• Structural Engineering and Mechanics
• /
• 제2권2호
• /
• pp.185-196
• /
• 1994

In this paper a spline function solution for the ultimate strength of steel members and member structures is derived based on total Lagrangian formulation. The displacements of members along longitudinal and transverse directions are interpolated by one-order B spline functions and three-order hybrid spline functions respectively. Equilibrium equations are established according to the principle of virtual work. All initial imperfections of members and effects of loading, unloading and reloading of material are taken into account. The influence of the instability of members on structural behavior can be included in analyses. Numerical examples show that the method of this paper can satisfactorily analyze the elasto-plastic large deflection problems of planar steel member and member structures.

• Structural Engineering and Mechanics
• /
• 제4권4호
• /
• pp.415-424
• /
• 1996

This paper presents a newly suggested calculation method in which an arbitrary quadrilateral element with curved sides is transformed to a normal rectangular one by mapping of coordinates, then the two-dimensional spline is adopted to approach the displacement function of this element. Finally the solution can be obtained by the least-energy principle. Thereby, the application field of Spline Finite Element Method will be extended.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제3권1호
• /
• pp.13-17
• /
• 2003

A continuous solution of the Dirichlet boundary value problem for the heat equation $u_t$＝$a2u_{xx}$ using a fuzzy system is described. We first apply the Crank-Nicolson method to obtain a discrete solution at the grid points for the heat equation. Then we find a continuous function to represent approximately the discrete values at the grid points in the form of a bicubic spline function (equation omitted) that can in turn be represented exactly by a fuzzy system. We show that the computed values at non-grid points using the bicubic spline function is much smaller than the ones obtained by linear interpolations of the values at the grid points. We also show that the fuzzy rule table in the fuzzy system representation of the bicubic spline function can be viewed as a gray scale image. Hence, the fuzzy rules provide a visual representation of the functions of two variables where the contours of different levels for the function are shown in different gray scale levels

• Journal of Ship and Ocean Technology
• /
• 제6권1호
• /
• pp.34-53
• /
• 2002

Numerical solution of the forward-speed radiation problem for a half-immersed cylinder advancing in regular waves is presented by making use of the improved Green integral equation in the frequency domain. The B-spline higher order panel method is employed stance the potential and its derivative are unknown at the same time. The present numerical solution of the improved Green integral equation by the B-spline higher order Kelvin panel method is shown to be free of irregular frequencies which are present in the Green integral equation using the forward-speed Kelvin-type Green function.

• Structural Engineering and Mechanics
• /
• 제12권3호
• /
• pp.313-328
• /
• 2001

A multi-span bridge has the peak value of resultant girder moment or membrane stress at the interior support. In this paper, the spline finite strip method (FSM) is modified to obtain the more appropriate solution at the interior support where the peak values of solution exist. The modification has been achieved by expressing the shape function with non-periodic B-splines which have multiple knots at the boundary. The modified B-splines have the useful feature for interpolating the curve with sudden change in curvature. Moreover, the modified spline FSM is very efficient in analyzing multi-span box girder bridges, since a bridge can be modeled by an assembly of strips extended along the entire bridge length. Numerical examples of the bridge analysis have been performed to verify the efficiency and accuracy of the new spline FSM.

• 대한전자공학회논문지
• /
• 제22권5호
• /
• pp.83-86
• /
• 1985

Fredholm 제 2종 적분 방정식의 수치해법에 관한 새로운 기범을 제시하였다. 문제 영역의 절점에 데이터를 혼합 형태로 가함으로써 근사해를 구하였다. 수치 해법에서 오차를 줄이기 위하여 모든 절정에서 2번 연속 미분가능한 cubic B-spline 함수를 기저함수로 사용하였다. 기저함수로서 cubit B-spline 함수를 이용한 본 기법의 결과와 기저함수로 pulse 함수 test 함수로는 delta 함수를 이용한 모멘트법의 결과를 예제를 통하여 비교하였다. 또한 이 방법에 대한 수렴 조건을 기술 하였다.

• Structural Engineering and Mechanics
• /
• 제18권2호
• /
• pp.247-262
• /
• 2004

In the earlier application of the spline finite strip method(FSM), the uniform B3-spline functions were used in the longitudinal direction while the conventional interpolation functions were used in the transverse direction to construct the displacement filed in a strip. To overcome the shortcoming of the uniform B3-spline, non-periodic B-spline was developed as the displacement function. The use of non-periodic B3-spline function requires no tangential vectors at both ends to interpolate the geometry of shell and the Kronecker delta property is also satisfied at the end boundaries. Recently, non-periodic spline FSM which was modified to have a multiple knots at the boundary was developed for the shell analysis and applied to the analysis of bridges. In the formulation of a non-symmetric spline finite strip method, the concepts of non-periodic B3-spline and a stress-resultant finite strip with drilling degrees of freedom for a shell are used. The introduction of non-symmetrically spaced knots in the longitudinal direction allows the selective local refinement to improve the accuracy of solution at the connections or at the location of concentrated load. A number of numerical tests were performed to prove the accuracy and efficiency of the present study.

• 한국CDE학회논문집
• /
• 제15권1호
• /
• pp.24-32
• /
• 2010

This paper introduces a B-spline based branch & bound algorithm for global optimization. The branch & bound is a well-known algorithm paradigm for global optimization, of which key components are the subdivision scheme and the bound calculation scheme. For this, we consider the B-spline hypervolume to approximate an objective function defined in a design space. This model enables us to subdivide the design space, and to compute the upper & lower bound of each subspace where the bound calculation is based on the LHS sampling points. We also describe a search tree to represent the searching process for optimal solution, and explain iteration steps and some conditions necessary to carry out the algorithm. Finally, the performance of the proposed algorithm is examined on some test problems which would cover most difficulties faced in global optimization area. It shows that the proposed algorithm is complete algorithm not using heuristics, provides an approximate global solution within prescribed tolerances, and has the good possibility for large scale NP-hard optimization.

• 한국전산응용수학회:학술대회논문집
• /
• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
• /
• pp.4.2-4
• /
• 2003

In this paper, we describe how to approximate the solutions of partial differential equations by bicubic spline functions whose interpolation errors at non-grid points are smaller in general than those by linear interpolations of the original solution at grid points. We show that the bicubic spline function can be represented exactly or approximately by a fuzzy system, and that the resulting fuzzy rule table shows the contours of the solution function. Thus, the fuzzy rule table is identified as a digital image and the contours in the rule table provide approximate contours of the solution of partial differential equations. Several illustrative examples are included.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• 제5권4호
• /
• pp.286-290
• /
• 2005

We consider the poisson equation where the functions involved are periodic including the solution function. Let $R=[0,1]{\times}[0,l]{\times}[0,1]$ be the region of interest and let $\phi$(x,y,z) be an arbitrary periodic function defined in the region R such that $\phi$(x,y,z) satisfies $\phi$(x+1, y, z)=$\phi$(x, y+1, z)=$\phi$(x, y, z+1)=$\phi$(x,y,z) for all x,y,z. We describe a very simple method for solving the equation ${\nabla}^2u(x, y, z)$ = $\phi$(x, y, z) based on the cubic spline interpolation of u(x, y, z); using the requirement that each interval [0,1] is a multiple of the period in the corresponding coordinates, the Laplacian operator applied to the cubic spline interpolation of u(x, y, z) can be replaced by a square matrix. The solution can then be computed simply by multiplying $\phi$(x, y, z) by the inverse of this matrix. A description on how the storage of nearly a Giga byte for $20{\times}20{\times}20$ nodes, equivalent to a $8000{\times}8000$ matrix is handled by using the fuzzy rule table method and a description on how the shape preserving property of the Laplacian operator will be affected by this approximation are included.