• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권2호
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• pp.67-78
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• 2010

An elastic field composed of symmetric cross-ply laminated material is analyzed in roller guided panel. The plane stress elasticity problem is formulated in terms of two displacement parameters with mixed boundary conditions. The numerical solution for two displacement parameters is obtained using a finite element method considering a panel of glass/epoxy laminated composite. Some components of stress and displacement at different sections of panel are displayed. The results makes sure that the formulation developed in this study can be applied to analyze the characteristics of elastic field made of laminated composite under any boundary conditions.

• International Journal of Aeronautical and Space Sciences
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• 제12권2호
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• pp.200-209
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• 2011

An analytical solution for rectangular laminated composite plates was obtained via a formal asymptotic method. From threedimensional static equilibrium equations, the microscopic one-dimensional and macroscopic two-dimensional equations were systematically derived by scaling of the thickness coordinate with respect to the characteristic length of the plate. The onedimensional through-the-thickness analysis was performed by applying a standard finite element method. The derived twodimensional plate equations, which take the form of recursive equations, were solved under sinusoidal loading with simplysupported boundary conditions. To demonstrate the validity and accuracy of the present method, various types of composite plates were studied, such as cross-ply, anti-symmetric angle-ply and sandwich plates. The results obtained were compared to those of the classical laminated plate theory, the first-order shear deformation theory and the three-dimensional elasticity. In the present analysis, the characteristic length of each composite was dependent upon the layup configurations, which affected the convergence rate of the method. The results shown herein are promising that it can serve as an efficient tool for the analysis and design of laminated composite plates.

• Structural Engineering and Mechanics
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• 제40권2호
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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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• 제39권2호
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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.

• 한국소음진동공학회논문집
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• 제22권8호
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• pp.791-799
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• 2012

In this paper free vibration analysis of symmetric and cross-ply elastic laminated shells based on FSDT was performed through discretization of equations of motion and boundary condition. Structural model of laminated composite cylindrical shells subjected to a combination of magnetic and thermal fields is developed via Hamilton's variational principle. These coupled equations of motion are based on the electromagnetic equations(Faraday, Ampere, Ohm, and Lorenz equations) and thermal equations which are involved in constitutive equations. Variations of dynamic characteristics of composite shells with applied magnetic field, temperature gradient, and stacking sequence are investigated and pertinent conclusions are derived.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2012년도 춘계학술대회 논문집
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• pp.748-754
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• 2012

In this paper free vibration analysis of symmetric and cross-ply elastic laminated shells based on FSDT was performed through discretization of equations of motion and boundary condition. Model of laminated composite shells subjected to a combination of magnetic and thermal fields is developed. These coupled equations of motion are based on the electromagnetic equations (Faraday, Ampere, Ohm, and Lorenz equations) and thermal equations which are involved in constitutive equations. Dynamic characteristic of composite shells for change of magnetic fields is investigated.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2012년도 추계학술대회 논문집
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• pp.653-660
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• 2012

In this paper free vibration analysis of symmetric and cross-ply elastic laminated shells based on FSDT with two different boundary conditions(C-C, S-S) was performed through discretization of equations of motion and boundary condition. Model of laminated composite cylindrical shells subjected to a combination of magnetic and thermal fields is developed via Hamilton's variational principle. These coupled equations of motion are based on the electromagnetic equations (Faraday, Ampere, Ohm, and Lorenz equations) and thermal equations which are involved in constitutive equations. Variations of dynamic characteristics of composite shells with applied magnetic field, temperature gradient, and stacking sequence for each boundary conditions are investigated and pertinent conclusions are derived.

• Advances in Computational Design
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• 제3권2호
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• pp.113-132
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• 2018

This paper presents the vibration and harmonic analysis of orthotropic laminated composite plate. The response of plate is determined using Finite Element Method. The eight noded shell 281 elements are used to analyze the orthotropic plates and results are obtained so that the right choice can be made in applications such as aircrafts, rockets, missiles, etc. to reduce the vibration amplitudes. Initially the model response for orthotropic plate and harmonic response for isotropic plate is verified with the available literature. The results are in good agreement with the available literature. Numerical results for the natural frequency and harmonic response amplitude are presented. Effects of boundary conditions, thickness to width ratio and number of layers on natural frequency and harmonic response of the orthographic plates are also investigated. The natural frequency, mode shape and harmonic analysis of laminated composite plate has been determined using finite element package ANSYS.

• Steel and Composite Structures
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• 제21권2호
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• pp.373-394
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• 2016

The postbuckling behavior of laminated composite plates and shells, subjected to various shear loadings, is presented, using a modified 8-ANS method. The finite element, based on a modified first-order shear deformation theory, is further improved by the combined use of assumed natural strain method. We analyze the influence of the shell element with the various location and number of enhanced membrane and shear interpolation. Using the assumed natural strain method with proper interpolation functions, the present shell element generates neither membrane nor shear locking behavior even when full integration is used in the formulation. The effects of various types of lay-ups, materials and number of layers on initial buckling and postbuckling response of the laminated composite plates and shells for various shear loading have been discussed. In addition, the effect of direction of shear load on the postbuckling behavior is studied. Numerical results and comparisons of the present results with those found in the literature for typical benchmark problems involving symmetric cross-ply laminated composites are found to be excellent and show the validity of the developed finite element model. The study is relevant to the simulation of barrels, pipes, wing surfaces, aircrafts, rockets and missile structures subjected to intense complex loading.

• 한국소음진동공학회논문집
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• 제23권9호
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• pp.797-805
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• 2013

In this paper vibration and stability analysis of laminated composite shells based on the first order shear deformation theory(FSDT) for two different boundary conditions(clamped-clamped, simply supported) are performed. Structural model of cross-ply symmetric laminated composite cylindrical shells subjected to a combination of magnetic and thermal fields is developed via Hamilton's variational principle. These coupled equations of motion are based on the electromagnetic equations(Faraday, Ampere, Ohm, and Lorenz equations)and thermal equations which are involved in constitutive equations. Extended Galerkin method is adopted to obtain the discretized equations of motion. Variations of dynamic characteristics of composite shells with applied magnetic field, temperature gradient, laminate thickness-ratio and radius ratio for two boundary conditions are investigated and pertinent conclusions are derived.