• Structural Engineering and Mechanics
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• v.44 no.4
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• pp.431-448
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• 2012

In this paper, the first-order shear deformation theory (FSDT) (Mindlin) for continuum incorporating surface energy is exploited to study the static behavior of ultra-thin functionally graded (FG) plates. The size-dependent mechanical response is very important while the plate thickness reduces to micro/nano scales. Bulk stresses on the surfaces are required to satisfy the surface balance conditions involving surface stresses. Unlike the classical continuum plate models, the bulk transverse normal stress is preserved here. By incorporating the surface energies into the principle of minimum potential energy, a series of continuum governing differential equations which include intrinsic length scales are derived. The modifications over the classical continuum stiffness are also obtained. To illustrate the application of the theory, simply supported micro/nano scaled rectangular films subjected to a transverse mechanical load are investigated. Numerical examples are presented to present the effects of surface energies on the behavior of functionally graded (FG) film, whose effective elastic moduli of its bulk material are represented by the simple power law. The proposed model is then used for a comparison between the continuum analysis of FG ultra-thin plates with and without incorporating surface effects. Also, the transverse shear strain effect is studied by a comparison between the FG plate behavior based on Kirchhoff and Mindlin assumptions. In our analysis the residual surface tension under unstrained conditions and the surface Lame constants are expected to be the same for the upper and lower surfaces of the FG plate. The proposed model is verified by previous work.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.6 s.177
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• pp.1363-1370
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• 2000

Dynamic stability of a flexible spinning disk with angular acceleration is considered. To avoid the coupling between the in-plane and out-of-plane displacements, the linearized strain-displacement relations are used in the Kirchhoff plate theory. The uncoupled governing equations are derived by using Hamilton's principle with considering the angular acceleration. Numerical tests show that existence of the angular acceleration makes a spinning disk dynamically unstable.

• Journal of KSNVE
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• v.9 no.4
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• pp.806-812
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• 1999

Dynamic behaviors are analyzed for a flexble spinning disk with angular acceleration, considering geometric nonlinearity. Based upon the Kirchhoff plate theory and the von Karman strain theory, the nonlinear governing equations are derived which are coupled equations with the in-plane and out-of-planedisplacements. The governing equations are discretized by using the Galerkin approximation. With the discretized nonlinear equations, the time responses are computed by using the generalized-$\alpha$ method and the Newton-Raphson method. The analysis shows that the existence of angular acceleration increases the displacements of the spinning disk and makes the disk unstable.

• Structural Engineering and Mechanics
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• v.8 no.4
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• pp.325-341
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• 1999

A procedure for the computation of the load carrying capacity of perfectly plastic plates in bending is presented. The approach, based on the kinematic theorem of limit analysis, requires the evaluation of the minimum of a convex, but non-smooth, function under linear equality constraints. A systematic solution procedure is devised, which detects and eliminates the finite elements which are predicted as rigid in the collapse mechanism, thus reducing the problem to the search for the minimum of a smooth and essentially unconstrained function of nodal velocities. Both Kirchhoff and Mindlin plate models are considered. The effectiveness of the approach is illustrated by means of some examples.

• Architectural research
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• v.16 no.2
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• pp.67-74
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• 2014

Free vibration analysis of thin shells is carried out by using isogeometric approach. For this purpose, a thin shell element based on Kirchhoff-Love shell theory is developed. Non-uniform rational B-spline surface (NURBS) definition is introduced to represent the geometry of shell and also used to derive all terms required in the isogeometric element formulation. Gauss integration rule is used for stiffness and mass matrices. The present shell element is then applied to examine vibrational behaviours of thin plate and shell structures. From numerical results, it is found be that reliable natural frequencies and associated mode shapes of thin shell structures can be predicted by the present isogeometric shell element.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2011.05a
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• pp.55-57
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• 2011

TLM method to analyize receiver gain characteristic of the FZPL antenna which is operated at 12GHz and can be applied to satellite TV system, radio telescope, and Geodetic System. Some numerical results computed by TLM method are compared with Kirchhoff's approximation and PO method. As a result, receiver gain characteristic on main axis of the 12GHz FZPL antenna is shown at the front side, which means that the focal length is 15% shorter than designed focal length.

• Computational Structural Engineering : An International Journal
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• v.1 no.1
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• pp.49-57
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• 2001

This paper presents exact solutions for the modal stress-resultant distributions for vibrating rectangular Mindlin plates involving two opposite sides simply supported while the other two sides free. These exact stress-resultants of vibrating plates with free edges, hitherto unavailable, are very important because they serve as benchmark solutions for checking numerical solutions and methods. Using the exact solutions of a square plate, this paper highlights the problem of determining accurate stress-resultants, especially the transverse shear forces and twisting moments in thin plates, when employing the widely used numerical methods such as the Ritz method and the finite element method. Thus, this study shows that there is a need for researchers to develop refinements to the Ritz method and the finite element method for determining very accurate stress-resultants in vibrating plates with free edges.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.10a
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• pp.45-51
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• 2002

An acoustic finite element model of a bridge is developed to evaluate the noise generated by the traffic-induced vibration of the bridge. The dynamic response of a multi-girder bridge, modeled by a 3-dimensional frame element model, is analyzed with a 3-axle 8 DOFs truck model and a 5-axle 13 DOFs semi-trailer. The flat plate element is used to analyze the acoustic pressure due to the fluid-structure interactions between the vibrating surface and contiguous acoustic fluid medium. The radiation fields of noise with a specified distribution of vibrating velocity and pressure on the structural surface are also computed using the Kirchhoff-Helmholtz integral. Although the noise produced by the bridge vibration is not serious in itself, which is below the audible frequency range, it should be considered as an interaction problem between vehicle noise and bridge vibration noise in order to evaluate the traffic noise around the bridge.

• 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.

• Proceedings of the KSME Conference
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• 2001.06b
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• pp.482-487
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• 2001

Time responses of a flexible spinning disk of which axis of symmetry is misaligned with the axis of rotation are analyzed in a numerical manner. Equations of motions are derived by Hamilton's principle based on Kirchhoff plate theory and von-Karman strain theory, and the equations are discretized by finite element method. In obtaining the time responses, Generalized-$\alpha$ method is used to solve the equations. Based on the result, the effects of the misalignment are analyzed on the vibration characteristics of a spinning disk.