• Structural Engineering and Mechanics
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• v.40 no.2
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• pp.257-277
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• 2011

In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson's method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author's previous papers.

• Steel and Composite Structures
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• v.39 no.2
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• pp.149-158
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• 2021

In this research paper, the free vibrational response of laminated composite plates is investigated using a non-polynomial refined shear deformation theory (NP-RSDT). The most interesting feature of this theory is the parabolic distribution of transverse shear deformations while ensuring the conditions of nullity of shear stresses at the free surfaces of the plate without requiring the Shear correction factor "Ks". A fourth-nodded isoparametric element with four degrees of freedom per node is employed for laminated composite plates. The numerical analysis of simply supported square anti-symmetric cross-ply and angle-ply laminated plate is carried out using a special discretization based on four-node finite element method which four degrees of freedom per node. Several numerical results are presented to show the effect of the coupling parameters of the plate such as the modulus ratios, the thickness ratio and the plate layers number on adimensional eigen frequencies. All numerical results presented using the current finite element method (FEM) is presented in 3D curve form.

• Structural Engineering and Mechanics
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• v.70 no.2
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• pp.233-243
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• 2019

This paper depicts the development and characterizations of laminated composites made with cellulosic giant cane (Arundinaria gigantea) fiber mats and epoxy resin. Zirconia-toughened mullite (ZTM) is used as a filler material in the laminated composite which was prepared from sillimanite through plasma processing technique. The mechanical characterizations of this composite have been carried out as per ASTM standards to evaluate its usability as a structural material. The effects of varying weight percentages of the filler and two different fiber orientations namely, angle-ply [$+45^{\circ}/-45^{\circ}/+45^{\circ}$] and balanced cross-ply [$0^{\circ}/90^{\circ}/0^{\circ}$] on the physical and mechanical properties such as density, microhardness, impact strength, tensile strength and interlaminar shear strength of the layered composite specimens have been investigated. The study indicates that the inclusion of zirconia-toughened mullite in the composite laminate as filler improves its mechanical properties. Moreover, the use of giant cane fiber mat in the laminate is more eco-friendly than the synthetic fibers. This research also helps in generating additional data to enrich the repository of natural fiber reinforced laminated composites.

• Composites Research
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• v.13 no.3
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• pp.9-20
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• 2000

Free vibration characteristics of a cantilevered laminated composite beam with multiple non-propagating transverse open cracks are investigated. In the present analysis a special ply-angle distribution referred to as asymmetric stiffness configuration inducing the elastic coupling between chord-wise bending and extension is considered. The multiple open cracks are modelled as equivalent rotational springs whose spring constants are calculated based on the fracture mechanics of composite material structures. Governing equations of a composite beam with open cracks are derived via Hamilton's Principle and Timoshenko beam theory encompassing transverse shear and rotary inertia effect is adopted. The effects of various parameters such as the ply angle, fiber volume fraction, crack numbers, crack positions and crack depthes on the free vibration characteristics of the beam with multiple cracks are highlighted. The numerical results show that the existence of the multiple cracks in an anisotropic composite beam affects the free vibration characteristics in a more complex fashion compared with the beam with a single crack.

• Journal of Korean Society of Steel Construction
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• v.9 no.4 s.33
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• pp.601-609
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• 1997

Bending and vibration results for a laminated plate base on a simplified higher-order plate theory with four variables are presented. Assuming a constant in-plane rotation tensor through the thickness in Reddy's higher-order shear deformation theory it is shown that a simpler higher-order theory can be obtained with the reduction of one variable without significant loss in the accuracy. This simple higher-order shear deformation theory is then used for predicting the natural frequencies and deflection of simply-supported laminated composite plates. The results obtained for antisymmetrical laminated composite plates compare favorably with third-order and first-order shear deformation theory. The information presented should be useful to composite-structure designers, to researchers seeking to obtain better correlation between theory and experiment and to numerical analysts in checking out their programs.

• Structural Engineering and Mechanics
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• v.37 no.2
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• pp.149-162
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• 2011

The aim of this research is a comprehensive review and evaluation of beam theories resting on elastic foundations that used to model mode-I delamination in multidirectional laminated composite by DCB specimen. A compliance based approach is used to calculate critical strain energy release rate (SERR). Two well-known beam theories, i.e. Euler-Bernoulli (EB) and Timoshenko beams (TB), on Winkler and Pasternak elastic foundations (WEF and PEF) are considered. In each case, a closed-form solution is presented for compliance versus crack length, effective material properties and geometrical dimensions. Effective flexural modulus ($E_{fx}$) and out-of-plane extensional stiffness ($E_z$) are used in all models instead of transversely isotropic assumption in composite laminates. Eventually, the analytical solutions are compared with experimental results available in the literature for unidirectional ($[0^{\circ}]_6$) and antisymmetric angle-ply ($[{\pm}30^{\circ}]_5$, and $[{\pm}45^{\circ}]_5$) lay-ups. TB on WEF is a simple model that predicts more accurate results for compliance and SERR in unidirectional laminates in comparison to other models. TB on PEF, in accordance with Williams (1989) assumptions, is too stiff for unidirectional DCB specimens, whereas in angle-ply DCB specimens it gives more reliable results. That it shows the effects of transverse shear deformation and root rotation on SERR value in composite DCB specimens.

• Journal of Korean Society of Steel Construction
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• v.18 no.2
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• pp.161-171
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• 2006

paper presents the results of a three-dimensional study of the natural vibration of laminated composite rectangular plates with various combinations of clamped and free boundaries. The Ritz method was used to obtain the stationary values of the associated Lagrangian, with displacements approximated using mathematicaly complete, characteristic orthogonal polynomials. The correctness of the three-dimensional model was established through a convergence study of the non-dimensional frequencies, followed by a comparison of the analytical findings in the existing literature. The wide scope of additional three-dimensional frequency results explains the influence of a number of geometrical and material parameters for angle-ply and cross-ply laminated plates, namely aspect ratio (${\mathcal{a/b}}$), thickness ratio (${\mathcal{a/h}}$), orthotropy of material, number of plies (${\mathcal{N}}$), fiber orientation angle (${\theta}$), and stacking sequence.

• Steel and Composite Structures
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• v.14 no.2
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• pp.121-132
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• 2013

This paper deals with multiobjective optimization of symmetrically laminated composite angle-ply annular sector plates subjected to axial uniform pressure load and thermal load. The design objective is the maximization of the weighted sum of the critical buckling load and fundamental frequency. The design variable is the fibre orientations in the layers. The performance index is formulated as the weighted sum of individual objectives in order to obtain the optimum solutions of the design problem. The first-order shear deformation theory is used for the mathematical formulation. Finally, the effects of different weighting factors, annularity, sector angle and boundary conditions on the optimal design are investigated and the results are compared.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2003.04a
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• pp.61-64
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• 2003

The finite element method based on the refined beam theory is applied to the vibration problem of rotation composite box beams. The present beam model includes a number of non-classical structural effects such as transverse shear, warping deformations, geometric non-linearities. The nonlinear finite element equations of motion are obtained from Hamilton's principle. Vibration characteristics versus various parameters such as ply angle, collective pitch angle, pretwist and precone are investigated for rotation box ben and relevant conclusions are outlined.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.7 s.94
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• pp.1686-1699
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• 1993

In this paper, the thermal buckling of thick composite angle-ply laminates subject to uniform temperature distribution is studied. For the plates of 4-edges simply supported condition and those of 4-edges clamped condition, the critical buckling temperatue is derived, using tile finite element method based on the shear deformation theory. The effects of lamination angle, layer number, laminate thickness, plate aspect ratio and boundary constraints upon the critical buckling temperature are presented.