• 한국전산구조공학회논문집
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• 제17권1호
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• pp.83-91
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• 2004

랜덤동요된 조화가진력을 받는 임팩트시스템의 비선형거동을 개발된 반해석적절차에 의해 확률영역에서 분석하였다. 반해석적절차는 path-integral solution을 이용하여 임팩트시스템의 추계론적 미분방정식으로부터 구함으로 얻어진다. 결합확률밀도함수의 전개를 구하고 시스템의 비선형거동 특성인 혼돈거동에 대하여 분석하고 노이즈의 영향을 시간영역과 확률영역에서 알아보았다. 결과로부터 반해석적절차는 결합확률밀도함수를 통하여 임팩트시스템의 거동에 대한 정보를 제공하는 것을 알 수 있었다. 노이즈의 영향은 혼돈거동의 특성을 약화시키며 궁극적으로 사라지게 함을 알 수 있었으며 또한 혼돈거동의 특성이 상대적으로 높은 노이즈아래에서도 남아있는 것을 밝혔다. 결합확률밀도함수는 응답앙상블이 약정상과정임을 확인시켜 주었다.

• Structural Engineering and Mechanics
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• 제54권4호
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• pp.607-622
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• 2015

This paper presents a comparative study of analytical method and finite element method (FEM) for analysis of a continuous contact problem. The problem consists of two elastic layers loaded by means of a rigid circular punch and resting on semi-infinite plane. It is assumed that all surfaces are frictionless and only compressive normal tractions can be transmitted through the contact areas. Firstly, analytical solution of the problem is obtained by using theory of elasticity and integral transform techniques. Then, finite element model of the problem is constituted using ANSYS software and the two dimensional analysis of the problem is carried out. The contact stresses under rigid circular punch, the contact areas, normal stresses along the axis of symmetry are obtained for both solutions. The results show that contact stresses and the normal stresses obtained from finite element method (FEM) provide boundary conditions of the problem as well as analytical results. Also, the contact areas obtained from finite element method are very close to results obtained from analytical method; disagree by 0.03-1.61%. Finally, it can be said that there is a good agreement between two methods.

• 대한기계학회논문집
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• 제18권8호
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• pp.1967-1973
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• 1994

The free vibration of a thin plate with three different boundary conditions is discussed in this paper. A semi-analytical approach to the plate problems has been exploited using computer algebra system(CAS). The approximate solutions are assumed as algebraic polynomials that satisfy the appropriate boundary conditions. In order to solve problems, Galerkin method is used, which is known as an ineffective tool for practical engineering problems, being involved with a large number of multiple integration and differentiation. All the admissible functions used in this paper are generated automatically by CAS otherwise a tedious algebraic manipulations should be done by hand. One, six and fifteen-term solutions in terms of frequency parameters are presented and compared with exact solutions. Even using one-term solution, the comparison with existing data shows good agreement and accuracy of the present method.

• Advances in Computational Design
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• 제3권3호
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• pp.303-318
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• 2018

This article presents a semi-analytical solution for an exponentially graded piezoelectric hollow sphere. The sphere interacts with electric displacement, elastic deformations, electric potentials, magneto-thermo-elasticity, and hygrothermal influences. The hollow sphere may be standing under both mechanical and electric potentials. Electro-magneto-elastic behavior of magnetic field vector can be described in the hollow sphere. All material, thermal and magnetic properties of hollow sphere are supposed to be graded in radial direction. A semi-analytical technique is improved to deduce all fields in which different boundary conditions for radial stress and electric potential are presented. Numerical examples for radial displacement, radial and hoop stresses, and electric potential are investigated. The influence of many parameters is studied. It is seen that the gradation of all material, thermal and magnetic properties has particular effectiveness in many applications of modern technology.

• Geosystem Engineering
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• 제21권6호
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• pp.309-317
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• 2018

We employ a three-dimensional indirect boundary element method (BEM) to simulate temperature change around an underground liquefied natural gas storage cavern. The indirect BEM (IBEM) uses fictitious heat source strength on boundary elements as basic variables which are solved from equations of boundary conditions and then used to compute the temperature change at other points in the considered problem domain. The IBEM requires evaluation of singular integration for temperature change due to heat conduction from a constant heat source on a planar (triangular) region. The singularity can be eliminated by a semi-analytical integration scheme. However, it is found that the semi-analytical integration scheme yields sharp temperature gradient for points close to vertices of triangle. This affects the accuracy of heat flux, if they are evaluated by finite difference method at these points. This difficulty can be overcome by a combination of using a direct numerical integration for these points and the semi-analytical scheme for other points distance away from the vertices. The IBEM and the hybrid integration scheme have been verified with an analytic solution and then used to the application of the underground storage.

• International Journal of Air-Conditioning and Refrigeration
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• 제6권
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• pp.14-26
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• 1998

This paper deals with approximate analytical solutions for the two-region one-dimensional model describing the charging process of stratified thermal storage tanks at variable inlet temperature with momentum-induced mixing. An arbitrarily increasing inlet temperature is decomposed into inherent step changes and intervals of continuous change. Each continuous interval is approximated as a finite number of piecewise linear functions, which admits an analytical solution for perfectly mixed region. Using the Laplace transform, the temperature profiles in plug flow region with both the semi-infinite and adiabatic ends are successfully derived in terms of well-defined functions. The effect of end condition on the solution proves to be negligible under the practical operating conditions. For a Quadratic variation of inlet temperature, the approximate solution employing a moderate number of pieces agrees excellently with the exact solution.

• Steel and Composite Structures
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• 제27권1호
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• pp.1-12
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• 2018

This paper presents a semi-analytical solution of simply supported horizontally composite curved I-beam by trigonometric series. The flexibility of the interlayer connectors between layers both in the tangential direction and in the radial direction is taken into account in the proposed formulation. The governing differential equations and the boundary conditions are established by applying the variational approach, which are solved by applying the Fourier series expansion method. The accuracy and efficiency of the proposed formulation are validated by comparing its results with both experimental results reported in the literature and FEM results.

• 대한기계학회논문집B
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• 제20권11호
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• pp.3655-3665
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• 1996

An analytical solution is presented for the conduction-dominated solidification of a binary mixture in a semi-infinite medium. The present approach differs from that of other solution by these four characteristics. (1) Solid fraction is determined from the phase diagram, (2) thermophysical properties in mushy zone are weighted according to the local solid fraction, (3) non-equilibrium solidification can be simulated and (4) the cooling condition of under-eutectic temperature can be simulated. Up to now, almost all analyses are based on the assumption of constant properties in mushy zone and solid fraction linearly with temperature or length. The validation for these assumptions, however, shows that serious error is found except some special cases. The influence of microscopic model on the macroscopic temperature profile is very small and can be ignored. But the solid fraction and average solid concentration which directly influence the quality of materials are drastically changed by the microscopic models. An approximate solution using the method of weighted residuals is also introduced and shows good agreement with the analytical solution. All calculations are performed for NH$_{4}$Cl-H$_{2}$O and Al-Cu system.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2000년도 춘계 학술발표회 논문집 Proceedings of EESK Conference-Spring
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• pp.451-457
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• 2000

In many dynamic problems such as foundation vibrations ultrasonic nondestructive evaluation and blasting analysts are confronted with the problem of wave propagation in an infinite or semi-infinite media. In order to simulate this situation by a finite analytical model provisions must be made to absorb the stress waves arriving at the boundary. Absorbing boundaries are mathematical artifacts used to prevent wave reflections at the boundaries of discrete models for infinite media under dynamic loads. An analytical study is carried out to examine the effectiveness of Lysmer-Kuhlemeyer model one of the most widely used absorbing boundaries. Validity of the absorbing boundary conditions suggested by Lymer-Kuhlemeyer is examined by adopting the solution of Ewing et al. to the problem of plane waves from a harmonic normal force on the surface of an elastic half-space. The Ewing's problem is than numerically simulated using the finite element method on a semi-circular mesh with and without absorbing boundaries which are represented by viscous dashpots. The absorption ratios are calculated by comparing the displacements at the absorbing boundaries to those at the free field without absorbing boudaries.

• 설비공학논문집
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• 제7권1호
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• pp.42-51
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• 1995

In order to establish a theoretical basis for the analyses of transient behaviors in stratified thermal storage tanks, analytical approaches to an improved one-dimensional model are made. In the present model the storage tank is treated as a finite region with an adiabatic tank exit, whereas it has been considered as a simple semi-infinite region previously. Application of the Laplace transformation and the Inversion theorem to the governing equations makes it possible to obtain an exact infinite-series solution, which is convergent only at sufficiently large time. Accordingly a complementary solution which is available for short times, i.e., the time range of this study is sought by an approximate method. The approximate solution which is rigorously validated through the examination of neglected terms in the solution procedure agrees quite well with the exact one. Moreover, it is simpler to use and more convenient to interpret the physical meaning of the solution. Comparison of the present solution with the previous ones shows relatively large difference near the tank bottom, which results from the more realistic boundary condition adopted in the present model. Some representative results by the approximate solution including effects of the Peclet number on temperature distrbutions are illustrated to show the utility of this study. In consequence, it is expected that the present results based on the improved model replace the foregoing ones as a new theoretical reference for studies of thermal stratification fields.