• 한국전산유체공학회:학술대회논문집
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• 2011.05a
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• pp.382-386
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• 2011

In this study, a CFD code is developed to perform simulation of the surface and internal flow of a three-dimensional rectangular cavity driven by an external gas flow. Investigated in this study are surface characteristic such as surface tension, surface dilational viscosity(or surface elasticity), and surface viscosity. Visualization of the surface of water is performed to compare with the numerical results obtained with the developed in-house code. We have found that the surface flow is very sensitive to the surface tension and other configurations. The surface flow velocity obtained from the numerical solution is lower than the experimental result.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.1
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• pp.65-76
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• 1994

A higher-oder laminated plate theory including the effect of transverse shear deformation is developed to calculate the gross response and the detailed stress distribution. The theory satisfies the continuity condition of transverse shear stress, and accounts for parabolic variation of the transverse shear stresses through the thickness of each layer. Exact closed-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and a simple higher-order theory solutions. The results of the present work exhibit acceptable accuracy when compared to the three-dimensional elasticity solutions.

• Interaction and multiscale mechanics
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• v.3 no.2
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• pp.123-143
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• 2010

The essential idea of the element-free Galerkin method (EFG) is that moving least-squares (MLS) approximation are used for the trial and test functions with the variational principle (weak form). By using the weighted orthogonal basis function to construct the MLS interpolants, we derive the formulae for an improved element-free Galerkin (IEFG) method for solving three-dimensional problems in linear elasticity. There are fewer coefficients in improved moving least-squares (IMLS) approximation than in MLS approximation. Also fewer nodes are selected in the entire domain with the IEFG method than is the case with the conventional EFG method. In this paper, we selected a few example problems to demonstrate the applicability of the method.

• Structural Engineering and Mechanics
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• v.50 no.6
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• pp.773-796
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• 2014

This paper deals with free vibration analysis of continuous grading fiber reinforced (CGFR) and bi-directional FG annular sector plates on two-parameter elastic foundations under various boundary conditions, based on the three-dimensional theory of elasticity. The plates with simply supported radial edges and arbitrary boundary conditions on their circular edges are considered. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. Results indicate that the non-dimensional natural frequency parameter of a functionally graded fiber volume fraction is larger than that of a discrete laminated and close to that of a 2-layer. It results that the CGFR plate attains natural frequency higher than those of traditional discretely laminated composite ones and this can be a benefit when higher stiffness of the plate is the goal and that is due to the reduction in spatial mismatch of material properties. Moreover, it is shown that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional one-dimensional functionally graded material. The multidirectional graded material can likely be designed according to the actual requirement and it is a potential alternative to the unidirectional functionally graded material. The new results can be used as benchmark solutions for future researches.

• Structural Engineering and Mechanics
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• v.69 no.5
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• pp.487-497
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• 2019

Rapid advances in the engineering applications can bring further areas to provide the opportunity to manipulate anisotropic structures for direct productivity in design of micro/nano-structures. For the first time, magnetic affected wave characteristics of nanosize plates made of anisotropic material is investigated via the three-dimensional bi-Helmholtz nonlocal strain gradient theory. Three small scale parameters are used to predict the size-dependent behavior of the nanoplates more accurately. After owing governing equations of wave motion, an analytical approach based harmonic series is utilized to fine the wave frequency as well as phase velocity. It is observed that the small scale parameters, magnetic field and wave number have considerable influence on the wave characteristics of anisotropic nanoplates. Due to the lack of any study on the mechanics of three-dimensional bi-Helmholtz gradient plates made of anisotropic materials, it is hoped that the present exact model may be used as a benchmark for future works of such nanostructures.

• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.239-263
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• 2016

The paper studies the natural oscillation of the three-layered solid sphere with a middle layer made of Functionally Graded Material (FGM). It is assumed that the materials of the core and outer layer of the sphere are homogeneous and isotropic elastic. The three-dimensional exact equations and relations of linear elastodynamics are employed for the investigations. The discrete-analytical method proposed by the first author in his earlier works is applied for solution of the corresponding eigenvalue problem. It is assumed that the modulus of elasticity, Poisson's ratio and density of the middle-layer material vary continuously through the inward radial direction according to power law distribution. Numerical results on the natural frequencies related to the torsional and spheroidal oscillation modes are presented and discussed. In particular, it is established that the increase of the modulus of elasticity (mass density) in the inward radial direction causes an increase (a decrease) in the values of the natural frequencies.

• Steel and Composite Structures
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• v.25 no.3
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• pp.361-374
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• 2017

In this study, the influences of triaxial magnetic field on the wave propagation behavior of anisotropic nanoplates are studied. In order to include small scale effects, nonlocal strain gradient theory has been implemented. To study the nanoplate as a continuum model, the three-dimensional elasticity theory is adopted in Cartesian coordinate. In our study, all the elastic constants are considered and assumed to be the functions of (x, y, z), so all kind of anisotropic structures such as hexagonal and trigonal materials can be modeled, too. Moreover, all types of functionally graded structures can be investigated. eigenvalue method is employed and analytical solutions for the wave propagation are obtained. To justify our methodology, our results for the wave propagation of isotropic nanoplates are compared with the results available in the literature and great agreement is achieved. Five different types of anisotropic structures are investigated in present paper and then the influences of wave number, material properties, nonlocal and gradient parameter and uniaxial, biaxial and triaxial magnetic field on the wave propagation analysis of anisotropic nanoplates are presented. From the best knowledge of authors, it is the first time that three-dimensional elasticity theory and nonlocal strain gradient theory are used together with no approximation to derive the governing equations. Moreover, up to now, the effects of triaxial magnetic field have not been studied with considering size effects in nanoplates. According to the lack of any common approximations in the displacement field or in elastic constant, present theory has the potential to be used as a bench mark for future works.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.193-212
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• 2004

A new model of generalized thermoelasticity equations for isotropic media with temperature-dependent mechanical properties is established. The modulus of elasticity is taken as a linear function of reference temperature. The present model is described both generalizations, Lord Shulman (L-S) theory with one relaxation time and Green-Lindsay (G-L) with two relaxation times, as well as the coupled theory, instantaneously. The method of the matrix exponential, which constitutes the basis of the state space approach of modern control theory, applied to two-dimensional equations. Laplace and Fourier integral transforms are used. The resulting formulation is applied to a problem of a thick plate subject to heating on parts of the upper and lower surfaces of the plate that varies exponentially with time. Numerical results are given and illustrated graphically for the problem considered. A comparison was made with the results obtained in case of temperature-independent modulus of elasticity in each theory.

• Steel and Composite Structures
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• v.43 no.1
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• pp.91-106
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• 2022

This paper has focused on presenting a three dimensional theory of elasticity for free vibration of 3D-graphene foam reinforced polymer matrix composites (GrF-PMC) cylindrical panels resting on two-parameter elastic foundations. The elastic foundation is considered as a Pasternak model with adding a Shear layer to the Winkler model. The porous graphene foams possessing 3D scaffold structures have been introduced into polymers for enhancing the overall stiffness of the composite structure. Also, 3D graphene foams can distribute uniformly or non-uniformly in the shell thickness direction. The effective Young's modulus, mass density and Poisson's ratio are predicted by the rule of mixture. Three complicated equations of motion for the panel under consideration are semi-analytically solved by using 2-D differential quadrature method. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. Because of using two-dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary at the curved edges. It is explicated that 3D-GrF skeleton type and weight fraction can significantly affect the vibrational characteristics of GrF-PMC panel resting on two-parameter elastic foundations.

• Steel and Composite Structures
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• v.27 no.2
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• pp.201-216
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• 2018

In this paper, three-dimensional (3D) elasticity theory in conjunction with nonlocal strain gradient theory (NSGT) is developed for mechanical analysis of anisotropic nanoparticles. The present model incorporates two scale coefficients to examine the mechanical characteristics much accurately. All the elastic constants are considered and assumed to be the functions of (r, ${\theta}$, ${\varphi}$), so all kind of anisotropic structures can be modeled. Moreover, all types of functionally graded spherical structures can be investigated. To justify our model, our results for the radial vibration of spherical nanoparticles are compared with experimental results available in the literature and great agreement is achieved. Next, several examples of the radial vibration and wave propagation in spherical nanoparticles including nonlocal strain gradient parameters are presented for more than 10 different anisotropic nanoparticles. From the best knowledge of authors, it is the first time that 3D elasticity theory and NSGT are used together with no approximation to derive the governing equations in the spherical coordinate. Moreover, up to now, the NSGT has not been used for spherical anisotropic nanoparticles. It is also the first time that all the 36 elastic constants as functions of (r, ${\theta}$, ${\varphi}$) are considered for anisotropic and functionally graded nanostructures including size effects. According to the lack of any common approximations in the displacement field or in elastic constant, present theory can be assumed as a benchmark for future works.