Earticle

본 연구에서는 실린더 형 쉘 구조물의 구조적 안정성에 대하여 해석 하였다. 임계하중은 하중을 점차적으로 증가하여 구조물이 파괴가 발생 할 때의 상태에서 가장 작은 하중을 의미한다. 셸 구조의 안정성을 임계하중의 크기로 기초를 두고 해석 하였다. 실린더 형 쉘의 차분해석은 일차적 원통형 판구조와 같으므로 최근에 많은 연구의 대상이 되어왔다. 차분법은 복잡한 구조물에서도 물론, 다양한 경계조건을 포함하는 문제에 이르기까지 효과적인 수치방법이다. 본 연구에서는 기본 쉘의 지배방정식을 유도하고 차분화 하여 직접적으로 접근하였다. 등분포 하중의 내압을 받고 있는 갇힌 실린더 형 쉘의 처짐 및 응력을 해석 하였다. 수치해석 결과를 해석해와 비교 검토하였으며 안정성에 대하여 임계 하중강도의 범위를 산출하였다

시간영역에서 변위만을 이용하여 수행되는 3차원 변위근사 유한차분 탄성파 모델링에서 자유면 경계조건을 정확히 묘사하기 위한 방법으로 육면체 내부에 매질의 물성을 정의할 것을 제안한다. 매질의 물성과 변위를 모두 격자점에 정의하는 기존의 방법과는 달리, 매질의 물성을 육면체 내부에 정의할 경우 추가적인 자유면 경계조건을 사용하지 않고도 매질의 물성의 변화만으로 자유면에서 응력이 사라진다는 자유면 경계조건을 만족시킬 수 있다. 무한 균질 매질과 반무한 균질 매질에 대하여 수치적인 해와 해석적인 해를 비교함으로써 육면체 내부에 매질의 물성을 정의하는 3차원 유한차분 탄성파 모델링법의 정확성을 확인하였다. 송신원과 수진기의 위치가 서로 바뀐 경우에 대하여 수치적으로 구한 해들을 비교함으로써 육면체 내부에 매질의 물성을 정의하는 3차원 유한차분 탄성파 모델링 알고리듬이 상반원리 (reciprocity theorem)를 만족시킨다는 것을 알 수 있었다. 또한, 수평층 구조 및 단층구조에 대하여 합성탄성파 단면도 및 스냅단면도를 성공적으로 작성할 수 있었다.

We describe a 3-D time-domain, displacement-based, finite-difference elastic wave modeling algorithm that is constructed by defining the material properties within cubes. In the conventional displacement-based finite-difference method, both displacements and material properties are defined at the nodal points, whereas in our finite-difference algorithm, displacements are still assigned to the nodal points but material properties are defined within cubes. In this case, free-surface boundary conditions, which describe stress-free at the free surface, are naturally satisfied by the changes of material properties. Through numerical examples for infinite homogeneous and semi-infinite homogeneous models, we could examine the accuracy of the 3-D finite-difference elastic wave modeling algorithm. Some numerical examples showed that the 3-D finite-differenc elastic wave modeling algorithm satisfies the reciprocity theorem and successfully generates synthetic seismograms and snapshots.

Since seismic anisotropy often appears in geological media, which may result from various causes, we need to describe anisotropic features in seismic modeling and inversion. Although a number of modeling algorithms were developed to describe seismic anisotropy, we still need to develop a simple but accurate modeling algorithm to simulate geological scale models. For such a modeling algorithm for anisotropic media, we extend a time-domain cell-based finite-difference method to anisotropic media. Since the cell-based finite-difference scheme only employs displacements, we can expect that our anisotropic modeling algorithm is computationally more efficient than the staggered-grid finite-difference method. Because our algorithm does not require any interpolations, it’s possible to simulate a model whose material properties abruptly change. In order to suppress artificial reflections originating from the outer boundaries of a given model, we apply Higdon’s absorbing boundary conditions. Numerical examples show that our modeling algorithm can properly describe anisotropic features.

Parameter identification problem has important research background and research value, has become in recent years inverse problem of heat conduction of top priority. This paper studies the Parabolic Equation Inverse Problems of parameter identification problem, and applies PSO to solve research. Firstly, this paper establishes the model of the inverse problem of partial differential equations. The content and classification of the inverse problem of partial differential equations are explained. Frequently, the construction and solution of the finite difference method for parabolic equations are studied, and two stable schemes for one dimensional parabolic equation are given. And two numerical simulations were given. Partial differential equation discretization was with difference quotient instead of partial derivative. The partial differential equations with initial boundary value problem into algebraic equations, and then solving the resulting algebraic equations. Then, the basic principles of PSO and its improved algorithms are studied and compared. Particle swarm optimization algorithm program implementation. Finally, the Parabolic Equation Inverse Problems of particle swarm optimization algorithm performed three simulations. We use a set of basis functions gradually approaching the true solution, selection of initial value. The reaction is converted into direct problem question, then use difference method Solution of the direct problem. The solution of the problem with the additional conditions has being compared. The reaction optimization problem is transformed into the final particle swarm optimization algorithm to solve. Verify the Parabolic Equation Inverse Problems of particle swarm optimization algorithm correctness and applicability.

As for heavy traffic, road congestion and the hard extraction of vehicles in dynamic video, an improved method of dynamic video background updating is proposed. By using frame-to-frame differences and mask technology, the hole of difference image is eliminated, then extracts the reliably initial background. The image is segmented by using double threshold based on the combination of Bacterial Foraging Optimization Algorithm and Otsu Algorithm to improve the effect and reliability of background updating. Experiments shows that it is an effective way that is good in speed and effective in background extraction, and provides a good foundation for further study of the vehicle tracking.

In this paper we propose a model of bone remodeling which takes in consideration the elasticity with damage properties of the material. Also the non linear equation of the bone apparent density is solved by a finite difference method, particularly a model with n unit elements. We will study the influence of damage damping on the adaptation of the structure under the effect of a controlled mechanical loading.

We discuss a finite difference preconditioner for the$C^1$ Lagrance quadratic spline collocation method for a uniformly elliptic operator with homogeneous Dirichlet boundary conditions. Using the generalized field of values argument, we analyzed eigenvalues of the matrix preconditioned by the matrix corresponding to a finite difference operator with zero boundary condition.

The straight rectangular fin is analyzed using the one-dimensional analytic method and the finite difference method. For the finite difference method, the numbers of nodes vary from 20 to 100. The relative errors of heat loss and temperature between the analytic method and the finite difference method are represented as a function of Biot Number and dimensionless fin length. One of the results shows that the relative error between the analytic method and the finite difference method decreases as the numbers of nodes for finite difference method increase.

In this paper, we develop an accurate explicit finite difference method for the two-dimensional Black-Scholes equation with a hybrid boundary condition. In general, the correlation term in multi-asset options is problematic in numerical treatments partially due to cross derivatives and numerical boundary conditions at the far field domain corners. In the proposed hybrid boundary condition, we use a linear boundary condition at the boundaries where at least one asset is zero. After updating the numerical solution by one time step, we reduce the computational domain so that we do not need boundary conditions. To demonstrate the accuracy and efficiency of the proposed algorithm, we calculate option prices and their Greeks for the two-asset European call and cash-or-nothing options. Computational results show that the proposed method is accurate and is very useful for nonlinear boundary conditions.

In this paper, we aim to construct a nonstandard finite difference (NSFD) scheme to solve numerically a mathematical model for cholera epidemic dynamics. We first show that if the basic reproduction number is less than unity, the disease-free equilibrium (DFE) is locally asymptotically stable. Moreover, we mainly establish the global stability analysis of the DFE and endemic equilibrium by using suitable Lyapunov functionals regardless of the time step size. Finally, numerical simulations with different time step sizes and initial conditions are carried out and comparisons are made with other well-known methods to illustrate the main theoretical results.

In this paper, a generalized discretization scheme is proposed that can derive general-order finite difference equations representing the joint probability density function of dynamic response of stochastic systems. The various order of finite difference equations are applied to solutions of the Fokker-Planck-Kolmogorov (FPK) equation. The finite difference equations derived by the proposed method can greatly increase accuracy even at the tail parts of the probability density function, giving accurate reliability estimations. Compared with exact solutions and finite element solutions, the generalized finite difference method showed increasing accuracy as the order increases. With the proposed method, it is allowed to use different orders and types (i.e. forward, central or backward) of discretization in the finite difference method to solve FPK and other partial differential equations in various engineering fields having requirements of accuracy or specific boundary conditions.

We present an accurate and efficient numerical method for solving the Black-Scholes equation. The method uses an adaptive grid technique which is based on a far-field boundary position and the Peclet condition. We present the algorithm for the automatic adaptive grid generation: First, we determine a priori suitable far-field boundary location using the mathematical model parameters. Second, generate the uniform fine grid around the non-smooth point of the payoff and a non-uniform grid in the remaining regions. Numerical tests are presented to demonstrate the accuracy and efficiency of the proposed method. The results show that the computational time is reduced substantially with the accuracy being maintained.

In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method (FChFD). The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. We tested this technique to solve numerically fractional BVPs. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The fractional derivatives are presented in terms of Caputo sense. The application of the method to fractional BVPs leads to algebraic systems which can be solved by an appropriate method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.

Transmission losses of various reactive silencers are predicted, using a time accurate finite difference method. The numerical scheme is the 3rd order upwind scheme for axisymmetric Euler equations. Main advantage of the present method is that it can simulate linear and non-linear wave propagation phenomena in a flow field directly with minimum numerical oscillation errors. The special treatments of incident wave condition, i.e. multiple harmonics of the transparent acoustic condition are applied to the transmission loss prediction for calculation efficiency. For the validation of the present approach, circular expansion chamber silencers without mean flow and an exponential pipe with mean flow are simulated in case of linear incident wave. The computed transmission losses have quite good agreements with those of the others. The nonlinear incident wave case is also investigated to check the usefulness of this method. The periodic N wave is clearly captured without numerical oscillation errors, and the insertion losses of two different incident frequencies are compared.

In this paper, finite difference method is applied to approximate the generalized solutions of Sobolev equations. Using the Steklov mollifier and Bramble-Hilbert Lemma, a priori error estimates in discrete $L^2$ as well as in discrete $H^1$ norms are derived frist for the semidiscrete methods. For the fully discrete schemes, both backward Euler and Crank-Nicolson methods are discussed and related error analyses are also presented.

In this paper we developed a finite difference method with the highest effect to solve the beam which is rest on elastic foundation. The method is superior to other well-known approaches to this problem in that it allows a wider range of boundary conditions to be dealt with, such as are encountered in complex engineering operations. Using the finite difference method, the equations are converted into algebraic simultaneous equations. Several example problems are discussed and illustrated, and comparisons are made with analytical results.

Thermoforming is one of the most versatile and economical process to produce polymer products. The drawback of thermoforming is difficult to control thickness of final products. Temperature distribution affects the thickness distribution of final products, but temperature difference between surface and center of sheet is difficult to decrease because of low thermal conductivity of ABS material. In order to decrease temperature difference between surface and center, heating profile must be expressed as exponential function form. In this study, Finite Difference Method was used to find out the coefficients of optimal heating profiles. Through investigation, the optimal results using Finite Difference Method show that temperature difference between surface and center of sheet can be remarkably minimized with satisfying Temperature of Forming Window.

In this paper we are concerned with the structural stability of circular arch structure. The critical load is defined as the smallest load at which the equilibrium of the structure fails to be stable as the load is slowly increased from zero. For arch structure the stability determination may be based on a criterion known as the critical load. The finite difference method for the analysis of circular arch is presented. Example problems were solved utilizing the circular curved beam formulation. These solutions were compared to those obtained by finite element results. Solutions include deflections, reactions, critical load and stress resultants in static, planar arches with partial distributed loads. Critical load range for stability will be estimated from the solutions.