• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 2001년도 가을 학술발표회 논문집
• /
• pp.53-58
• /
• 2001

This paper deals with the application of numerical differentiation in the structural analysis. In the structural analysis, the derivative values of the given function are sometimes used in calculation of structural behaviors. For calculating the derivative values, both the time and labor are needed when the structures consist of non-linear geometries such as arches or curved beams. From this viewpoint the numerical differentiation scheme is applied into the structural analysis. The numerical results obtained from the numerical differentiation are agreed very well with those obtained from the exact derivatives by analytical method. It is expected that the numerical differentiation can be utilized practically in the structural analysis.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제7권1호
• /
• pp.47-61
• /
• 2003

Two principally different statements of the problem of stable numerical differentiation are considered. It is analyzed when it is possible in principle to get a stable approximation to the derivative ${\Large f}'$ given noisy data ${\Large f}_{\delta}$. Computational aspects of the problem are discussed and illustrated by examples. These examples show the practical value of the new understanding of the problem of stable differentiation.

• 한국자동차공학회논문집
• /
• 제7권5호
• /
• pp.141-153
• /
• 1999

A finite element procedure for the analysis of rubber-like hyperelastic material is developed. The volumetric incompressiblity conditions of the rubber deformation is included in the formulation by using penalty method. In this paper, the behavior of the rubber deformation is represented by hyperelastic constitutive relations based on a generalized Mooney-Rivlin model. The principle of virtual work is used to derive nonlinear finite element equation for the large displacement problem and presented in total-Lagrangian description. The finite element procedure using analytic differentiation resulted in very close solution to the result of the well known commercial packages NISAII AND ABAQUS. Numerical tests show that the results from the numerical differentiation method coincide very well with those from the analytic method and the well known commercial packages in static analysis. The convergency of rubber usingν iteration method is also discussed.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2003년도 추계학술대회논문집
• /
• pp.814-818
• /
• 2003

This paper deals with the application of numerical differentiation in free vibration analysis. In the free vibration analysis, the derivative values of the given function are certainly used in calculation of structural parameters. For deriving the derivative values, both the time and labor are needed when the structures consist of non-linear geometries such as arches or curved beams. From this viewpoint, the numerical differentiation scheme is applied into the free vibration analysis. The numerical results obtained from the numerical differentiations are agreed very well with those obtained from the exact derivatives by analytical method. It is expected that the numerical differentiations can be utilized practically in the free vibration analysis.

• Journal of applied mathematics & informatics
• /
• 제19권1_2호
• /
• pp.527-535
• /
• 2005

Numerical differentiation is one of the main topics which have been studied by many researchers. If we use the forward difference scheme or the centered difference scheme, the convergence rates to the derivative are O(h) and O($h^2$), respectively. In this paper, using the Lagrange Interpolation, we construct a simple high order numerical differentiation scheme which has the convergence rate O($h^{2k}$) if we have 2k+1 equally spaced nodes. Our scheme is constructive.

• 한국전산구조공학회논문집
• /
• 제19권4호
• /
• pp.441-447
• /
• 2006

이 논문은 구조해석에서 수치미분의 적용성에 관한 연구이다. 구조물 선형식의 미분은 구조물의 거동해석에서 반드시 필요한 수학적 계산 중의 하나이다. 아치와 같이 구조물의 선형식이 곡선인 경우에 미분식의 산출은 많은 시간과 노력을 필요로 한다. 이 연구에서는 구조해석에서 수치미분의 적용성을 아치의 자유진동 문제를 통하여 검증하였다. 전진 5차다항식으로부터 아치 곡률항의 미분값을 계산하고 이를 대수적으로 구한 곡률항과 비교하였다 이렇게 얻은 곡률항을 이용하여 최종적으로 산출한 아치의 고유진동수는 문헌해와 아주 우수하게 근접하였다. 이러한 결과로부터 구조해석에서 수치미분의 적용성과 그 결과의 정확성을 입증할 수 있었다.

• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 1999년도 가을 학술발표회 논문집
• /
• pp.359-369
• /
• 1999

The paper describes the study of concurrent subspace optimization(CSSO) for coupled multidisciplinary design optimization (MDO) techniques in mechanical systems. This method is a solution to large scale coupled multidisciplinary system, wherein the original problem is decomposed into a set of smaller, more tractable subproblems. Key elements in CSSO are consisted of global sensitivity equation(GSE), subspace optimization (SSO), optimum sensitivity analysis(OSA), and coordination optimization problem(COP) so as to inquiry valanced design solutions finally, Automatic differentiation has an ability to provide a robust sensitivity solution, and have shown the numerical numerical effectiveness over finite difference schemes wherein the perturbed step size in design variable is required. The present paper will develop the automatic differentiation based concurrent subspace optimization(AD-CSSO) in MDO. An automatic differentiation tool in FORTRAN(ADIFOR) will be employed to evaluate sensitivities. The use of exact function derivatives in GSE, OSA and COP makes Possible to enhance the numerical accuracy during the iterative design process. The paper discusses how much influence on final optimal design compared with traditional all-in-one approach, finite difference based CSSO and AD-CSSO applying coupled design variables.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제12권4호
• /
• pp.275-287
• /
• 2005

Geometric invariants are basic tools for geometric processing and computer vision. In this paper, we give a linear approximation for the differentiation of the binormal vector field of a space curve by using the forward and backward differences of discrete binormal vectors. Two kind of discrete torsion, say, back-ward torsion $T_b$ and forward torsion $T_f$ can be defined by the dot product of the (backward and forward) discrete differentiation of binormal vectors that are linear approximations of torsion. Using Frenet formula and Taylor series expansion, we give error estimations for the discrete torsions. We also give numerical tests for a curve. Notably the average of $T_b$ and $T_f$ looks more stable in errors.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2004년도 추계학술대회
• /
• pp.492-497
• /
• 2004

Three methods for design sensitivity such as numerical differentiation, analytical method and semi-analytical method have been developed for the last three decades. Although analytical design sensitivity analysis is exact, it is hard to implement for practical design problems. Therefore, numerical method such as finite difference method is widely used to simply obtain the design sensitivity in most cases. The numerical differentiation is sufficiently accurate and reliable for most linear problems. However, it turns out that the numerical differentiation is inefficient and inaccurate because its computational cost depends on the number of design variables and large numerical errors can be included especially in nonlinear design sensitivity analysis. Thus semi-analytical method is more suitable for complicated design problems. Moreover semi-analytical method is easy to be performed in design procedure, which can be coupled with an analysis solver such as commercial finite element package. In this paper, implementation procedure for the semi-analytical design sensitivity analysis outside of the commercial finite element package is studied and computational technique is proposed, which evaluates the pseudo-load for design sensitivity analysis easily by using the design variation of corresponding internal nodal forces. Errors in semi-analytical design sensitivity analysis are examined and numerical examples are illustrated to confirm the reduction of numerical error considerably.

• 한국소음진동공학회논문집
• /
• 제17권2호
• /
• pp.185-193
• /
• 2007

이 논문은 곡선부재의 구조해석에서 수치미분의 적용에 관한 연구이다. 구조물 선형식의 미분은 구조물의 거동해석에서 반드시 필요한 수학적 계산 중의 하나이다. 구조물의 선형이 곡선인 경우에 미분식의 산출은 많은 노력과 시간을 필요로 한다. 이 연구에서는 곡선부재의 구조해석에서 미분구적(DQ)을 이용한 수치미분의 적용성을 검증하기 위하여 아치의 자유진동 문제를 택하였다. 미분구적을 이용하여 아치 곡률항의 미분값을 계산하고 이를 대수적으로 구한 정학한 값과 비교하였다. 이 연구에서 얻어진 곡률항을 이용하여 최종적으로 산출한 아치의 고유진동수는 문헌해와 매우 우수하게 근접하였다. 이러한 결과로부터 구조해석에서 미분구적을 이용한 수치미분의 적용성을 입증할 수 있었다.