• Structural Engineering and Mechanics
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• 제49권5호
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• pp.661-672
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• 2014

Laminated Rectangular plates embedded in elastic foundations are used in many mechanical structures. This study presents an analytical approach for transverse bending analysis of an embedded symmetric laminated rectangular plate using Mindlin plate theory. The surrounding elastic medium is simulated using Pasternak foundation. Adopting the Mindlin plate theory, the governing equations are derived based on strain-displacement relation, energy method and Hamilton's principle. The exact analysis is performed for this case when all four ends are simply supported. The effects of the plate length, elastic medium and applied force on the plate transverse bending are shown. Results indicate that the maximum deflection of the laminated plate decreases when considering an elastic medium. In addition, the deflection of the laminated plate increases with increasing the plate width and length.

• Journal of Mechanical Science and Technology
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• 제16권5호
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• pp.655-665
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• 2002

Two-dimensional elastic analysis of doubly periodic circular holes in an infinite plane is given in this paper. Two cases of loading, remote tension and remote shear, are considered. A rectangular cell is cut from the infinite plane. In both cases, the boundary value problem can be reduced to a complex mixed one. It is found that the eigenfunction expansion variational method is efficient to solve the problem. Based on the deformation response under certain loading, the notched medium could be modeled by an orthotropic medium without holes. Elastic properties for the equivalent orthotropic medium are investigated, and the stress concentration along the hole contour is studied. Finally, numerical examples and results are given.

• 대한전자공학회논문지
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• 제13권6호
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• pp.1-6
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• 1976

탄성파 지연선의 진동자에서 전단과 지연매질사이의 접착제의 두께를 고려하여 변환손실을 계산하는 방법을 제안하며, 수치계산결과 접착제의 두께가 진동자 두께의 1/100정도 이하로 하여야 하며 전극의 두께가 진동자 두께의 1/10정도 될 때 중심주파수의 이동이 생진다. 접착제의 두께를 진동자와 거의 같거나 그 이상으로 하면 주파수 대역폭에서 현상이 점점 커지게 된다. In this paper, the methode of calculating conversion loss is proposed by considering the thickness of bonding medium between electrode and delay material in the vibrator of Elastic delay lines. As the result of computations using digital computer, it is shown that the thickness of bonding medium must be less than about 1/100 of the thickness of vibrator and when the thickness of electrode is about 1110 of vibrator, the center fnequency is shifted. When the thickness of bonding medium is equal to or more than the thickness of vibrator, the 리uctuations in frequency Bandwidth become larger and larger.

• Steel and Composite Structures
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• 제21권4호
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• pp.883-919
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• 2016

In this research, buckling analysis of an embedded laminated composite plate is investigated. The elastic medium is simulated with spring constant of Winkler medium and shear layer. With considering higher order shear deformation theory (Reddy), the total potential energy of structure is calculated. Using Principle of Virtual Work, the constitutive equations are obtained. The analytical solution is performed in order to obtain the buckling loads. A detailed parametric study is conducted to elucidate the influences of the layer numbers, orientation angle of layers, geometrical parameters, elastic medium and type of load on the buckling load of the system. Results depict that the highest buckling load is related to the structure with angle-ply orientation type and with increasing the angle up to 45 degrees, the buckling load increases.

• Structural Engineering and Mechanics
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• 제70권3호
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• pp.269-277
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• 2019

Using the non-local elasticity theory, Timoshenko beam model is developed to study the non- local buckling of Triple-walled carbon nanotubes (TWCNTs) embedded in an elastic medium under axial compression. The chirality and small scale effects are considered. The effects of the surrounding elastic medium based on a Winkler model and van der Waals' (vdW) forces between the inner and middle, also between the middle and outer nanotubes are taken into account. Considering the small-scale effects, the governing equilibrium equations are derived and the critical buckling loads under axial compression are obtained. The results show that the critical buckling load can be overestimated by the local beam model if the small-scale effect is overlooked for long nanotubes. In addition, significant dependence of the critical buckling loads on the chirality of zigzag carbon nanotube is confirmed. Furthermore, in order to estimate the impact of elastic medium on the non-local critical buckling load of TWCNTs under axial compression, the use of these findings are important in mechanical design considerations, improve and reinforcement of devices that use carbon nanotubes.

• Structural Engineering and Mechanics
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• 제62권1호
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• pp.113-123
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• 2017

The bi-material elastic system consisting of the circular hollow cylinder and the infinite elastic medium surrounding this cylinder is considered and it is assumed that on the inner free face of the cylinder a point-located axisymmetric time harmonic force, with respect to the cylinder's axis and which is uniformly distributed in the circumferential direction, acts. The shear-spring type imperfect contact conditions on the interface between the constituents are satisfied. The mathematical formulation of the problem is made within the scope of the exact equations of linear elastodynamics. The focus is on the frequency-response of the interface normal and shear stresses and the influence of the problem parameters, such as the ratio of modulus of elasticity, the ratio of the cylinder thickness to the cylinder radius, and the shear-spring type parameter which characterizes the degree of the contact imperfectness, on these responses. Corresponding numerical results are presented and discussed. In particular, it is established that the character of the influence of the contact imperfection on the frequency response of the interface stresses depends on the values of the vibration frequency of the external forces.

• Geomechanics and Engineering
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• 제14권1호
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• pp.19-27
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• 2018

It follows from the basic principles of mechanics of deformable solids relating to the strength, stability and propagation of elastic waves that the Earth's inner core cannot exist in the form of a spherical structure in the assumed thermobaric conditions and calculation values of physico-mechanical parameters. Pressure level reaches a value that is significantly greater than the theoretical limit of medium strength in the model approximations at the surface of the sphere of the inner core. On the other hand, equilibrium state of the sphere is unstable on the geometric forming at much lower loads under the influence of the "dead" surface loads. In case of the action of "follower" loads, the assumed pressure value on the surface of the sphere is comparable with the value of the critical load of "internal" instability. In these cases, due to the instability of the equilibrium state, propagation of homogeneous deformations becomes uneven in the sphere. Moreover, the elastic waves with actual velocity cannot propagate in such conditions in solid medium. Violation of these fundamental conditions of mechanics required in determining the physical and mechanical properties of the medium should be taken into account in the integrated interpretations of seismic and laboratory (experimental) data. In this case, application of the linear theory of elasticity and elastic waves does not ensure the reliability of results on the structure and composition of the Earth's core despite compliance with the required integral conditions on the mass, moment of inertia and natural oscillations of the Earth.

• Structural Engineering and Mechanics
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• 제64권4호
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• pp.403-411
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• 2017

In this article, analytical solution for free vibration of micro composite laminated beam on elastic medium based on modified couple stress are presented. The surrounding elastic medium is modeled as the Winkler elastic foundation. The governing equations and boundary conditions are obtained by using the principle of minimum potential energy for EulerBernoulli beam. For investigating the effect of different parameters including material length scale, beam thickness, some numerical results on different cross ply laminated beams such as (90,0,90), (0,90,0), (90,90,90) and (0,0,0) are presented on elastic medium. Free vibration analysis of a simply supported beam is considered utilizing the Fourier series. Also, the fundamental frequency is obtained using the principle of Hamilton for four types of cross ply laminations with hinged-hinged boundary conditions and different beam theories. The fundamental frequency for different thin beam theories are investigated by increasing the slenderness ratio and various foundation coefficients. The results prove that the modified couple stress theory increases the natural frequency under the various foundation for free vibration of composite laminated micro beams.

• Interaction and multiscale mechanics
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• 제4권4호
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• pp.313-320
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• 2011

This paper proposes an approximate formulation to estimate the bifurcation buckling loads of cylindrical shells with soft elastic cores under the conditions of axial compression. In general, thin-walled, axially compressed cylindrical shells buckle into a diamond pattern in the elastic range. However, buckling symmetrical with respect to the axis of the cylinder may occur when the cylindrical shell is supported by an elastic medium. By considering this characteristic, we introduce the simplified approximate formulation that can give sufficiently accurate results for the bifurcation buckling loads of cylindrical shells. Moreover the results are compared with the exact buckling loads in order to confirm the accuracy of the proposed approximate formulation.

• Interaction and multiscale mechanics
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• 제5권1호
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• pp.13-26
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• 2012

In this paper, the wave propagation in a generalized thermo elastic plate embedded in an elastic medium (Winkler model) is studied based on the Lord-Schulman (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 foundation are obtained by the traction free boundary conditions using the Bessel function solutions. The numerical calculations are carried out for the material Zinc and the computed non-dimensional frequency 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 foundation parameter. A comparison of the results for the case with no thermal effects shows well agreement with those by the membrane theory.