plates and shells for bending and natural vibration. Many of the numerical results presented here should serve as references for future investigations. Three major conclusions resulted from the research: First, for thick laminates, shear deformation theories predict deflections, stresses and vibration frequencies significantly different from those predicted by classical theories. Second, even for thin laminates, shear deformation effects are significant in dynamic and geometrically nonlinear analyses. Third, the present third-order theory is more accurate compared to the classical and firt-order theories in predicting static and dynamic response of laminated plates and shells made of high-modulus composite materials.
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In this paper, a refined higher-order shear deformation theory including the stretching effect is developed for the analysis of bending analysis of the simply supported functionally graded (FG) sandwich plates resting on elastic foundation. This theory has only five unknowns, which is even less than the other shear and normal deformation theories. The theory presented is variationally consistent, without the shear correction factor. The present one has a new displacement field which introduces undetermined integral variables. Equations of motion are obtained by utilizing the Hamilton's principles and solved via Navier's procedure. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.
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This work presents a new multilayered laminated composite structure model to predict the mechanical behaviour of multilayered laminated composite structures. This new multilayered structure model describes the shear stress distribution model through the thickness respecting free boundary conditions on the top and bottom surfaces by an exponential function. This model has the same order of complexity as Touratier's model ‘Sine’, so a shear correction factor is not required like in the first-order shear deformation theory. This model is more precise than all other existing refined theories. This theory is based on the kinematic approach in which the shearing is represented by an exponential function. The virtual power principal is used to deduce the boundary value problem. To verify the precision of the present model, several significant problems on bending, vibration, and buckling of laminated and sandwich structures have been studied. The results by the present model are compared with the exact three-dimensional elasticity theory and with several other well-known theories. The proposed model is found to be more precise for analysing multilayered structures.
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In the present study, new nonpolynomial shear-deformation theories are proposed and implemented for structural responses of laminated-composite and sandwich plates. The theories assume nonlinear distribution of transverse shear stresses, and also satisfy the traction-free boundary conditions at the top and bottom layers of the laminates. The governing differential equations are derived for a generalized shear-deformation theory by implementing the dynamic version of principle of virtual work and calculus of variations. A generalized closed-form solution methodology of the Navier type is implemented to ensure the validity and efficiency of the present theories for bending, buckling, and free-vibration responses of the laminated-composite and sandwich plates. It is observed that the proposed formulation in conjunction with the solution methodology is capable of handling all existing five-degree-of-freedom-based shear-deformation theories. The comparison of results also shows that the adequate choice of shear deformation leads to an accurate prediction of structural responses. The influence of shear deformation on the type of analysis performed is also observed in this study. The theories are also capable of an efficient prediction of the responses of structures at a similar computational cost as that of other equivalent single-layer theories.
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