• Structural Engineering and Mechanics
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• v.90 no.5
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• pp.517-530
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• 2024

This paper presents a new four-unknown equivalent single layer (ESL) refined plate theory for the buckling analysis of functionally graded (FG) rectangular plates with all simply supported edges and subjected to in-plane mechanical loading conditions. The present model accounts for a parabolic variation of transverse shear stress over the thickness, and accommodates correctly the zero shear stress conditions on the top and bottom surfaces of the plate. The material properties are supposed to vary smoothly in the thickness direction through the rules of mixture named power-law gradation. The governing equilibrium equations are formulated based on the total potential energy principle and solved for simply supported boundary conditions by implementing the Navier's method. A numerical result on elastic buckling using the current theory was computed and compared with those published in the literature to examine the accuracy of the proposed analytical solution. The effects of changing power-law exponent, aspect ratio, thickness ratio and modulus ratio on the critical buckling load of FG plates under different in-plane loading conditions are investigated in detail. Moreover, it was found that the geometric parameters and power-law exponent play significant influences on the buckling behavior of the FG plates.

• Water for future
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• v.24 no.4
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• pp.41-48
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• 1991

This paper describes the characteristics of tidal currents in the Gamag Bay by using the two-dimensional nonlinear hydrodynamic euation. The basic equations are derived by Navier-Stokes momentum equation and continuity equation and its characteristics critically are reviewed, and they are analysed by the implicit finite difference method. The numerical model is constructed two-dimensional(depth-averaged) simple layer model. This paper investigates the stability of solution and convergence of solution in application of the method to Gamag Bay, and the reproducibility of the simulation is also discussed in comparison with the results of field survey. The following items are clarifide through the numerical investigation; i)the reproduc-ibility of tidal range and currents are quite acceptable, comparing with the results of model tests and field data, and ii) tidal cycle for convergent solution is four tidal cycle, also, iii) bottom friction is successfully represented as c=(1/n))$h^{1/6}$.

• Structural Engineering and Mechanics
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• v.12 no.2
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• pp.135-156
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• 2001

Analytical solutions and finite element results of laminated composite plates with smart material layers embedded in them are presented in this study. The third-order plate theory of Reddy is used to study vibration suppression characteristics. The analytical solution for simply supported boundary conditions is based on the Navier solution procedure. The velocity feedback control is used. Parametric effects of the position of the smart material layers, material properties, and control parameters on the suppression time are investigated. It has been found that (a) the minimum vibration suppression time is achieved by placing the smart material layers farthest from the neutral axis, (b) using thinner smart material layers have better vibration attenuation characteristics, and, (c) the vibration suppression time is larger for a lower value of the feedback control coefficient.

• Computers and Concrete
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• v.21 no.1
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• pp.31-37
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• 2018

This paper deals with the stability analysis of concrete pipes mixed with nanoparticles conveying fluid. Instead of cement, the $Fe_2O_3$ nanoparticles are used in construction of the concrete pipe. The Navier-Stokes equations are used for obtaining the radial force of the fluid. Mori-Tanaka model is used for calculating the effective material properties of the concrete $pipe-Fe_2O_3$ nanoparticles considering the agglomeration of the nanoparticles. The first order shear deformation theory (FSDT) is used for mathematical modeling of the structure. The motion equations are derived based on energy method and Hamilton's principal. An exact solution is used for stability analysis of the structure. The effects of fluid, volume percent and agglomeration of $Fe_2O_3$ nanoparticles, magnetic field and geometrical parameters of pipe are shown on the stability behaviour of system. Results show that considering the agglomeration of $Fe_2O_3$ nanoparticles, the critical fluid velocity of the concrete pipe is decreased.

• Smart Structures and Systems
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• v.13 no.4
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• pp.637-657
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• 2014

This paper presents a dynamic analysis of three-dimensional beams. Structures made of functionally graded materials are considered. Several higher-order as well as classical theories are derived by means of a compact notation for the a-priori expansion order of the displacement field over the beam cross-section. The governing differential equations and boundary conditions are obtained in a condensed nuclear form that does not depend on the kinematic hypotheses. The problem is, then, exactly solved in space by means of a Navier-type solution, whereas time integration is performed by means of Newmark's solution scheme. Slender and short simply supported beams are investigated. Results are validated towards three-dimensional FEM results obtained via the commercial software ANSYS. Numerical investigations show that good accuracy can be obtained through the proposed formulation provided that the appropriate expansion order is considered.

• Smart Structures and Systems
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• v.17 no.2
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• pp.257-274
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• 2016

The nonlocal static bending, buckling, free and forced vibrations of graphene nanosheets are examined based on the Kirchhoff plate theory and Taylor expansion approach. The nonlocal nanoplate model incorporates the length scale parameter which can capture the small scale effect. The governing equations are derived using Hamilton's principle and the Navier-type solution is developed for simply-supported graphene nanosheets. The analytical results are proposed for deflection, natural frequency, amplitude of forced vibration and buckling load. Moreover, the effects of nonlocal parameter, half wave number and three-dimensional sizes on the static, dynamic and stability responses of the graphene nanosheets are discussed. Some illustrative examples are also addressed to verify the present model, methodology and solution. The results show that the new nanoplate model produces larger deflection, smaller circular frequencies, amplitude and buckling load compared with the classical model.

• Structural Engineering and Mechanics
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• v.70 no.5
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• pp.571-589
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• 2019

This paper aims to develop a quasi-3D shear deformation theory for the study of bending, buckling and free vibration responses of functionally graded (FG) sandwich thick plates. For that, in the present theory, both the components of normal deformation and shear strain are included. The displacement field of the proposed model contains undetermined integral terms and involves only four unknown functions with including stretching effect. Using Navier's technique the solution of the problem is derived for simply supported sandwich plate. Numerical results have been reported, and compared with those available in the open literature were excellent agreement was observed. Finally, a detailed parametric study is presented to demonstrate the effect of the different parameters on the flexural responses, free vibration and buckling of a simply supported sandwich plates.

• Advances in concrete construction
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• v.15 no.4
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• pp.269-286
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• 2023

In the present study, we aim to utilize the numerical solution frequency results of functionally graded beam under thermal and dynamic loadings to train and test an artificial neural network. In this regard, shear deformable functionally-graded beam structure is considered for obtaining the natural frequency in different conditions of boundary and material grading indices. In this regard, both analytical and numerical solutions based on Navier's approach and differential quadrature method are presented to obtain effects of different parameters on the natural frequency of the structure. Further, the numerical results are utilized to train an artificial neural network (ANN) using AdaGrad optimization algorithm. Finally, the results of the ANN and other solution procedure are presented and comprehensive parametric study is presented to observe effects of geometrical, material and boundary conditions of the free oscillation frequency of the functionally graded beam structure.

• Advances in nano research
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• v.10 no.3
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• pp.235-251
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• 2021

In the current study, the free vibrational behavior of a Porous Micro (PM) beam which is integrated with Functionally Graded Piezoelectric (FGP) layers with initial curvature is considered based on the two trigonometric shear deformation theories namely SSDBT and Tan-SDBT. The structure's mechanical properties are varied through its thicknesses following the given functions. The curved microbeam is exposed to electro-mechanical preload and also is rested on a Pasternak type of elastic foundation. Hamilton's principle is used to extract the motion equations and the MCST is used to capture the size effect. Navier's solution method is selected as an analytical method to solve the motion equations for a simply supported ends case and by validating the results for a simpler state with previously published works, effects of different important parameters on the behavior of the structure are considered. It is found that although increasing the porosity reduces the natural frequency, but enhancing the volume fraction of CNTs increasing it. Also, by increasing the central angle of the curved beam the vibrations of the structure increases. Designing and manufacturing more efficient smart structures such as sensors and actuators are of the aims of this study.

• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.145-150
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• 2005

Generally, Compressible Navier-Stokes codes are used to solve high mach number flows. But, Most of high mach number flows embrace low mach number flows. This phenomenon results in low convergence rate and non-physical solution in CFD analysis. So Many researchers developed preconditioning technique to solve these problems. This Study presents how to modify previous compressible N-S computer code with little changes of structure into preconditioned compressible N-S code applying Roe's Approximate Riemann Solver. And this study show developed preconditioning code is very well operated at all mach number flows.