• Structural Engineering and Mechanics
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• v.70 no.3
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• pp.325-337
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• 2019

In the present article, cross ply laminated composite plates are considered and a simple sinusoidal shear deformation model is tested for analyzing their flexural, stability and dynamic behaviors. The model contains only four unknown variables that are five in the first order shear deformation theory (FSDT) or other higher order models. The in-plane kinematic utilizes undetermined integral terms to quantitatively express the shear deformation influence. In the proposed theory, the conditions of zero shear stress are respected at bottom and top faces of plates without considering the shear correction coefficient. Equations of motion according to the proposed formulation are deduced by employing the virtual work principle in its dynamic version. The analytical solution is determined via double trigonometric series proposed by Navier. The stresses, displacements, natural frequencies and critical buckling forces computed using present method are compared with other published data where a good agreement between results is demonstrated.

• Smart Structures and Systems
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• v.26 no.3
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• pp.311-318
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• 2020

The goal of this study is to analytically and non-stochastically generate structural uncertainty behaviors of isotropic beams and laminated composite plates under plane stress conditions by using an interval finite element method. Uncertainty parameters of structural properties considering resistance and load effect are formulated by interval arithmetic and then linked to the finite element method. Under plane stress state, the isotropic cantilever beam is modeled and the laminated composite plate is cross-ply lay-up [0/90]. Triangular shape with a clamped-free boundary condition is given as geometry. Through uncertainties of both Young's modulus for resistance and applied forces for load effect, the change of structural maximum deflection and maximum von-Mises stress are analyzed. Numerical applications verify the effective generation of structural behavior uncertainties through the non-stochastic approach using interval arithmetic and immediately the feasibility of the present method.

• Advanced Composite Materials
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• v.17 no.1
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• pp.57-73
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• 2008

The present paper focuses on experimental verification of the ply-by-ply basis inelastic analysis of multidirectional laminates. First of all, rate dependence of the tensile behavior of balanced symmetric cross-ply T800H/epoxy laminates with a $[0/90]_{3S}$ lay-up under off-axis loading conditions at $100^{\circ}C$ is examined. Uniaxial tension tests are performed on plain coupon specimens with various fiber orientations $[{\theta}/(90-{\theta})]_{3S}$ ($\theta$ = 0, 5, 15, 45 and $90^{\circ}C$) at two different strain rates (1.0 and 0.01%/min). The off-axis stress.strain curves exhibit marked nonlinearity for all the off-axis fiber orientations except for the on-axis fiber orientations $\theta$ = 0 and $90^{\circ}$, regardless of the strain rates. Strain rate has significant influences not only on the off-axis flow stress in the regime of nonlinear response but also on the apparent off-axis elastic modulus in the regime of initial linear response. A macromechanical constitutive model based on a ply viscoplasticity model and the classical laminated plate theory is applied to predictions of the rate-dependent off-axis nonlinear behavior of the cross-ply CFRP laminate. The material constants involved by the ply viscoplasticity model are identified on the basis of the experimental results on the unidirectional laminate of the same carbon/epoxy system. It is demonstrated that good agreements between the predicted and observed results are obtained by taking account of the fiber rotation induced by deformation as well as the rate dependence of the initial Young's moduli.

• Steel and Composite Structures
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• v.26 no.4
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• pp.473-484
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• 2018

Free vibration of cross-ply laminated plates using a higher-order shear deformation theory is studied. The arbitrary number of layers is oriented in symmetric and anti-symmetric manners. The plate kinematics are based on higher-order shear deformation theory (HSDT) and the vibrational behaviour of multi-layered plates are analysed under simply supported boundary conditions. The differential equations are obtained in terms of displacement and rotational functions by substituting the stress-strain relations and strain-displacement relations in the governing equations and separable method is adopted for these functions to get a set of ordinary differential equations in term of single variable, which are coupled. These displacement and rotational functions are approximated using cubic and quantic splines which results in to the system of algebraic equations with unknown spline coefficients. Incurring the boundary conditions with the algebraic equations, a generalized eigen value problem is obtained. This eigen value problem is solved numerically to find the eigen frequency parameter and associated eigenvectors which are the spline coefficients.The material properties of Kevlar-49/epoxy, Graphite/Epoxy and E-glass epoxy are used to show the parametric effects of the plates aspect ratio, side-to-thickness ratio, stacking sequence, number of lamina and ply orientations on the frequency parameter of the plate. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.8
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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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2012.04a
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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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2012.10a
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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.

• Steel and Composite Structures
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• v.21 no.2
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.7
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• pp.2223-2233
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• 1996

The analytical solutions for the free vibration of cross-ply laminated composite cyllindrical shell with axial stiffeners(stringers) are presented usint the energy method. The stiffeners are taken to be smeared over the surface of shell with the smeared stffener theory. The effect of the parameters such as the stacking sequences, the shell thichness, the shell radius-to stringer depth ratio, the stringer depth-to width ratio, the shell length-to radius ratio are studied. By comparison with the previously published experimental results and the analytical results for the stiffened isotropic cylindrical shell and the unstiffened orthotropic composite laminated cylindrical shell, it is shown that natural frequencies can be determined with adequate accuracy.

• Steel and Composite Structures
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• v.37 no.1
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• pp.37-49
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• 2020

In this paper, free vibration finite element analysis of axially moving laminated composite beams subjected to axial tension is studied. It is assumed that the beam has a constant axial velocity and is subject to uniform axial tension. The analysis is based on higher-order theories that have been presented by Carrera Unified Formulation (CUF). In the CUF technique, the three dimensional (3D) displacement fields are expressed as the approximation of the arbitrary order of the displacement unknowns over the cross-section. This higher-order expansion is considered in equivalent single layer (ESL) model. The governing equations of motion are obtained via Hamilton's principle. Finally, several numerical examples are presented and the effect of the ply-angle, travelling speed and axial tension on the natural frequencies and beam stability are demonstrated.