• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.1-21
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• 2015

This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r > d, $r{\leq}d$, long-time or short-time maturity T.

• Structural Engineering and Mechanics
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• v.18 no.1
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• pp.41-58
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• 2004

The postbuckling behaviour of thin shells has fascinated researchers because the theoretical prediction and their experimental verification are often different. In reality, shell panels possess small imperfections and these can cause large reduction in static buckling strength. This is more relevant in thin laminated composite shells. To study the postbuckling behaviour of thin, imperfect laminated composite shells using finite elements, explicit incremental or secant matrices have been presented in this paper. These incremental matrices which are derived using Marguerre's shallow shell theory can be used in combination with any thin plate/shell finite element (Classical Laminated Plate Theory - CLPT) and can be easily extended to the First Order Shear deformation Theory (FOST). The advantage of the present formulation is that it involves no numerical approximation in forming total potential energy of the shell during large deformations as opposed to earlier approximate formulations published in the literature. The initial imperfection in shells could be modeled by simply adjusting the ordinate of the shell forms. The present formulation is very easy to implement in any existing finite element codes. The secant matrices presented in this paper are shown to be very accurate in tracing the postbuckling behaviour of thin isotropic and laminated composite shells with general initial imperfections.

• Structural Engineering and Mechanics
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• v.16 no.1
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• pp.17-34
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• 2003

This paper presents a damage assessment procedure applied to periodic spring mass systems using an eigenvalue sensitivity-based method. The damage is directly related to the stiffness reduction of the damage element. The natural frequencies of periodic structures with one single disorder are found by adopting the transfer matrix approach, consequently, the first order approximation of the natural frequencies with respect to the disordered stiffness in different elements is used to form the sensitivity matrix. The analysis shows that the sensitivity of natural frequencies to damage in different locations depends only on the mode number and the location of damage. The stiffness changes due to damage can be identified by solving a set of underdetermined equations based on the sensitivity matrix. The issues associated with many possible damage locations in large structural systems are addressed, and a means of improving the computational efficiency of damage detection while maintaining the accuracy for large periodic structures with limited available measured natural frequencies, is also introduced in this paper. The incomplete measurements and the effect of random error in terms of measurement noise in the natural frequencies are considered. Numerical results of a periodic spring-mass system of 20 degrees of freedom illustrate that the proposed method is simple and robust in locating single or multiple damages in a large periodic structure with a high computational efficiency.

• Journal of the Korean Institute of Navigation
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• v.17 no.1
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• pp.37-48
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• 1993

When the vessel is running at the very low Froude numbers, the free-surface is difficult to be disturbed, wave-making is negligible, and the double -model velocity potential gives a very good approximation for calculating the velocity distribution just outside the boundary layer. If the speed of incident flow is gradually increased, the most perceptible change is the rise of the flow surface at stem. With further increase in speed, the nature of the flow at the bow changes completely, The flow ahead of the bow becomes more distrubed, the rise at the stem to stagnation height disappear, and the first wave crest, of less than the stagnation height, appears a small distance downstream from the stem. The present study is concerned with a small region of this flow, mainly in the bow region. The present investigation is primarily an experimental study of the flow in the bow region of s ship model, and it is undertaken in order to investigated systematically, the effect of bow geometry on this flow. The long-range objective is to use these results to guide the development of a mathematical model for predicting the flow about a ship's bow.

• Journal of the Korean Society for Railway
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• v.12 no.1
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• pp.65-71
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• 2009

The pressure transient inside the passenger cabin of high-speed train has been assessed using computational fluid dynamics (CFD) based on the axi-symmetric Navier-Stokes equation. The pressure change inside a train have been calculated using first order difference approximation based on a linear equation between the pressure change ratio inside a train and the pressure difference of inside and outside of the train. The numerical results show that the pressure change inside the new Korean high-seed train passing through a tunnel of Seoul-Busan high-speed line at the speed of 330km/h satisfied well the Korean regulation for pressure change inside a passenger cabin if the train is satisfying the train specification for airtightness required by the regulation.

• The Journal of the Acoustical Society of Korea
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• v.23 no.3
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• pp.206-213
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• 2004

This paper presents a steering angle error compensation (SAEC) algorithm that is appropriate for rapidly moving sources. The Proposed algorithm utilizes a modal covariance matrix from multiple frequency components instead of the multiple snapshots in a narrowband SAEC, and estimates the steering error by maximizing the wideband WVDR output power using a first-order Taylor series approximation of the modal steering vector in terms of the steering error. As such, the steering error can be compensated with short observation times. Several simulations using artificial and sea trial data are used to demonstrate the Performance of the proposed algorithm.

• Structural Engineering and Mechanics
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• v.8 no.5
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• pp.513-529
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• 1999

A concept of hierarchical modeling, the newest modeling technology, has been introduced in early 1990's. This new technology has a great potential to advance the capabilities of current computational mechanics. A first step to implement this concept is to construct hierarchical models, a family of mathematical models sequentially connected by a key parameter of the problem under consideration and have different levels in modeling accuracy, and to investigate characteristics in their numerical simulation aspects. Among representative model problems to explore this concept are elastic structures such as beam-, arch-, plate- and shell-like structures because the mechanical behavior through the thickness can be approximated with sequential accuracy by varying the order of thickness polynomials in the displacement or stress fields. But, in the numerical, analysis of hierarchical models, two kinds of errors prevail, the modeling error and the numerical approximation error. To ensure numerical simulation quality, an accurate estimation of these two errors is definitely essential. Here, a local a posteriori error estimator for elastic structures with thin domain such as plate- and shell-like structures is derived using the element residuals and the flux balancing technique. This method guarantees upper bounds for the global error, and also provides accurate local error indicators for two types of errors, in the energy norm. Compared to the classical error estimators using the flux averaging technique, this shows considerably reliable and accurate effectivity indices. To illustrate the theoretical results and to verify the validity of the proposed error estimator, representative numerical examples are provided.

• Structural Engineering and Mechanics
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• v.18 no.5
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• pp.591-607
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• 2004

The substance of the use of the derived non-linear creep constitutive equations under variable stress levels (see first part of the paper, Kmet 2004) is explained and the strategy of their application is outlined using the results of one-step creep tests of the steel spiral strand rope as an example. In order to investigate the creep strain increments of cables an experimental set-up was originally designed and a series of tests were carried out. Attention is turned to the individual main steps in the production and application procedure, i.e., to the one-step creep tests, definition of loading history, determination of the kernel functions, selection and definition of constitutive equation and to the comparison of the resulting values considering the product and the additive forms of the approximation of the kernel functions. To this purpose, the parametrical study is performed and the results are presented. The constitutive equations of non-linear creep of cable under variable stress history offer a strong tool for the real simulation of stochastic variable load history and prediction of realistic time-dependent response (current deflection and stress configuration) of structures with cable elements. By means of suitable stress combination and its gradual repeating various loads and times effects can be modelled.

• Structural Engineering and Mechanics
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• v.16 no.2
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• pp.195-217
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• 2003

This paper, which is an extension of a previous work by Viola et al. (2002), deals with the dynamic stability of beams under a triangularly distributed sub-tangential forces when the effect of an elastically restrained end is taken into account. The sub-tangential forces can be realised by a combination of axial and tangential follower forces, that are conservative and non-conservative forces, respectively. The studied beams become unstable in the form of either flutter or divergence, depending on the degree of non-conservativeness of the distributed sub-tangential forces and the stiffness of the elastically restrained end. A non-conservative parameter ${\alpha}$ is introduced to provide all possible combinations of these forces. Problems of this kind are usually, at least in the first approximation, reduced to the analysis of beams according to the Bernoulli-Euler theory if shear deformability and rotational inertia are negligible. The equation governing the system may be derived from the extended form of Hamilton's principle. The stability maps will be obtained from the eigenvalue analysis in order to define the divergence and flutter domain. The passage from divergence to flutter is associated with a noticeable lowering of the critical load. A number of particular cases can be immediately recovered.

• Wind and Structures
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• v.18 no.3
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• pp.253-265
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• 2014

The platform and floating structure of spar type offshore wind turbine systems should be designed in order for the 6-DOF motions to be minimized, considering diverse loading environments such as the ocean wave, wind, and current conditions. The objective of this study is to optimally design the platform and substructure of a 3MW spar type wind turbine system with the maximum postural stability in 6-DOF motions as well as the minimum material cost. Therefore, design variables of the platform and substructure were first determined and then optimized by a hydrodynamic analysis. For the hydrodynamic analysis, the body weight of the system was considered, and the ocean wave conditions were quantified to the wave forces using the Morison's equation. Moreover, the minimal number of computation analysis models was generated by the Design of Experiments (DOE), and the design variables of the platform and substructure were finally optimized by using a genetic algorithm with a neural network approximation.