• Journal of Mechanical Science and Technology
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• 제17권7호
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• pp.986-998
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• 2003

In this paper, an adaptive numerical integration scheme, which does not need non-overlapping and contiguous integration meshes, is proposed for the MLPG (Meshless Local Petrov-Galerkin) method. In the proposed algorithm, the integration points are located between the neighboring nodes to properly consider the irregular nodal distribution, and the nodal points are also included as integration points. For numerical integration without well-defined meshes, the Shepard shape function is adopted to approximate the integrand in the local symmetric weak form, by the values of the integrand at the integration points. This procedure makes it possible to integrate the local symmetric weak form without any integration meshes (non-overlapping and contiguous integration domains). The convergence tests are performed, to investigate the present scheme and several numerical examples are analyzed by using the proposed scheme.

• 한국수학교육학회지시리즈A:수학교육
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• 제37권1호
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• pp.101-114
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• 1998

In this thesis, We tried to introduce definite integration to the curriculum of high school mathematics with numerical integration, which had been introduced with quadrature method. For this purpose, We used new experimental mathematics approaches, so-called investigation and examination. In chapter II, We examined how much computers had been used in teaching mathematics. In chapter III, We presented the theoretical background of approximation integration within numerical integration. In chapter IV, We studied and compared various methods of numerical integration, and examined the relation between curvature of a curved line and numerical integration. In order to study more easily, We used some of computer programs. We hope that this thesis will be a turning point in developing new teaching methods and improving curriculum of mathematics in high school.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.1249-1253
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• 2001

Numerical analysis is sometimes used to solve the problems in the engineering and natural science fields. On this reason, the faster, more practical system in computing the numerical solution is required. This paper deals with the numerical evaluation of various numerical integration methods which is frequently used in the engineering fields. This paper choices four integration methods such as Euler method, Heun's method, Runge-Kutta method and Gill's method for evaluating the each integration method. In numerical examples, the free vibration problem on an elastic foundation is chosen. As the numerical results, the natural frequencies and the running time are obtained, and these results are compared to examine the practicality of integration methods.

• Journal of Mechanical Science and Technology
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• 제20권1호
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• pp.94-109
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• 2006

An improved meshfree method called the Petrov-Galerkin natural element (PG-NE) method is introduced in order to secure the numerical integration accuracy. As in the Bubnov-Galerkin natural element (BG-NE) method, we use Laplace interpolation function for the trial basis function and Delaunay triangles to define a regular integration background mesh. But, unlike the BG-NE method, the test basis function is differently chosen, based on the Petrov-Galerkin concept, such that its support coincides exactly with a regular integration region in background mesh. Illustrative numerical experiments verify that the present method successfully prevents the numerical accuracy deterioration stemming from the numerical integration error.

• Structural Engineering and Mechanics
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• 제65권1호
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• pp.91-98
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• 2018

Three structure-dependent integration methods with no numerical dissipation have been successfully developed for time integration. Although these three integration methods generally have the same numerical properties, such as unconditional stability, second-order accuracy, explicit formulation, no overshoot and no numerical damping, there still exist some different numerical properties. It is found that TLM can only have unconditional stability for linear elastic and stiffness softening systems for zero viscous damping while for nonzero viscous damping it only has unconditional stability for linear elastic systems. Whereas, both CEM and CRM can have unconditional stability for linear elastic and stiffness softening systems for both zero and nonzero viscous damping. However, the most significantly different property among the three integration methods is a weak instability. In fact, both CRM and TLM have a weak instability, which will lead to an adverse overshoot or even a numerical instability in the high frequency responses to nonzero initial conditions. Whereas, CEM possesses no such an adverse weak instability. As a result, the performance of CEM is much better than for CRM and TLM. Notice that a weak instability property of CRM and TLM might severely limit its practical applications.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1988년도 전기.전자공학 학술대회 논문집
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• pp.950-953
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• 1988

The equations of motion for linearly elastic bodies undergoing large displacement motion are derived. This produces a set of equations which are efficient to numerically integrate. The equations for the elastic bodies are formulated and simplified to provide as much efficiency as possible in their numerical solution. A futher efficiency is obtained through the use of floating reference frame. The equation are presented in two forms for numerical integration. 1) Explicit numerical integration 2) Implicit numerical integration. In this paper, there was used the numerical integration. The implicit numerical integration is extended to solved second order equation, futher reducing the numerical effort required. The formulation given is seen to be occulate and is expected to be efficient for many types of problems.

• 한국지반공학회지:지반
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• 제14권4호
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• pp.129-140
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• 1998

탄소성 유한 요소 해석은 기지의 변형률 증분에 대한 응력 적분을 필요로 하며, 탄소성 구성 모델의 경우 특별한 경우를 제외하고는 해석적인 응력 적분이 불가능하고 수치적인 방법을 필요로 한다. 이때 응력 수치 적분의 정확도가 비선형 유한요소해의 전체적인 정확도에 상당히 큰 영향을 미치게 된다. 본 연구에서는 탄소성 구성 관계의 응력 적분을 위하여 외연적 방법중의 하나로서 Sloan이 제안한 단계분할 절차를 보완하여 안정적이고 정착한 응력 수치 적분법을 제시하고자 한다. 수정 오일러 절차에 따른 오차 조절의 기본 개념은 그대로 사용하고 오차를 평가하는 기준에 응력 수준이 영향을 미치는 단점을 보완하여 응력 수준에 관계없는 안정적이고 정확한 수치 적분법을 제시하였으며, 그 결과의 신뢰성을 삼축시험모사를 이용하여 검증하였다.

• 항공우주기술
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• 제13권2호
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• pp.60-65
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• 2014

본 논문에서는 적분 행렬을 이용한 수치적분 방법을 연구하였다. 비선형 운동방정식에 대한 빠른 수치적분을 수행하기 위해, 적분 행렬을 이용한 개선된 fixed point iteration 방법을 소개한다. 예제로는 궤도 운동에 대한 수치적분 예를 고려한다. 수치 예제를 통하여, 본 논문에서 연구되는 알고리듬이 적분의 정밀도는 크게 저하시키지 않음과 동시에, 계산시간 측면에서 효과적이라는 것을 보인다.

• Journal of Mechanical Science and Technology
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• 제14권1호
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• pp.103-112
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• 2000

Numerical simulations of unsteady opposed-flow flames are performed using an adaptive time integration method designed for differential-algebraic systems. The compressibility effect is considered in deriving the system of equations, such that the numerical difficulties associated with a high-index system are alleviated. The numerical method is implemented for systems with detailed chemical mechanisms and transport properties by utilizing the Chemkin software. Two test simulations are performeds hydrogen/air diffusion flames with an oscillatory strain rate and transient ignition of methane against heated air. Both results show that the rapid transient behavior is successfully captured by the numerical method.

• Structural Engineering and Mechanics
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• 제65권1호
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• pp.121-128
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• 2018

Three structure-dependent integration methods with no numerical dissipation have been successfully developed for time integration. Although these three integration methods generally have the same numerical properties, such as unconditional stability, second-order accuracy, explicit formulation, no overshoot and no numerical damping, there still exist some different numerical properties. It is found that TLM can only have unconditional stability for linear elastic and stiffness softening systems for zero viscous damping while for nonzero viscous damping it only has unconditional stability for linear elastic systems. Whereas, both CEM and CRM can have unconditional stability for linear elastic and stiffness softening systems for both zero and nonzero viscous damping. However, the most significantly different property among the three integration methods is a weak instability. In fact, both CRM and TLM have a weak instability, which will lead to an adverse overshoot or even a numerical instability in the high frequency responses to nonzero initial conditions. Whereas, CEM possesses no such an adverse weak instability. As a result, the performance of CEM is much better than for CRM and TLM. Notice that a weak instability property of CRM and TLM might severely limit its practical applications.