• Structural Engineering and Mechanics
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• v.66 no.5
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• pp.557-568
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• 2018

An investigation is made in the present work on the post-buckling and geometrically nonlinear behaviors of moderately thick perfect and imperfect rectangular plates made-up of functionally graded materials. Spectral collocation approach based on Legendre basis functions is developed to analyze the functionally graded plates while they are subjected to end-shortening strain. The material properties in this study are varied through the thickness according to the simple power law distribution. The fundamental equations for moderately thick rectangular plates are derived using first order shear deformation plate theory and taking into account both geometric nonlinearity and initial geometric imperfections. In the current study, the domain of interest is discretized with Legendre-Gauss-Lobatto nodes. The equilibrium equations will be obtained by discretizing the Von-Karman's equilibrium equations and also boundary conditions with finite Legendre basis functions that are substituted into the displacement fields. Due to effect of geometric nonlinearity, the final set of equilibrium equations is nonlinear and therefore the quadratic extrapolation technique is used to solve them. Since the number of equations in this approach will always be more than the number of unknown coefficients, the least squares technique will be used. Finally, the effects of boundary conditions, initial geometric imperfection and material properties are investigated and discussed to demonstrate the validity and capability of proposed method.

• Steel and Composite Structures
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• v.29 no.3
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• pp.319-332
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• 2018

This paper investigates the free vibration of geometrically imperfect functionally graded car-bon nanotube-reinforced composite (FG-CNTRC) beams that are integrated with two sur-face-bonded piezoelectric layers and subjected to a combined action of a uniform temperature rise, a constant actuator voltage and an in-plane force. The material properties of FG-CNTRCs are assumed to be temperature-dependent and vary continuously across the thick-ness. A generic imperfection function is employed to simulate various possible imperfections with different shapes and locations in the beam. The governing equations that account for the influence of initial geometric imperfection are derived based on the first-order shear deformation theory. The postbuckling configurations of FG-CNTRC hybrid beams are determined by the differential quadrature method combined with the modified Newton-Raphson technique, after which the fundamental frequencies of hybrid beams in the postbuckled state are obtained by a standard eigenvalue algorithm. The effects of CNT distribution pattern and volume fraction, geometric imperfection, thermo-electro-mechanical load, as well as boundary condition are examined in detail through parametric studies. The results show that the fundamental frequency of an imperfect beam is higher than that of its perfect counterpart. The influence of geometric imperfection tends to be much more pronounced around the critical buckling temperature.

• International Journal of Aeronautical and Space Sciences
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• v.12 no.2
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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.

• Journal of Ocean Engineering and Technology
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• v.17 no.2
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• pp.72-76
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• 2003

This paper presents the design concept and operation results of float-off for FSO (340,000 DWT Class, ELF AMENAM KPONO Project) built on the ground, without dry dock facilities. It was the first attempt to build FSO, completely, on the ground and launch it using DBU (Double Barge Unit, which was connected by rigid frame structure.) The major characteristics of FSO, which are similar to general VLCC type hull, including topside structure, weigh 51,000 metric ton. In order to have sufficient stability during the deck immersion of DBU, while passing through a minimum water plane area zone, proper trim control was completed with LMC (Load Master Computer). The major features of the monitoring system include calculation for transverse bending moment, shear force, local strength check of each connector, based on component stress, and deformation check during the load-out and float-off. Another major concern during the operation was to avoid damages at the bottom and sides of FSO, due to motion & movement after free-floating; therefore, adequate clearances between DBU and FSO were to be provided, and guide posts were installed to prevent side damage of the DBU casings. This paper also presents various measures that indecate the connector bending moment, damage stability analysis, and mooring of DBU during float off.

• Steel and Composite Structures
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• v.28 no.5
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• pp.541-557
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• 2018

This paper presents the influence of carbon nanotubes (CNTs) waviness and aspect ratio on the vibrational behavior of functionally graded nanocomposite sandwich annular sector plates resting on two-parameter elastic foundations. The carbon nanotube-reinforced (CNTR) sandwich plate has smooth variation of CNT fraction along the thickness direction. The distributions of CNTs are considered functionally graded (FG) or uniform along the thickness and their mechanical properties are estimated by an extended rule of mixture. In this study, the classical theory concerning the mechanical efficiency of a matrix embedding finite length fibers has been modified by introducing the tube-to-tube random contact, which explicitly accounts for the progressive reduction of the tubes' effective aspect ratio as the filler content increases. Effects of CNT distribution, volume fraction, aspect ratio and waviness, and also effects of Pasternak's elastic foundation coefficients, sandwich plate thickness, face sheets thickness and plate aspect ratio are investigated on the free vibration of the sandwich plates with wavy CNT-reinforced face sheets. The study is carried out based on three-dimensional theory of elasticity and in contrary to two-dimensional theories, such as classical, the first- and the higher-order shear deformation plate theories, this approach does not neglect transverse normal deformations. The sandwich annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free.

• Structural Engineering and Mechanics
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• v.74 no.6
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• pp.809-819
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• 2020

For the first time, the influence of in-plane magnetic field on wave propagation of Graphene Nano-Platelets (GNPs) polymer composite nanoplates is investigated here. The impact of three- parameter Kerr foundation is also considered. There are two different reinforcement distribution patterns (i.e. uniformly and non-uniformly) while the material properties of the nanoplate are estimated through the Halpin-Tsai model and a rule of mixture. To consider the size-dependent behavior of the structure, Eringen Nonlocal Differential Model (ENDM) is utilized. The equations of wave motion derived based on a higher-order shear deformation refined theory through Hamilton's principle and an analytical technique depending on Taylor series utilized to find the wave frequency as well as phase velocity of the GNPs reinforced nanoplates. A parametric investigation is performed to determine the influence of essential phenomena, such as the nonlocality, GNPs conditions, Kerr foundation parameters, and wave number on the both longitudinal and flexural wave characteristics of GNPs reinforced nanoplates.

• Structural Engineering and Mechanics
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• v.18 no.1
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• pp.41-58
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• 2004

The postbuckling behaviour of thin shells has fascinated researchers because the theoretical prediction and their experimental verification are often different. In reality, shell panels possess small imperfections and these can cause large reduction in static buckling strength. This is more relevant in thin laminated composite shells. To study the postbuckling behaviour of thin, imperfect laminated composite shells using finite elements, explicit incremental or secant matrices have been presented in this paper. These incremental matrices which are derived using Marguerre's shallow shell theory can be used in combination with any thin plate/shell finite element (Classical Laminated Plate Theory - CLPT) and can be easily extended to the First Order Shear deformation Theory (FOST). The advantage of the present formulation is that it involves no numerical approximation in forming total potential energy of the shell during large deformations as opposed to earlier approximate formulations published in the literature. The initial imperfection in shells could be modeled by simply adjusting the ordinate of the shell forms. The present formulation is very easy to implement in any existing finite element codes. The secant matrices presented in this paper are shown to be very accurate in tracing the postbuckling behaviour of thin isotropic and laminated composite shells with general initial imperfections.

• Structural Engineering and Mechanics
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• v.67 no.6
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• pp.617-628
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• 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
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• v.68 no.3
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• pp.359-368
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• 2018

This paper deals with the dynamic stability of nanocomposite pipes conveying pulsating ferrofluid. The pipe is reinforced by carbon nanotubes (CNTs) where the agglomeration of CNTs are considered based on Mori-Tanaka model. Due to the existence of CNTs and ferrofluid flow, the structure and fluid are subjected to axial magnetic field. Based on Navier-Stokes equation and considering the body forced induced by magnetic field, the external force of fluid to the pipe is derived. For mathematical modeling of the pipe, the first order shear deformation theory (FSDT) is used where the energy method and Hamilton's principle are used for obtaining the motion equations. Using harmonic differential quadrature method (HDQM) and Bolotin's method, the motion equations are solved for calculating the excitation frequency and dynamic instability region (DIR) of the structure. The influences of different parameters such as volume fraction and agglomeration of CNTs, magnetic field, structural damping, viscoelastic medium, fluid velocity and boundary conditions are shown on the DIR of the structure. Results show that with considering agglomeration of CNTs, the DIR shifts to the lower excitation frequencies. In addition, the DIR of the structure will be happened at higher excitation frequencies with increasing the magnetic field.

• Composites Research
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• v.25 no.6
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• pp.217-223
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• 2012

This study investigates a geometrical nonlinear dynamic behaviors of laminated skew plates made of advanced composite materials (ACM). Based on the first-order shear deformation plate theory (FSDT), the Newmark method and Newton-Raphson iteration are used for the nonlinear dynamic solution. The effects of cutout sizes, skew angles and lay up sequences on the nonlinear dynamic response for various parameters are studied using a nonlinear dynamic finite element program developed for this study. The several numerical results were in good agreement with those reported by other investigators for square composite plates with or without central cutouts, and the new results reported in this paper show the significant interactions between the cutout, skew angles and layup sequence in the laminate. Key observation points are discussed and a brief design guideline of skew laminates is given.