• Structural Engineering and Mechanics
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• v.62 no.3
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• pp.325-344
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• 2017

The present paper investigates the propagation of Love-type wave in a composite structure comprised of imperfectly bonded piezoelectric layer with lower fiber-reinforced half-space with rectangular shaped irregularity at the common interface. Closed-form expression of phase velocity of Love-type wave propagating in the composite structure has been deduced analytically for electrically open and short conditions. Some special cases of the problem have also been studied. It has been found that the obtained results are in well-agreement to the Classical Love wave equation. Significant effects of various parameters viz. irregularity parameter, flexibility imperfectness parameter and viscoelastic imperfectness parameter associated with complex common interface, dielectric constant and piezoelectric coefficient on phase velocity of Love-type wave has been reported. Numerical computations and graphical illustrations have been carried out to demonstrate the deduced results for various cases. Moreover, comparative study has been performed to unravel the effects of the presence of reinforcement and piezoelectricity in the composite structure and also to analyze the existence of irregularity and imperfectness at the common interface of composite structure in context of the present problem which serves as a salient feature of the present study.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.791-812
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• 2011

This is a survey on American options. An American option allows its owner the privilege of early exercise, whereas a European option can be exercised only at expiration. Because of this early exercise privilege American option pricing involves an optimal stopping problem; the price of an American option is given as a free boundary value problem associated with a Black-Scholes type partial differential equation. Up until now there is no simple closed-form solution to the problem, but there have been a variety of approaches which contribute to the understanding of the properties of the price and the early exercise boundary. These approaches typically provide numerical or approximate analytic methods to find the price and the boundary. Topics included in this survey are early approaches(trees, finite difference schemes, and quasi-analytic methods), an analytic method of lines and randomization, a homotopy method, analytic approximation of early exercise boundaries, Monte Carlo methods, and relatively recent topics such as model uncertainty, backward stochastic differential equations, and real options. We also provide open problems whose answers are expected to contribute to American option pricing.

• Computational Structural Engineering
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• v.8 no.4
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• pp.129-136
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• 1995

This paper presents a boundary element method for obtaining approximate solutions of 2-dimensional consolidation problems based on the Biot's linear theory. Laplace transform is applied to differential equation system in order to eliminate the time dependency. The boundary integral equations in transformed space are formulated and the fundamental solutions are shown in a closed form. In order to convert the transformed solutions to the ones in real space, the Hosono's numerical Laplace transform inversion method is applied. As a numerical example, a half-space consolidation problem subjected to a strip local load is selected and the applicability of the method is demonstrated through the comparison with the exact solutions.

• International Journal of Ocean Engineering and Technology Speciallssue:Selected Papers
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• v.6 no.1
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• pp.60-68
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• 2003

This paper proposes an optimum design method of structural and control systems, using a 2-D truss structure as an example. The structure is subjected to initial static loads and disturbances. For the structure, a FEM model is formed. Using modal transformation, the equation of motion is transformed into modal coordinates, in order to decrease D.O.F. of the FEM model. To suppress the effect of the disturbances, the structure is controlled by an output feedback $H_{\infty}$ controller. The design variables of the combined optimal design of the control-structure systems are the cross sectional areas of truss members. The structural objective function is the structural weight. The control objective function is the $H_{\infty}$ norm, the performance index of control. The second structural objective function is the energy of the response related to the initial state, which is derived from the time integration of the quadratic form of the state in the closed-loop system. In a numerical example, simulations have been perform. Through the consideration of structural weight and $H_{\infty}$ norm, an advantage of the combined optimum design of structural and control systems is shown. Moreover, since the performance index of control is almost nearly optimiz, we can acquire better design of structural strength.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.59-64
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• 2006

A new method to obtain explicit re-parameterization that preserves the curve degree and parametric domain is presented in this paper. The re-parameterization brings a curve very close to the arc length parameterization under $L_2$ norm but with less segmentation. The re-parameterization functions we used are $C^1$ continuous piecewise rational linear functions, which provide more flexibility and can be easily identified by solving a quadratic equation. Based on the outstanding performance of Mobius transformation on modifying pieces with monotonic parametric speed, we first create a partition of the original curve, in which the parametric speed of each segment is of monotonic variation. The values of new parameters corresponding to the subdivision points are specified a priori as the ratio of its cumulative arc length and its total arc length. $C^1$ continuity conditions are imposed to each segment, thus, with respect to the new parameters, the objective function is linear and admits a closed-form optimization. Illustrative examples are also given to assess the performance of our new method.

• Transactions of Materials Processing
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• v.18 no.8
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• pp.607-616
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• 2009

There are three sub-processes associated with the assembly of the valve seat and cylinder head; heat fitting, cold fitting, and shrink fitting. In the heat fitting stage, the cylinder head is heated to a specified temperature and then squeezed toward the outer diameter of the valve seat. The cold fitting process cools the valve seat and safely squeezes it toward the inner diameter of cylinder head. However, these methods increased the installations & running cost and curtailed productivity. To address these problems, we analyzed the shrink fitting process using the contact pressure caused by fitting interference between the outer diameter of the valve seat and the inner diameter of the cylinder head. In this study, a closed form equation for predicting the contact pressure and fitting load is proposed. For quality control of the assembly line, principal factors of the shrink fitting process influenced in contact pressure were simulated by the FEM. Actual loads measured in the field showed good agreement with the results obtained by theoretical and finite element analysis.

• Journal of the Korean Society for Precision Engineering
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• v.28 no.4
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• pp.463-473
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• 2011

The warm shrink fitting process is generally used to assemble automobile transmission parts (shaft/gear). But the fitting process can cause the dimensions of addendum and dedendum of the gear to change with respect to the fitting interference and the profile of the gear. As a result, there may be additional noise and vibration between gears. To address these problems, we analyzed the warm shrink fitting process according to process parameters; the fitting interference between the outer diameter of the shaft and the inner diameter of the gear, the inner diameter of the gear, addendum and dedendum of the gear, the heating temperature. In this study, a closed form equation for predicting the amount of deformation of addendum and dedendum in the R-direction was proposed. And the FEA method to analyze the cooling process was proposed for thermal-structural-thermal coupled field analysis of the warm shrink fitting process (heating-fitting-cooling process).

• Korean Journal of Computational Design and Engineering
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• v.7 no.4
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• pp.219-232
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• 2002

In numerically controlled(NC) machining simulation, a Z-map has been used frequently for representing a workpiece. Since the Z-map is usually represented by a set of Z-axis aligned vectors, the machining process can be simulated through calculating the intersection points between the vectors and the surface swept by a machining tool. In this paper, we present an efficient method to calculate those intersection points when an APT-type tool moves along a linear tool path. Each of the intersection points can be expressed as the solution of a system of non-linear equations. We transform this system of equations into a single-variable equation, and calculate the candidate interval in which the unique solution exists. We prove the existence of a solution and its uniqueness in this candidate interval. Based on these characteristics, we can effectively apply numerical methods to finally calculate the solution of the non-linear equations within a given precision. The whole process of NC simulation can be achieved by updating the Z-map properly. Our method can provide more accurate results with a little more processing time, in comparison with the previous closed-form solution.

• KIPS Transactions on Computer and Communication Systems
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• v.4 no.11
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• pp.361-368
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• 2015

In AAGFCS the effective range is regarded as a range for the bullet's speed exceeding the speed of sound to damage the stationary target. Hence the real engagement range might be extended over the effective range for the approaching target since bullet's relative speed to the target increases depending on the approaching speed. However previous TOF equations have good computation accuracy within the effective range only, and they can not be used above that range due to their bad accuracy. We propose an accurate TOF computation method which can be used both within and above the effective range in real time. Some simulation results are shown to demonstrate usefulness of our algorithm for the 30mm projectile.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.6_spc
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• pp.635-643
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• 2016

A stability theory of a damped cantilever column under sub-tangential follower forces is first summarized based on the stability map. It is then demonstrated that internal and external damping can be exactly transformed to Rayleigh damping so that the damping coefficients can be effectively determined using proportional damping. Particularly a parametric study with variation of damping coefficients is performed in association with flutter loads of Beck's column and it is shown that two damping coefficients can be correctly estimated for real systems under the assumption of Rayleigh damping. Finally a frequency equation of a cantilever beam subjected to both a sub-tangentially follower force and two kinds of damping forces is presented in the closed-form and its stability maps are constructed and compared with FE solutions in the practical range of damping coefficients.