• Advances in Computational Design
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• v.3 no.3
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• pp.213-232
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• 2018

First time, an exact solution for free vibration of the Levy-type rectangular laminated plate is developed considering the most efficient Zig-Zag theory (ZIGT) and third order theory (TOT). The plate is subjected to hard simply supported boundary condition (Levy-type) along x axis. Using the equilibrium equations and the plate constitutive relations, a set of 12 m first order differential homogenous equations are obtained, containing displacements and stress resultant as primary variables. The natural frequencies of a single-layer isotropic, multi-layer composites and sandwich plates are tabulated for three values of length-to-thickness ratio (S) and five set of boundary conditions and further assessed by comparing with existing literature and recently developed 3D EKM (extended Kantorovich method) solution. It is found that for the symmetric composite plate, TOT produces better results than ZIGT. For antisymmetric and sandwich plates, ZIGT predicts the frequency for different boundary conditions within 3% error with respect to 3D elasticity solution while TOT gives 10% error. But, ZIGT gives better predictions than the TOT concerning the displacement and stress variables.

• Steel and Composite Structures
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• v.46 no.6
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• pp.719-729
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• 2023

This paper studies electro-magneto-mechanical bending studying of the cylindrical panels based on shear deformation theory. The cylindrical panel is constrained with two simply-supported edges at longitudinal direction and two clamped boundary conditions at circumferential direction. The governing equations are derived based on the principle of virtual work in cylindrical coordinate system. Levy-type solution of the governing equations is derived to reduce two dimensional PDEs to a 2D ODEs. The reduced ordinary differential equation is solved using the Eigen-value Eigen-vector method for the clamped-clamped boundary condition. The electro-magneto-mechanical bending results are obtained to show that every displacement, rotation and electromagnetic potentials how change with changes of initial electromagnetic potentials and mechanical loads along longitudinal and circumferential directions.

• Korean Management Science Review
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• v.25 no.3
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• pp.1-12
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• 2008

The Swaption is one of the popular Interest rates derivatives. In spite of such a popularity, the swaption pricing formula is hard to derived within the theoretical consistency. Most of swaption pricing model are heavily depending on the simulation technique. We present a new class of swaption model based on the multi-factor HJM levy-mixture model. A key contribution of this paper is to provide a generalized swaption pricing formula encompassing many market stylize facts. We provide an approximated closed form solution of the swaption price using the Gram-Charlier expansion. Specifically, the solution form is similar to the market models, since our approximation is based on the Lognormal distribution. It can be directly compared with the traditional Black's formula when the size of third and fourth moments are not so large. The proposed extended levy model is also expected to be capable of producing the volatility smiles and skewness.

• Structural Engineering and Mechanics
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• v.62 no.6
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• pp.675-693
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• 2017

In this paper, based on the first-order shear deformation plate theory, buckling analysis of piezoelectric coupled transversely isotropic rectangular plates is investigated. By assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for buckling analysis of plate with surface bonded piezoelectric layers are established. The Maxwell's equation and all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. The analytical solution is obtained for Levy type of boundary conditions. The accurate buckling load of laminated plate is presented for both open and closed circuit conditions. From the numerical results it is found that, the critical buckling load for open circuit is more than that of closed circuit in all boundary and loading conditions. Furthermore, the critical buckling loads and the buckling mode number increase by increasing the thickness of piezoelectric layers for both open and closed circuit conditions.

• Journal of the Korean Society of Industry Convergence
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• v.5 no.1
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• pp.45-52
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• 2002

In this study, an exact solution of governing differential equation for the bending problem of partially loaded orthotropic rectangular plates is presented and also its computer program is developed. The method requires that two opposite edges be clamped or simply supported, or one edge clamped and the other simply supported. Any combination of boundary conditions could exist along the other edges. The plate could he subjected to uniform, partially uniform, and line loads. The solution for the deflection of rectangular plate is expressed as a Levy type single Fourier series and the loads arc expressed as a corresponding series. The advantage of the solution is that it overcomes the limitations of the previous Navier's and Levy's methods (limitation of boundary condition and loading conditions of plate), it is easy to program on a computer and it becomes fast to solve the bending problem with computer program. Calculations are presented for isotropic and orthotropic plates with different loading and boundary conditions. Comparisons are made for the isotropic plate with various boundary conditions between the result of this paper and the result of Navier, Levy and Szilard. The deflections were in excellent agreement.

• Interaction and multiscale mechanics
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• v.5 no.2
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• pp.105-114
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• 2012

The study of rigid roadway pavement under dynamic traffic loads with variable velocity is investigated in this paper. Rigid roadway pavement is modeled as a rectangular damped orthotropic plate supported by elastic Pasternak foundation. The boundary supports of the plate are the steel dowels and tie bars which provide elastic vertical support and rotational restraint. The natural frequencies of the system and the mode shapes are solved using two transcendental equations, obtained from the solution of two auxiliary Levy's type problems, known as the Modified Bolotin Method. The dynamic moving traffic load is expressed as a concentrated load of harmonically varying magnitude, moving straight along the plate with a variable velocity. The dynamic response of the plate is obtained on the basis of orthogonality properties of eigenfunctions. Numerical example results show that the velocity and the angular frequency of the loads affected the maximum dynamic deflection of the rigid roadway pavement. It is also shown that a critical speed of the load exists. If the moving traffic load travels at critical speed, the rectangular plate becomes infinite in amplitude.

• Journal of Korean Society of Steel Construction
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• v.22 no.3
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• pp.241-251
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• 2010

This paper presents the development of a new analytical solution to the governing differential equation for isotropic annular sector plates subjected to uniform loading in a three-dimensional polar coordinate system. The 4th order governing partial differential equation (PDE) was converted to an ordinary differential equation (ODE) by assuming the Levy-type series solution form and the subsequent mathematical operations. Finally, a series-type solution was assembled with homogeneous and nonhomogeneous solution parts after operating real values and complex conjugates derived from the characteristic equation. To demonstrate the convergence rate and the accuracy of the featured method, several examples with various sector angles were selected and solved. The deflections and internal moments in the example annular sector plates that were obtained from the proposed solution were compared with those obtained from other analytical studies and numerical analyses using the finite element analysis package program, ABAQUS. Very good agreement with the results of other analytical and numerical methodologies was shown.

• Earthquakes and Structures
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• v.1 no.3
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• pp.307-326
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• 2010

This paper is concerned with the optimal seismic design of added viscous dampers in yielding plane frames. The total added damping is minimized for allowable values of local performance indices under the excitation of an ensemble of ground motions in both regular and irregular structures. The local performance indices are taken as the maximal inter-story drift of each story and/or the normalized hysteretic energy dissipated at each of the plastic hinges. Gradients of the constraints with respect to the design variables (damping coefficients) are derived, via optimal control theory, to enable an efficient first order optimization scheme to be used for the solution of the problem. An example of a ten story three bay frame is presented. This example reveals the following 'fully stressed characteristics' of the optimal solution: damping is assigned only to stories for which the local performance index has reached the allowable value. This may enable the application of efficient and practical analysis/redesign type methods for the optimal design of viscous dampers in yielding plane frames.