• Structural Engineering and Mechanics
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• 제67권5호
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• pp.517-525
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• 2018

In this study, we investigate the vibration of single-walled carbon nanotubes embedded in a polymeric matrix using nonlocal elasticity theories with account arbitrary boundary conditions effects. A Winkler type elastic foundation is employed to model the interaction of nanobeam and the surrounding elastic medium. Influence of all parameters such as nonlocal small-scale effects, Winkler modulus parameter, vibration mode and aspect ratio of nanobeam on the vibration frequency are analyzed and discussed. The mechanical properties of carbon nanotubes and polymer matrix are treated and an analytical solution is derived using the governing equations of the nonlocal Euler-Bernoulli beam models. Solutions have been compared with those obtained in the literature and The results obtained show that the non-dimensional natural frequency is significantly affected by the small-scale coefficient, the vibrational mode number and the elastic medium.

• 대한기계학회논문집A
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• 제23권6호
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• pp.1018-1025
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• 1999

For the effective analysis of two dimensional plane problems with geometrical discontinuities, singular finite element has been proposed. The element matrix equation was formulated on the basis of hybrid variational principle and Trefftz function sets derived consistently from the complex theory of plane elasticity by introducing a conformal mapping function. In order to suggest the accuracy characteristics of the proposed singular finite element, typical plane problems were analyzed and these results were compared with exact solutions. The singular finite element gives the comparatively exact values of stress concentration factors or stress intensity factors and can be effectively used for the analysis of mechanical structures containing various geometrical discontinuities.

• 대한기계학회논문집
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• 제16권12호
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• pp.2241-2251
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• 1992

본 연구에서는 Fig.1에서와 같은 축대칭 평판과 속이 찬 실린더(이하 단순히 실린더라고만 칭함)가 붙은 구조물에서 실린더의 끝단효과가 응력분포에 미치는 영향 을 해석해를 사용하여 고려해 보고자 한다. 이를 위해 얇은 평판에서는 2차원 고전 평판 이론을, 등방성 실린더에서는 끝단효과를 고려하기 위해서 3차원 선형 탄성이론 을 사용하고자 한다. 실린더와 평판의 접합부에서, 평판의 이차원 해와 실린더의 3 차원 해를 연결시키기 위해 접합부에서의 실린더의 유연성을 나타내는 유연성 행렬을 유도한다. 이러한 실린더의 유연성 행렬은 원형평판의 내부 경계조건으로 사용되는 데, 이와 유사한 해석절차는 셀구조물에 활용되어 왔다.

• Structural Engineering and Mechanics
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• 제13권1호
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• pp.103-116
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• 2002

A solution based on the linear three-dimensional theory of elasticity is developed for vibration and elastostatic problems of hollow toroids. The theory is developed for transversely isotropic toroids of arbitrary thickness, and has the potential to validate some vehicle and aircraft tire models in the linear range. In the semi-analytical method that is adopted Fourier series are written in the circumferential direction, forming a set of two-dimensional problems. These problems are solved using the differential quadrature method. A commercial finite element program is used to determine alternative solutions. For validation both problems of vibration and elastostatics are considered. Finally results are determined for local surface loading problems, and conclusions are drawn.

• Structural Engineering and Mechanics
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• 제9권2호
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• pp.153-168
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• 2000

This paper presents four incompatible but convergent Rational quadrilateral elements, two four-node elements (RQ4Z and RQ4B) and two five-node elements (RQ5Z and RQ5B). The difference between the so-called Rational Finite Element (Zhong and Zeng 1996) and the Free Formulation (Bergan and Nygard 1984) are discussed and compared. The importance of the mode completeness in these formulations is emphasized. Numerical results for several benchmark problems show the good performance of these elements. The two five-nodes elements RQ5Z and RQ5B, which can be viewed as complete quadratic mode elements (with seven stress modes), always give better results than the four nodes elements RQ4Z and RQ4B.

• Steel and Composite Structures
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• 제20권5호
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• pp.963-981
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• 2016

A nonlocal trigonometric shear deformation beam theory based on neutral surface position is developed for bending, buckling, and vibration of functionally graded (FG) nanobeams using the nonlocal differential constitutive relations of Eringen. The present model is capable of capturing both small scale effect and transverse shear deformation effects of FG nanobeams, and does not require shear correction factors. The material properties of the FG nanobeam are assumed to vary in the thickness direction. The equations of motion are derived by employing Hamilton's principle, and the physical neutral surface concept. Analytical solutions are presented for a simply supported FG nanobeam, and the obtained results compare well with those predicted by the nonlocal Timoshenko beam theory.

• Structural Engineering and Mechanics
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• 제46권6호
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• pp.827-842
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• 2013

In this paper, the wave propagation in generalized thermo elastic plate immersed in fluid is studied based on the Lord-Shulman (LS) and Green-Lindsay (GL) generalized two dimensional theory of thermo elasticity. Two displacement potential functions are introduced to uncouple the equations of motion. The frequency equations that include the interaction between the plate and fluid are obtained by the perfect-slip boundary conditions using the Bessel function solutions. The numerical calculations are carried out for the material Zinc and the computed non-dimensional frequency, phase velocity and attenuation coefficient are plotted as the dispersion curves for the plate with thermally insulated and isothermal boundaries. The wave characteristics are found to be more stable and realistic in the presence of thermal relaxation times and the fluid interaction.

• 항공우주시스템공학회지
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• 제1권1호
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• pp.25-35
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• 2007

In this paper, the interlaminar crack problems of a fiber metal laminate (FML) under generalized plane deformation are studied using the theory of anisotropic elasticity. The crack is considered to be embedded in the matrix interlaminar region (including adhesive zone and resin rich zone) of the FML. Based on Fourier integral transformation and the stress matrix formulation, the current mixed boundary value problem is reduced to solving a system of Cauchy-type singular integral equations of the 1st kind. Within the theory of linear fracture mechanics, the stress intensity factors are defined on terms of the solutions of integral equations and numerical results are obtained for in-plane normal (mode I) crack surface loading. The effects of location and length of crack in the 3/2 and 2/1 ARALL, GLARE or CARE type FML's on the stress intensity factors are illustrated.

• Structural Engineering and Mechanics
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• 제64권4호
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• pp.505-513
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• 2017

In this paper, a receding contact problem for an elastic layer resting on a half plane is considered. The layer is pressed by two rectangular stamps placed symmetrically. It is assumed that the contact surfaces are frictionless and only compressive traction can be transmitted through the contact surfaces. In addition the effect of body forces is neglected. Firstly, the problem is solved analytically based on theory of elasticity. In this solution, the problem is reduced into a system of singular integral equations in which half contact length and contact pressures are unknowns using boundary conditions and integral transform techniques. This system is solved numerically using Gauss-Jacobi integral formulation. Secondly, two dimensional finite element analysis of the problem is carried out using ANSYS. The dimensionless quantities for the contact length and the contact pressures are calculated under various stamp size, stamp position and material properties using both solutions. The analytic results are verified by comparison with finite element results.

• Structural Engineering and Mechanics
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• 제4권5호
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• pp.469-484
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• 1996

Green's functions are obtained in exact closed-forms for the elastic fields in bi-material elastic solids with slipping interface and differing transversely isotropic properties induced by concentrated point and ring force vectors. For the concentrated point force vector, the Green functions are expressed in terms of elementary harmonic functions. For the concentrated ring force vector, the Green functions are expressed in terms of the complete elliptic integral. Numerical results are presented to illustrate the effect of anisotropic bi-material properties on the transmission of normal contact stress and the discontinuity of lateral displacements at the slipping interface. The closed-form Green's functions are systematically presented in matrix forms which can be easily implemented in numerical schemes such as boundary element methods to solve elastic problems in computational mechanics.