• Structural Engineering and Mechanics
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• v.31 no.5
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• pp.481-506
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• 2009

The present study is concerned with the stochastic linear free vibration study of laminated composite plate embedded with piezoelectric layers with random material properties. The system equations are derived using higher order shear deformation theory. The lamina material properties of the laminate are modeled as basic random variables for accurate prediction of the system behavior. A $C^0$ finite element is used for spatial descretization of the laminate. First order Taylor series based mean centered perturbation technique in conjunction with finite element method is outlined for the problem. The outlined probabilistic approach is used to obtain typical numerical results, i.e., the mean and standard deviation of natural frequency. Different combinations of simply supported, clamped and free boundary conditions are considered. The effect of side to thickness ratio, aspect ratio, lamination scheme on scattering of natural frequency is studied. The results are compared with those available in literature and an independent Monte Carlo simulation.

• Steel and Composite Structures
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• v.34 no.5
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• pp.733-742
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• 2020

Vibration analysis in nanocomposite plate with smart layer is studied in this article. The plate is reinforced by carbon nanotubes where the Mori-Tanaka law is utilized for obtaining the effective characteristic of structure assuming agglomeration effects. The nanocomposite plate is located in elastic medium which is simulated by spring element. The motion equations are derived based on first order shear deformation theory and Hamilton's principle. Utilizing Navier method, the frequency of the structure is calculated and the effects of applied voltage, volume percent and agglomeration of Carbon nanotubes, elastic medium and geometrical parameters of structure are shown on the frequency of system. Results indicate that with applying negative voltage, the frequency of structure is increased. In addition, the agglomeration of carbon nanotubes reduces the frequency of the nanocomposite plate.

• Coupled systems mechanics
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• v.1 no.2
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• pp.115-131
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• 2012

Paper presents an improved solution algorithm based on Finite Element Method to analyse piled raft foundation. Piles are modelled as beam elements with soil springs. Finite element analysis of raft is based on the classical theory of thick plates resting on Winkler foundation that accounts for the transverse shear deformation of the plate. Four node, isoparametric rectangular elements with three degrees of freedom per node are considered in the development of finite element formulation. Independent bilinear shape functions are assumed for displacement and rotational degrees of freedom. Effect of raft thickness, soil modulus and load pattern on the response is considered. Significant improvement in the settlements and moments in the raft is observed.

• Advances in aircraft and spacecraft science
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• v.5 no.6
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• pp.691-729
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• 2018

In this paper the hygro-thermo-mechanical vibration and buckling behavior of embedded FG nano-plates are investigated. The Eringen's and Gurtin-Murdoch theories are applied to study the small scale and surface effects on frequencies and critical buckling loads. The effective material properties are modeled using Mori-Tanaka homogenization scheme. On the base of RPT and HSDPT plate theories, the Hamilton's principle is employed to derive governing equations. Using iterative and GDQ methods the governing equations are solved and the influence of different parameters on natural frequencies and critical buckling loads are studied.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.539-543
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• 2011

LNG cargo containment system (CCS) has the primary function of ensuring adequate thermal insulation with keeping natural gas below its boiling point. From the viewpoint of structural design, this LNG CCS can be treated as a laminated composite structure showing complex structural responses under the sloshing load which can be defined as a violent behavior of the liquid contents in cargo tanks due to external forced motions. As LNG CCS type, Mark III containment system from TGZ is considered in this paper and then its structural strength assessment is performed based on a simple higher-order shear deformation theory and maximum stress, maximum strain, Tsai-Wu failure criteria developed for laminated composite plates. The assessment is performed to the initial failure of the Mark III CS plate by investigating failure locations and loads.

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

• Geomechanics and Engineering
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• v.13 no.6
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• pp.1027-1044
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• 2017

Membrane penetration is the most important factor influencing the measurement of volume change for triaxial consolidated-drained shear test for coarse-grained soil. The effective pressure p, average particle size $d_{50}$, thickness $t_m$ and elastic modulus $E_m$ of membrane, contact area between membrane and soil $A_m$ as well as the initial void ratio e are the major factors influencing membrane penetration. According to the membrane deformation model given by Kramer and Sivaneswaran, an analytical solution of the membrane penetration considering the initial void ratio is deduced using the energy conservation law. The basic equations from theory of plates and shells and the elastic mechanics are employed during the derivation. To verify the presented solution, isotropic consolidation tests of a coarse-grained soil are performed by using the method of embedding different diameter of iron rods in the triaxial samples, and volume changes due to membrane penetration are obtained. The predictions from presented solution and previous analytical solutions are compared with the test results. It is found that the prediction from presented analytical solution agrees well with the test results.

• Structural Engineering and Mechanics
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• v.5 no.4
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• pp.433-450
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• 1997

The objective of this work is to predict the failure loads, associated maximum transverse displacements, locations and the modes of failure, including the onset of delamination, of thin, flat, square symmetric laminates under the action of uni-axial compression. Two progressive failure analyses, one using Hashin criterion and the other using Tensor polynomial criteria, are used in conjunction with the finite element method. First order shear deformation theory and geometric nonlinearity in the von Karman sense have been employed. Five different types of lay-up sequence are considered for laminates with all edges simply supported. In addition, two boundary conditions, one with all edges fixed and other with mixed boundary conditions for $(+45/-45/0/90)_{2s}$ quasi-isotropic laminate have also been considered to study the effect of boundary restraints on the failure loads and the corresponding modes of failure. A comparison of linear and nonlinear results is also made for $({\pm}45/0/90)_{2s}$ quasi-isotropic laminate. It is observed that the maximum difference between the failure loads predicted by various criteria depend strongly on the laminate lay-ups and the flexural boundary restraints. Laminates with clamped edges are found to be more susceptible to failure due to the transverse shear and delamination, while those with the simply supported edges undergo total collapse at a load slightly higher than the fiber failure load.

• Steel and Composite Structures
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• v.44 no.5
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• pp.633-649
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• 2022

This paper is first implemented with the bending behavior of three-dimensional functionally graded (3DFG) plates in the framework of level set-based topology optimization (LS-based TO). Besides, due to the suitable properties of the current design domain, the thin-plate spline (TPS) is recognized as a RBF to construct the LS function. The overall mechanical properties of the 3DFG plate are assessed using a power-law distribution scheme via Mori-Tanaka micromechanical material model. The bending response is obtained using the first-order shear deformation theory (FSDT). The mixed interpolation of four elements of tensorial components (MITC4) is also implemented to overcome a well-known shear locking problem when the thickness becomes thinner. The Hamilton-Jacobi method is utilized in each iteration to enforce the necessary boundary conditions. The mathematical formulas are expressed in great detail for the LS-based TO using 3DFG materials. Several numerical examples are exhibited to verify the efficiency and reliability of the current methodology with the previously reported literature. Finally, the influences of FG materials in the optimized design are explained in detail to illustrate the behaviors of optimized structures.

• Journal of the Society of Naval Architects of Korea
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• v.29 no.1
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• pp.158-172
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• 1992

In ships and offshore structures, there are many local structures formed of thick plates and/or having the form of double wall panels. For the vibration analysis of such a kind of structures, Mindlin plate theory which includes the effects of shear deformation and rotary inertia is usually adopted. In this paper, the vibration and dynamic sensitivity analysis of Mindlin plates having the boundary conditions elastically restrained against rotation have been accomplished using the Rayleigh-Ritz method. Polynomials having the property of the Timoshenko beam functions are introduced and used as trial functions in the spatial representation of the deflection and rotations of cross sections in two directions of the plates. The results obtained by the introduced polynomials gave nearly the same numerical results as those by the Timoshenko beam functions with the remarkable reduction of computational efforts especially in the dynamic sensitivity analysis.