• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2001년도 춘계학술대회논문집B
• /
• pp.590-595
• /
• 2001

To improve the modeling accuracy for the finite element method, this paper proposes a method to make a combined use of finite elements and exact dynamic elements. Exact interpolation functions for a Timoshenko beam element are derived and compared with interpolation functions of the finite element method (FEM). The exact interpolation functions are tested with the Laplace variable varied. The exact interpolation functions are used to gain more accurate mode shape functions for the finite element method. This paper also presents a combined use of finite elements and exact dynamic elements in design problems. A Timoshenko frame with tapered sections is tested to demonstrate the design procedure with the proposed method.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2000년도 하계학술대회 논문집 D
• /
• pp.2918-2920
• /
• 2000

A new multi-planar interpolation technique for three dimensional medical image rendering is proposed. In medical imaging. resolution in the slice direction is usually much lower than those in the transverse planes. The proposed method is based on the solution of the Laplace's equation used in the electrostatics. In this approach. two contours in the source and destination planes for a given object is assumed to have equi-potentials. Some preprocessing and post-processing including scaling. displacement. rotation from the centers of mass are involved in the algorithm. The interpolation solution assumes mostly smoothing changes in between the source and destination planes. Simultaneous multiple interpolation planes are inherently obtained in the proposed method. Some experimental and simulation results are shown.

• 한국소음진동공학회논문집
• /
• 제12권2호
• /
• pp.141-149
• /
• 2002

Although the finite element method has become an indispensible tool for the dynamic analysis of structures, difficulty remains to quantify the errors associated with discretization. To improve the modeling accuracy, this paper proposes a method to make a combined use of finite elements and exact dynamic elements. Exact interpolation functions for the Timoshenko beam element are derived using the exact dynamic element modeling (EDEM) and compared with interpolation functions of the finite element method (FEM). The exact interpolation functions are tested with the Laplace variable varied. A combined use of finite element method and exact interpolation functions is presented to gain more accurate mode shape functions. This paper also presents a combined use of finite elements and exact dynamic elements in design/reanalysis problems. Timoshenko flames with tapered sections are tested to demonstrate the design procedure with the proposed method. The numerical study shows that the combined use of finite element model and exact dynamic element model is very useful.

• 한국전산유체공학회지
• /
• 제1권1호
• /
• pp.9-18
• /
• 1996

This study examines effect of various interpolations of interior control function for analytic methods such as Thomas-Middlecoff and Sorenson methods. Laplace interpolation is developed and compared among linear interpolation and exponential interpolation systematically.

• 한국전산유체공학회:학술대회논문집
• /
• 한국전산유체공학회 1995년도 추계 학술대회논문집
• /
• pp.104-109
• /
• 1995

This study examines effect of various interpolations of interior control function for analytic methods such as Thomas-Middlecoff and Sorenson methods. Laplace interpolation is developed and compared among linear interpolation and exponential interpolation systematically.

• Journal of Mechanical Science and Technology
• /
• 제20권1호
• /
• pp.94-109
• /
• 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
• /
• 제76권4호
• /
• pp.505-512
• /
• 2020

This paper presents an error estimation technique for 2-D crack analysis by an enriched natural element (more exactly, enriched Petrov-Galerkin NEM). A bare solution was approximated by PG-NEM using Laplace interpolation functions. Meanwhile, an accurate quasi-exact solution was obtained by a combined use of enriched PG-NEM and the global patch recovery. The Laplace interpolation functions are enriched with the near-tip singular fields, and the approximate solution obtained by enriched PG-NEM was enhanced by the global patch recovery. The quantitative error amount is measured in terms of the energy norm, and the accuracy (i.e., the effective index) of the proposed method was evaluated using the errors which obtained by FEM using a very fine mesh. The error distribution was investigated by calculating the local element-wise errors, from which it has been found that the relative high errors occurs in the vicinity of crack tip. The differences between the enriched and non-enriched PG-NEMs have been investigated from the effective index, the error distribution, and the convergence rate. From the comparison, it has been justified that the enriched PG-NEM provides much more accurate error information than the non-enriched PG-NEM.

• 한국항해항만학회지
• /
• 제34권5호
• /
• pp.367-373
• /
• 2010

수치해석을 수행할 경우 좀 더 정확한 수치모의를 위하여 해석영역의 특성에 따라 적절하게 요소를 배치하는 것이 필요하다. 본 연구에서 사용한 개별요소법(DEM)은 입자의 마찰력 및 항력을 제외한 반발력과 인장력만을 적용하였다. 초기 쿼드트리(Quad-tree)형식으로 충진된 입자들을 DEM을 이용하여 재배치할 경우 입자의 형상이 원형이기 때문에 입자사이에 존재하는 빈 공간을 최소화 할 수 있다. 결국 입자 중심점의 배치가 정삼각형에 가깝게 되는 특징을 보여준다. 이 재배치된 입자를 대상으로 Delaunay 삼각기법을 이용하여 삼각망을 구성하고, Laplace 보간을 수행하여 격자 품질을 향상시켰다. Laplace 보간 전 후의 형상비(Aspect Ratio: AR)를 비교한 결과 DEM을 이용하여 작성한 격자의 품질도 우수하지만, Laplace보간을 수행한 이후 보다 높은 품질의 격자가 생성되는 것을 확인하였다. 본 연구에서 개발한 기법은 기존의 삼각격자망 생성기법에 비해 다소 계산시간이 오래 걸리는 단점이 있지만, 복잡한 형상과 정확한 지형의 재현을 필요로 하는 파랑 해석용 유한요소 격자망 작성 및 다양한 수치모의 분야에서 그 적용 가능성이 매우 높다고 사료된다.

• Structural Engineering and Mechanics
• /
• 제56권4호
• /
• pp.589-603
• /
• 2015

The mixed-mode stress intensity factors of 2-D angled cracks are evaluated by Petrov-Galerkin natural element (PG-NE) method in which Voronoi polygon-based Laplace interpolation functions and CS-FE basis functions are used for the trial and test functions respectively. The interaction integral is implemented in a frame of PG-NE method in which the weighting function defined over a crack-tip integral domain is interpolated by Laplace interpolation functions. Two Cartesian coordinate systems are employed and the displacement, strains and stresses which are solved in the grid-oriented coordinate system are transformed to the other coordinate system aligned to the angled crack. The present method is validated through the numerical experiments with the angled edge and center cracks, and the numerical accuracy is examined with respect to the grid density, crack length and angle. Also, the stress intensity factors obtained by the present method are compared with other numerical methods and the exact solution. It is observed from the numerical results that the present method successfully and accurately evaluates the mixed-mode stress intensity factors of 2-D angled cracks for various crack lengths and crack angles.

• 한국전산구조공학회논문집
• /
• 제13권1호
• /
• pp.37-49
• /
• 2000

본 논문은 구조물의 동역학 및 열탄성 연성문제 해석을 위한 통합된 유한요소법을 개발하는데 초점을 두고있다. 첫째로, 열전도 방정식에 열변위라는 물리량을 도입하여 동역학의 운동 방정식과 유사하도록 유도한 후, 변분법과 일반좌표계를 이용하여 시간영역에서 정식화하였다. 둘째로, 두 방정식에 라플라스 변환을 동시에 도입하고, 공간변수만을 갖는 형상함수와 가중잔여법을 적용하여 유한요소식을 변환영역에서 표현하였다. 연성된 방정식을 문제의 특성에 따라서 분류하였고 정식화 과정을 검증하였다. 또한 수치해석 알고리듬이 갖는 수치 역 변환의 정성적인 경향에 대하여 검토하였다.