• Steel and Composite Structures
• /
• v.24 no.6
• /
• pp.697-709
• /
• 2017

The current study addresses the local buckling analysis of an infinite thin rectangular symmetrically laminated composite plate restrained by a tensionless Winkler foundation and subjected to uniform in-plane shear loading. An analytic method (i.e., one-dimensional mathematical method) is used to achieve the analytical solution estimate of the contact buckling coefficient. In addition, to study the effect of ply angle and foundation stiffness on the critical buckling coefficients for the laminated composite plates, the parametric studies are implemented. Moreover, the convergence for finite element (FE) mesh is analysed, and then the examples in the parametric study are validated by the FE analysis. The results show that the FE analysis has a good agreement with the analytical solutions. Finally, an example with the analytical solution and FE analysis is presented to demonstrate the availability and feasibility of the presented analytical method.

• Journal of Korean Society of Steel Construction
• /
• v.15 no.2
• /
• pp.97-107
• /
• 2003

To obtain a more accurate response from larninated composite structures, the effect of transverse shear deformation, transverse normal strain/stress, and nonlinear variation of in-plane displacements vis-$\\grave{a}$-vis the thickness coordinate should be considered in the analysis. The improved higher-order theory was used to determine the critical buckling load and natural frequencies of laminated composite structures. Solutions of simply supported laminated composite plates and sandwiches were obtained in closed form using Navier's technique, with the results compared with calculated results using the first order and other higher-order theories. Numerical results were presented for fiber-reinforced laminates, which show the effects of ply orientation, number of layers, side-toithickness ratio, and aspects ratio.

• Structural Engineering and Mechanics
• /
• v.3 no.2
• /
• pp.121-133
• /
• 1995

It is well known that two-dimensional simplified third-order theories satisfy the layer interface continuity of transverse shear strains, thus these theories violate the continuity of transverse shear stresses when two consecutive layers differ either in fibre orientation or material. The third-order theories considered herein involve four/or five dependent unknowns in the displacement field and satisfy the condition of vanishing of transverse shear stresses at the bounding planes of the plate. The objective of this investigation is to examine (i) the flexural response prediction accuracy of these third-order theories compared to exact elasticity solution (ii) the effect of layer interface continuity conditions on the flexural response. To investigate the effect of layer interface continuity conditions, three-dimensional elasticity solutions are developed by enforcing the continuity of different combinations of transverse stresses and/or strains at the layer interfaces. Three dimensional twenty node solid finite element (having three translational displacements as degrees of freedom) without the imposition of any of the conditions on the transverse stresses and strains is also employed for the flexural analysis of the laminated plates for the purposes of comparison with the above theories. These shear deformation theories and elasticity approaches in terms of accuracy, adequacy and applicability are examined through extensive numerical examples.

• Steel and Composite Structures
• /
• v.21 no.4
• /
• pp.883-919
• /
• 2016

In this research, buckling analysis of an embedded laminated composite plate is investigated. The elastic medium is simulated with spring constant of Winkler medium and shear layer. With considering higher order shear deformation theory (Reddy), the total potential energy of structure is calculated. Using Principle of Virtual Work, the constitutive equations are obtained. The analytical solution is performed in order to obtain the buckling loads. A detailed parametric study is conducted to elucidate the influences of the layer numbers, orientation angle of layers, geometrical parameters, elastic medium and type of load on the buckling load of the system. Results depict that the highest buckling load is related to the structure with angle-ply orientation type and with increasing the angle up to 45 degrees, the buckling load increases.

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

• Structural Engineering and Mechanics
• /
• v.67 no.6
• /
• pp.617-628
• /
• 2018

This paper deals with the maximization of the critical buckling load of simply supported antisymmetric angle-ply plates resting on Pasternak foundation subjected to compressive loads using teaching learning based optimization method (TLBO). The first order shear deformation theory is used to obtain governing equations of the laminated plate. In the present optimization problem, the objective function is to maximize the buckling load factor and the design variables are the fibre orientation angles in the layers. Computer programming is developed in the MATLAB environment to estimate optimum stacking sequences of laminated plates. A comparison also has been performed between the TLBO, genetic algorithm (GA) and differential evolution algorithm (DE). Some examples are solved to show the applicability and usefulness of the TLBO for maximizing the buckling load of the plate via finding optimum stacking sequences of the plate. Additionally, the influences of different number of layers, plate aspect ratios, foundation parameters and load ratios on the optimal solutions are investigated.

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

• Journal of Korean Society of Steel Construction
• /
• v.18 no.2
• /
• pp.161-171
• /
• 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
• /
• v.17 no.1
• /
• pp.1-19
• /
• 2014

Buckling and vibration characteristics of circular laminated plates under in-plane edge loads and resting on Winkler-type foundation are solved by the Ritz method. Inclusive numerical data are presented for the first three eigen-frequencies as a function of in-plane load for different classical edge conditions. Moreover, the effects of fiber orientation on the natural frequencies and critical buckling loads of laminated angle-ply plates with stacking sequence of $[({\beta}/-{\beta}/{\beta}/-{\beta})]_s$, are studied. Also, selected deformation mode shapes are illustrated. The correctness of results is established using finite element software as well as by comparison with the existing results in the literature.

• Steel and Composite Structures
• /
• v.22 no.6
• /
• pp.1261-1280
• /
• 2016

We study chaotic motion in a nonlinear laminated composite plate under subsonic fluid flow and a simultaneous external load in this paper. We derive equations of motion of the plate using the von-$K{\acute{a}}rm{\acute{a}}n^{\prime}s$ hypothesis and the Hamilton's principle. Galerkin's approach is adopted as the solution method. We then conduct a divergence analysis to obtain critical velocities of the transient flow. Melnikov's integral approach is used to find the critical parameters in which chaos takes place. Effects of different parameters including the aspect ratio, plate material and the ply angle in laminates on the critical flow speed are investigated. In a parametric study, we show that how the linear and nonlinear stiffness of the plate and the load frequency and amplitude would influence the chaotic behavior of the plate.