• Interaction and multiscale mechanics
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• 제3권3호
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• pp.235-255
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• 2010

This paper investigates the heat equation for domains subjected to an internal source with a sharp spatial gradient. The solution is first approximated using linear finite elements, and sufficiently small time-step sizes to yield stable simulations. The main area of interest is then in the ability to approximate the solution using Generalized Finite Elements, and again explore the time-step limitations required for stable simulations. Both high order elements, as well as elements with special enrichments are used to generate solutions. When compared to linear finite elements, the high order elements deliver better accuracy at a given level of mesh refinement, but do not offer an increase in critical time-step size. When special enrichment functions are used, the solution can be approximated accurately on very coarse meshes, while yielding solutions which are both accurate and computationally efficient. The major conclusion of interest is that the significantly larger element size yields larger allowable time-step sizes while still maintaining stability of the time-stepping algorithm.

• Journal of Theoretical and Applied Mechanics
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• 제3권1호
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• pp.66-80
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• 2002

The bilinear formulation proposed earlier by Peters and Izadpanah to develop finite elements in time to solve undamped linear systems, Is extended (and found to be readily amenable) to develop time finite elements to obtain transient responses of both linear and nonlinear, and damped and undamped systems. The formulation Is used in the h-, p- and hp-versions. The resulting linear and nonlinear algebraic equations are differentiated to obtain the first- and second-order sensitivities of the transient response with respect to various system parameters. The present developments were tested on a series of linear and nonlinear examples and were found to yield, when compared with results obtained using other methods, excellent results for both the transient response and Its sensitivity to system parameters. Mostly. the results were obtained using the Legendre polynomials as basis functions, though. in some cases other orthogonal polynomials namely. the Hermite. the Chebyshev, and integrated Legendre polynomials were also employed (but to no great advantage). A key advantage of the time finite element method, and the one often overlooked in its past applications, is the ease In which the sensitivity of the transient response with respect to various system parameters can be obtained. The results of sensitivity analysis can be used for approximate schemes for efficient solution of design optimization problems. Also. the results can be applied to gradient-based parameter identification schemes.

• Structural Engineering and Mechanics
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• 제5권4호
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• pp.385-398
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• 1997

High order finite element have a greater convergence rate than low order finite elements, and in general produce more accurate results. These elements have the disadvantage of being more computationally expensive and often require a longer time to solve the finite element analysis. High order elements have been used in this paper to obtain a new eigenvalue solution with out re-solving the new model. The optimisation of the eigenvalue via the differentiation of the Rayleigh quotient has shown that the additional nodes associated with the higher order elements can be condensed out and solved using the original finite element solution. The higher order elements can then be used to calculate an improved eigenvalue for the finite element analysis.

• 한국전산구조공학회논문집
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• 제19권1호
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• pp.39-46
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• 2006

본 연구는 파 해석에 있어서 공간-시간 분할 개념을 도입하여 켈러킨 방법으로 해석하였다. 공간-시간 유한요소법은 오직 공간에 대해서만 분할하는 일반적인 유한요소법보다 간편하다. 비교적 큰 시간간격에 대해서 공간과 시간을 동시에 분할하는 방법을 제시하며 가중잔차법이 공간-시간 영역에서 유한요소 정식화에 이용되었다. 큰 시간 간격으로 인하여 문제의 해가 발산하는 경우가 동적인 문제에서 흔히 발생한다. 이러한 결점을 보완한 사각형 공간-시간 요소를 취하여 문제를 해석하고 해의 안정에 대해 기술하였다. 다수의 수치해석을 통하여 이 방법이 효과적 임을 알 수 있었다.

• 한국농업기계학회:학술대회논문집
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• 한국농업기계학회 1993년도 Proceedings of International Conference for Agricultural Machinery and Process Engineering
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• pp.1222-1229
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• 1993

An advanced design environment , which is based on adaptive and knowledge -based finite elements (INTELMESH), has been developed. Unlike other approaches, INTEMMESH incorporates the information about the object geometry as well as the boundary and loading conditions to generate an ${\alpha}$-priori finite element mesh which is more refined around the critical regions of the problem domain. INTEMMESH is designed for planar domains and axisymmetric 3-D structures of elasticity and heat transfer subjected to mechanical and thermal loading . It intelligently identifies the critical regions/points in the problem domain and utilize the new concepts of substructuring and wave propagation to choose the proper mesh size for them. INTEMMESH generates well-shaped triangular elements by applying trangulartion and Laplacian smoothing procedures. The adaptive analysis involves the intial finite elements analyze and an efficient ${\alpha}$-posteriori error analysis involves the initial finite element anal sis and an efficient ${\alpha}$-posteriori error analysis and estimation . Once a problem is defined , the system automatically builds a finite element model and analyzes the problem though automatic iterative process until the error reaches a desired level. It has been shown that the proposed approach which initiates the process with an ${\alpha}$-priori, and near optimum mesh of the object , converges to the desired accuracy in less time and at less cost. Such an advanced design/analysis environment will provide the capability for rapid product development and reducing the design cycle time and cost.

• 전산구조공학
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• 제8권3호
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• pp.91-102
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• 1995

지하터널은 그 경계가 반무한영역에서 설정되고 재료나 형상의 복잡성을 갖고 있기 때문에, 동적하중에 대하여 정확한 거동을 해석하기 위해서는 3차원 동적해석이 필요하다. 이때 일반적인 수치해석기법인 유한요소만을 이용한 방법은 인위적 경계에서의 파의 반사, 입력자료의 방대함 등으로 인하여 효율적이지 못하게 된다. 본 연구는 이러한 점을 고려하여 지하터널에 직접 가해지는 동적하중에 대한 효율적인 해석기법을 개발하는데 그 목적이 있다. 개발된 프로그램에서 지반의 반무한성은 3차원 경계요소로 고려되었으며, 구조물에는 3차원 동적해석을 수행한 결과 기존의 2차원 터널해석에서 고려가 곤란했던 차량의 진행하중으로 인한 반복효과가 합리적으로 반영되는 것으로 분석되었다.

• 한국전산구조공학회논문집
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• 제23권6호
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• pp.659-665
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• 2010

The finite element method(FEM) is proven to be an effective approximate method of structural analysis if proper element types and meshes are chosen, and recently, the method is often applied to solve complex dynamic and nonlinear problems. A properly chosen element type and mesh yields reliable results for dynamic finite element structural analysis. However, dynamic behavior of a structure may include unpredictably large strains in some parts of the structure, and using the initial mesh throughout the duration of a dynamic analysis may include some elements to go through strains beyond the elements' reliable limits. Thus, the finite element mesh for a dynamic analysis must be dynamically adaptive, and considering the rapid process of analysis in real time, the dynamically adaptive finite element mesh generating schemes must be computationally efficient. In this paper, a computationally efficient dynamically adaptive finite element mesh generation scheme for dynamic analyses of structures is described. The concept of representative strain value is used for error estimates and the refinements of meshes use combinations of the h-method(node movement) and the r-method(element division). The shape coefficient for element mesh is used to correct overly distorted elements. The validity of the scheme is shown through a cantilever beam example under a concentrated load with varying values. The example shows reasonable accuracy and efficient computing time. Furthermore, the study shows the potential for the scheme's effective use in complex structural dynamic problems such as those under seismic or erratic wind loads.

• 한국안전학회지
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• 제21권2호
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• pp.143-149
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• 2006

본 논문은 2차원 동적 진동문제를 공간-시간 유한요소법으로 해석하고 있다. 공간-시간 유한요소법은 공간만 분할하는 재래식 유한요소해석에 비해 보다 해를 빠르고 쉽게 얻을 수 있다. 상대적으로 큰 시간간격에 대해서 공간과 시간을 동시에 분할하는 공간-시간 유한요소 근사법을 제시한다. 가중잔차법으로 공간-시간 영역에 대해 유한요소법을 정식화하였으며 선형 사변형 공간-시간 유한요소를 선택하여 해의 안정성에 관하여 언급하였다. 일반적 동적문제에서는 상대적인 큰 시간간격으로 인하여 해의 불안정을 야기 시키고 있으나 본 연구에서는 수치의 안정성을 보여주고 있다. 비구조 공간-시간 유한요소법은 재래식 수치해석에서 흔히 발생하는 해의 불안정성에 대한 결점을 보완함은 물론 효과적인 계산방법을 지니고 있다. 이 방법의 효율성을 위해 수치예제들을 제시하였다.

• 한국자동차공학회논문집
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• 제4권5호
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• pp.16-25
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• 1996

In the present work a rigid-plastic finite element formulation using dynamic explicit time integration scheme is proposed for numerical analysis of auto-body panel stamping processes. The rigid-plastic finite element method based on membrane elements has long been employed as a useful numerical technique for the analysis of sheet metal forming because of its time effectiveness. A damping scheme is proposed in order to achieve a stable solution procedure in dynamic sheet forming problems. In order to improve the drawbacks of the conventional membrane elements, BEAM(abbreviated from Bending Energy Augmented Membrane) elements are employed. Rotational damping and spring about the drilling direction are introduced to prevent a zero energy mode. The lumping scheme is employed for the diagonal mass matrix and linearizing dynamic formulation. A contact scheme is developed by combining the skew boundary condition and the direct trial-and-error method. Computations are carried out for analysis of complicated auto-body panel stamping processes such as forming of an oilpan, a fuel tank and a front fender. The numerical results of explicit analysis are compared with the implicit results with good agreements and it is shown that the explicit scheme requires much shorter computational time, especially when the problem becomes more complicated. It is thus shown that the proposed dynamic explicit rigid-plastic finite element method enables an effective computation for complicated autobody panel stamping processes.

• 대한기계학회논문집A
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• 제24권3호
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• pp.550-559
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• 2000

One of the most important factor to be considered for the analysis of sheet metal forming processes is the tool surface description for arbitrarily- shaped sheet metal parts. In the present study , finite element approach is used to describe the arbitrarily shaped tool surface. In finite element mesh approach, tool surfaces ar, described by finite elements. The finite elements mesh description of the tool surface, which is originally described by CAD data, needs much time and time-consuming graphic operation. The method, however, has been widely used to describe a complex tool surface. In the present study, the contact searching algorithm for the finite element mesh approach is developed based on cell strategy method and sheet surface normal scheme. For the verification purpose, a clover cup drawing, Baden-Baden oilpan problem and a trunk floor drawing were investigated. The computational results based on the finite element approach were compared with the results of available parametric patch approach and experiments.