• Structural Engineering and Mechanics
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• v.62 no.3
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• pp.345-355
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• 2017

The aim of the present study is to develop an elemental approach based on the differential quadrature method for free vibration analysis of cracked thin plate structures. For this purpose, the equations of motion are established using the classical plate theory. The well-known Generalized Differential Quadrature Method (GDQM) is utilized to discretize the governing equations on each computational subdomain or element. In this method, the differential terms of a quantity field at a specific computational point should be expressed in a series form of the related quantity at all other sampling points along the domain. However, the existence of any geometric discontinuity, such as a crack, in a computational domain causes some problems in the calculation of differential terms. In order to resolve this problem, the multi-block or elemental strategy is implemented to divide such geometry into several subdomains. By constructing the appropriate continuity conditions at each interface between adjacent elements and a crack tip, the whole discretized governing equations of the structure can be established. Therefore, the free vibration analysis of a cracked thin plate will be provided via the achieved eigenvalue problem. The obtained results show a good agreement in comparison with those found by finite element method.

• Proceedings of the Korea Water Resources Association Conference
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• 2008.05a
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• pp.1624-1629
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• 2008

The governing equations in generalized curvilinear coordinates for a 3D pulsatile flow are the Incompressible Navier-Stokes (INS) equations with the artificial dissipative terms and continuity equation discretized using a second-order accurate, finite volume method on the nonstaggered computational grid. This method adopts a dual or pseudo time-stepping Artificial Compressibility (AC) method integrated in pseudo-time. The computational technique implements the implicit approximate factorization method of the Beam and Warming method (1978), which is the extension of the Alternate Direction Implicit (ADI) method. The algorithm yields practically identical velocity profiles and secondary flows that are in excellent overall agreement with an experimental measurement (Rindt & Steenhoven, 1991).

• Proceedings of the KSR Conference
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• 1998.05a
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• pp.299-306
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• 1998

Design sensitivity analysis of a mechanical system is an essential tool for design optimization and trade-off studies. This paper presents an efficient algorithm for the design sensitivity analysis of railway vehicle systems, using the direct differentiation method. The cartesian coordinate is employed as the generalized coordinate. The governing equations of the design sensitivity analysis are formulated as the differential equations. Design sensitivity analysis of railway vehicle systems is performed to show the validity and efficiency of the proposed method.

• Structural Engineering and Mechanics
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• v.63 no.2
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• pp.161-169
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• 2017

In this paper, using consistent couple stress theory and Hamilton's principle, the free vibration analysis of Euler-Bernoulli nano-beams made of bi-directional functionally graded materials (BDFGMs) with small scale effects are investigated. To the best of the researchers' knowledge, in the literature, there is no study carried out into consistent couple-stress theory for free vibration analysis of BDFGM nanostructures with arbitrary functions. In addition, in order to obtain small scale effects, the consistent couple-stress theory is also applied. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-tensor is skew-symmetric by adopting the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in both axial and thickness directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of Hamilton principle. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of BDFG nano-beam. At the end, some numerical results are presented to study the effects of material length scale parameter, and inhomogeneity constant on natural frequency.

• Steel and Composite Structures
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• v.26 no.6
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• pp.663-672
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• 2018

This paper contains a consistent couple-stress theory to capture size effects in Euler-Bernoulli nano-beams made of three-directional functionally graded materials (TDFGMs). These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in all three axial, thickness and width directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of minimum potential energy. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of TDFG nano-beam. At the end, some numerical results are performed to investigate some effective parameter on buckling load. In this theory the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor.

• 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.

• Steel and Composite Structures
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• v.25 no.4
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• pp.415-426
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• 2017

The thermo-mechanical vibration behavior of two dimensional functionally graded (2D-FG) porous nanobeam is reported in this paper. The material properties of the nanobeam are variable along thickness and length of the nanobeam according to the power law function. The nanobeam is modeled within the framework of Timoshenko beam theory. Eringen's nonlocal elasticity theory is used to develop the governing equations. Using the generalized differential quadrature method (GDQM) the governing equations are solved. The effect of porosity, temperature distribution, nonlocal value, L/h, FG power indexes along thickness and length and are investigated using parametric studies.

• Steel and Composite Structures
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• v.39 no.5
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• pp.565-581
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• 2021

In this paper the buckling analysis of the nanoplate made of arbitrary bi-directional functionally graded (BDFG) materials with small scale effects are investigated. To study the small-scale effects on buckling load, the Eringen's nonlocal theory is applied. Employing the principle of minimum potential energy, the governing equations are obtained. Generalize differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the buckling load of BDFG nanoplates. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. Comparison between the results of GDQ method and other papers for buckling analysis of a simply supported rectangular nano FGM plate reveals the accuracy of GDQ method. At the end some numerical results are presented to study the effects of material length scale parameter, plate thickness, aspect ratio, Poisson's ratio boundary condition and side to thickness ratio on size dependent Frequency.

• Earthquakes and Structures
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• v.24 no.2
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• pp.111-126
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• 2023

Highly reliable and versatile methods artificial intelligence (AI) have found multiple application in the different fields of science, engineering and health care system. In the present study, we aim to utilize AI method to investigated vibrations in the human leg bone. In this regard, the bone geometry is simplified as a thick cylindrical shell structure. The deep neural network (DNN) is selected for prediction of natural frequency and critical buckling load of the bone cylindrical model. Training of the network is conducted with results of the numerical solution of the governing equations of the bone structure. A suitable optimization algorithm is selected for minimizing the loss function of the DNN. Generalized differential quadrature method (GDQM), and Hamilton's principle are used for solving and obtaining the governing equations of the system. As well as this, in the results section, with the aid of AI some predictions for improving the behaviors of the various sport systems will be given in detail.

• Advances in nano research
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• v.12 no.2
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• pp.167-183
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• 2022

In this paper, the free and forced vibration analysis of rotating cantilever nanoscale cylindrical beams and tubes is investigated under the external dynamic load to examine the nonlocal effect. A couple of nonlocal strain gradient theories with different beams and tubes theories, involving the Euler-Bernoulli, Timoshenko, Reddy beam theory along with the higher-order tube theory, are assumed to the mathematic model of governing equations employing the Hamilton principle in order to derive the nonlocal governing equations related to the local and accurate nonlocal boundary conditions. The two-dimensional functional graded material (2D-FGM), made by the axially functionally graded (AFG) in conjunction with the porosity distribution in the radial direction, is considered material modeling. Finally, the derived Partial Differential Equations (PDE) are solved via a couple of the generalized differential quadrature element methods (GDQEM) with the Newmark-beta techniques for the time-dependent results. It is indicated that the boundary conditions equations play a crucial task in responding to nonlocal effects for the cantilever structures.