• Geomechanics and Engineering
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• 제6권3호
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• pp.213-233
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• 2014

The present paper is dealing with the investigation of the stress field around the infinitely long cylindrical cavity, of a circular cross section, contained in the transversally isotropic elastic continuum. Investigation is based upon the determination of the stress function that satisfies the biharmonic equation, for the given boundary conditions and for rotationaly symmetric loading. The solution of the partial differential equation of the problem is given in the form of infinite series of Bessel's functions. Determination of the stress-strain field around cavities is a common requirement for estimation of safety of underground rock excavations.

• Smart Structures and Systems
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• 제14권2호
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• pp.225-246
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• 2014

The present paper develops piezo-thermo-elastic analysis of a thick spherical shell for generalized functionally graded piezoelectric material. The assumed structure is loaded under thermal, electrical and mechanical loads. The mechanical, thermal and electrical properties are graded along the radial direction based on a power function with three different non homogenous indexes. Primarily, the non homogenous heat transfer equation is solved by applying the general boundary conditions, individually. Substitution of stress, strain, electrical displacement and material properties in equilibrium and Maxwell equations present two non homogenous differential equation of order two. The main objective of the present study is to improve the relations between mechanical and electrical loads in hollow spherical shells especially for functionally graded piezoelectric materials. The obtained results can evaluate the effect of every non homogenous parameter on the mechanical and electrical components.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권3호
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• pp.93-106
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• 2021

In this paper, an efficient hybrid numerical method for solving two-asset option pricing problem is presented based on the Crank-Nicolson and the radial basis function methods. For this purpose, the two-asset Black-Scholes partial differential equation is considered. Also, the convergence of the proposed method are proved and implementation of the proposed hybrid method is specifically studied on Exchange and Call on maximum Rainbow options. In addition, this method is compared to the explicit finite difference method as the benchmark and the results show that the proposed method can achieve a noticeably higher accuracy than the benchmark method at a similar computational time. Furthermore, the stability of the proposed hybrid method is numerically proved by considering the effect of the time step size to the computational accuracy in solving these problems.

• Structural Engineering and Mechanics
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• 제28권2호
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• pp.129-152
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• 2008

This paper considers the solution of the stochastic differential equations (SDEs) with random operator and/or random excitation using the spectral SFEM. The random system parameters (involved in the operator) and the random excitations are modeled as second order stochastic processes defined only by their means and covariance functions. All random fields dealt with in this paper are continuous and do not have known explicit forms dependent on the spatial dimension. This fact makes the usage of the finite element (FE) analysis be difficult. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used to represent these processes to overcome this difficulty. Then, a spectral approximation for the stochastic response (solution) of the SDE is obtained based on the implementation of the concept of generalized inverse defined by the Neumann expansion. This leads to an explicit expression for the solution process as a multivariate polynomial functional of a set of uncorrelated random variables that enables us to compute the statistical moments of the solution vector. To check the validity of this method, two applications are introduced which are, randomly loaded simply supported reinforced concrete beam and reinforced concrete cantilever beam with random bending rigidity. Finally, a more general application, randomly loaded simply supported reinforced concrete beam with random bending rigidity, is presented to illustrate the method.

• Advances in concrete construction
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• 제9권1호
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• pp.43-54
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• 2020

This paper presents an innovative stress-function variational approach in formulating the interfacial shear and normal stresses in an externally bonded concrete joint using carbon fiber-reinforced plastic (CFRP) plies. The joint is subjected to surface traction loadings applied at both ends of the concrete substrate layer. By introducing two interfacial shear and normal stress functions on the CFRP-concrete interface, based on Euler-Bernoulli beam idea and static stress equations of equilibrium, the entire stress fields of the joint were determined. The complementary strain energy was minimized in order to solve the governing equation of the joint. This yields an ordinary differential equation from which the interfacial normal and shear stresses were proposed explicitly, satisfying all the multiple traction boundary conditions. Lamination theory for composite materials was also employed to obtain the interfacial stresses. The proposed approach was validated by the analytic models in the literature as well as through a comprehensive computational code generated by the authors. Furthermore, a numerical verification was carried out via the finite element software ABAQUS. In the end, a scaling analysis was conducted to analyze the interfacial stress field dependence of the joint upon effective issues using the devised code.

• 한국연소학회:학술대회논문집
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• 한국연소학회 1999년도 제19회 KOSCO SYMPOSIUM 논문집
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• pp.117-128
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• 1999

The removal of nitrogen oxides(NOx) from $N_{2}/O_{2}$ gas using a pulsed corona discharge was investigated as a function of the reduced electric field(E/N) and the energy density(J/L). A kinetic model was developed to characterize the chemical reactions taking place in a pulsed corona discharge reactor. The model calculates the fractional concentrations of radical species at each pulse-on period and utilizes the radicals to remove NOx for the subsequent pulse-off period. Electron collision reaction data are calculated using ELENDIF program to solve Boltzmann equation for electron energy distribution function, and the subsequent chemical reactions are calculated using CHEMKIN-II program to solve stiff ODE(ordinary differential equation) problems for species concentrations. The corona discharge energy per pulse and the time-space averaged E/N were obtained by fitting the model to experimental data. The model calculation shows good agreement with the experimental data, and predicts the formation of other species such as $NO_{2}$, $O_{3}$ and $N_{2}O$.

• Computers and Concrete
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• 제2권2호
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• pp.125-146
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• 2005

The objective of this paper is setting out, for a cable-stayed bridge with a curtain suspension, a method to determine the modes of vibration of the structure. The system of differential equations governing the vibrations of the bridge, derived by means of a variational formulation in a nonlinear field, is reported in Appendix C. The whole analysis results from the application of Hamilton's principle, using the expressions of potential and kinetic energies and of the virtual work made by viscous damping forces of the various parts of the bridge (Monaco and Fiore 2003). This paper focuses on the equation concerning the transversal motion of the girder of the cable-stayed bridge and in particular on its final form obtained, restrictedly to the linear case, neglecting some quantities affecting the solution in a non-remarkable way. In the hypotheses of normal mode of vibration and of steady-state, we propose the resolution of this equation by a particular method based on a numerical approach. Respecting the boundary conditions, we derive, for each mode of vibration, the corresponding frequency, both natural and damped, the shape-function of the girder axis and the exponential function governing the variability of motion amplitude in time. Finally the results so obtained are compared with those deriving from the dynamic analysis performed by a finite elements calculation program.

• 한국전자파학회지:전자파기술
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• 제4권1호
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• pp.38-43
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• 1993

다충유전체주로 부터 전자장산란 문제를 해석하기 위하여 혼합유한요소방법을 적용하였다. 실질적으로 펀미분방정식의 해가 주어지는 무경계화된 영역은 국소경계영역으로 나누어지게 되고, 나머지 무경 계영역은 경계적분방정식으로 나타내게 된다. 나누어진 국소표면은 원천, 비균질성과 비등방성을 포함 하도록 정의한다. 따라서, 정의된 국소경계영역에서 미분볍이 사용된다. 또한 나머지 경계영역에서 경계 적분방정식이 단지 자유공간Green 함수를 사용하도록 수식화 될 것이다. 그 결과로서, 국소경계는 경계조건을 갖는 경계값 문제로 나타나게 되고, 유한요소법으로 해석된다. 제시된 방법의 장점은 전자장 산란연구에 보다 간략하고, 효율적이다. 결과의 타당성은 다른방볍(경계 요소법)파 비교하여 입증하였다. 확장된 수치해석의 예로서 임의의 단면을 갖는 손실유전체주의 산란장을 해석하여 제시했다.

• 대한조선학회논문집
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• 제50권4호
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• pp.224-231
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• 2013

The concept of the natural frequency is useful for understanding the characters of oscillating systems. However, when a circular cylinder floating horizontally on the water surface is heaving, due to the hydrodynamic forces, the system is not governed by the equation like that of the harmonic one. In this paper, in order to shed some lights on the more correct use of the concept of the natural frequency, a problem of the heaving circular cylinder is analyzed in the time domain. The equation of motion, an integro-differential equation, was derived following the fashion of Cummins (1962), and its coefficients including the retardation function were obtained using the numerical solution of Lee (2012). The equation was solved numerically, and the experiment was also carried out in the CNU flume. Using our numerical and experimental results, the natural frequency was defined as its average value given by the motion data excluding those of the initial stage. Our results were then compared with those of the existing investigations such as Maskell and Ursell (1970), Ito (1977) and Yeung (1982) as well as the newly obtained results of Lee (2012). Comparison showed that the natural frequency obtained here agrees well with that of Lee (2012), which was found through the frequency domain analysis. It was also shown that the approximation of heaving motion by a damped harmonic oscillation, which was regarded as suitable by most previous investigators, is not physically suitable for the reason that can be clearly shown through comparing the shape of MCFRs(Modulus of Complex Frequency Response). Furthermore, we found that although the previous approximations yield the damping ratio significantly different from our result the magnitude of natural frequency is not much different from our result.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.519-536
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• 2005

The purpose of this paper is to propose several approximating methods to obtain the American option prices under jump-diffusion processes. The first method is to extend an approximating method to the optimal exercise boundary by a multipiece exponential function suggested by Ju [17]. The second approach is to modify the analytical methods of MacMillan [20] and Zhang [25] in a discrete time space. The third approach is to apply the simulation technique of Ibanez and Zapareto [14] to the problem of American option pricing when the jumps are allowed. Finally, we compare the numerical performance of each suggesting method with those of the previous numerical approaches.