• Structural Engineering and Mechanics
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• 제18권6호
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• pp.731-744
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• 2004

Modified virtual crack closure integral (MVCCI) technique has become very popular for computation of strain energy release rate (SERR) and stress intensity factor (SIF) for 2-D crack problems. The objective of this paper is to propose a numerical integration procedure for MVCCI so as to generalize the technique and make its application much wider. This new procedure called as numerically integrated MVCCI (NI-MVCCI) will remove the dependence of MVCCI equations on the type of finite element employed in the basic stress analysis. Numerical studies on fracture analysis of 2-D crack (mode I and II) problems have been conducted by employing 4-noded, 8-noded (regular & quarter-point), 9-noded and 12-noded finite elements. For non-singular (regular) elements at crack tip, NI-MVCCI technique generates the same results as MVCCI, but the advantage for higher order regular and singular elements is that complex equations for MVCCI need not be derived. Gauss numerical integration rule to be employed for 8-noded singular (quarter-point) element for accurate computation of SERR and SIF has been recommended based on the numerical studies.

• 한국통신학회논문지
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• 제18권1호
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• pp.143-149
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• 1993

An approach is presented for efficient numerical integration of the Sormnerfeld type integrals pertinent to the microstrip surface Green's function arising in the problem of an electric current point source on an infinite planar grounded dielectric substrate. This approach, valid for both lossless and lossy dielectric substrates, is based on the deformation of the integration contour via a coordinate transformation and Cauchy's residue theory, and identifies clearly the effects of surface waves. I ts useful application is in a rigorous moment method analysis of micros trip antenna arrays and microstrip guided wave structures. The efficiency and the usefulness of the present approach are emphasized through some numerical calculations of the impedance matrix elements with associated CPU times.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 추계학술대회논문집A
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• pp.324-329
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• 2001

A novel method for non-matching interfaces on the boundaries of the finite elements in partitioned domains is presented by introducing interface elements in this paper. The interface element method (IEM) satisfies the continuity conditions exactly through interfaces without recourse to the Lagrange multiplier technique. The moving least square (MLS) approximation in the present study is implemented to construct the shape functions of the interface elements. Alignment of the boundaries of sub-domains in the MLS approximation and integration domains provides a consistent numerical integration due to one form of rational functions in an integration domain. The compatibility of displacements on the boundaries of the finite elements and the interface elements is always preserved in this method, and the completeness of the shape functions of the interface elements guarantees the convergence of numerical solutions. The numerical examples show that the interface element method is a useful tool for the analysis of a partitioned system and for a global-local analysis.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제26권2호
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• pp.155-176
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• 2012

미분적분학에서 정적분의 수치계산법에 대한 팀프로젝트(Team Project) 문제를 제시한다. 제시한 팀프로젝트 문제는 흉부 CT 사진을 통해서 폐의 부피를 구하는 것으로 특별히 의학을 공부하는 학생들에게 흥미를 유발할 수 있는 전문화 및 특성화된 미분적분학(정적분의 수치계산법) 수업이 될 것이다. 또한 프로젝트 해결 과정에서 다양한 테크놀로지(MATLAB, MATHEMATICA, MS-Excel)를 도입한다.

• 대한기계학회논문집A
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• 제30권12호
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• pp.1626-1633
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• 2006

In the present paper, in the context of the meshless interpolation of a moving least squares (MLS) type, a novel method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order to improve the accuracy of solution. The secondary nodes can be placed at any location where one needs to obtain a better resolution. The support domains for the shape functions in the MLS approximation are defined from the primary nodes, and the secondary nodes use the same support domains. The shape functions based on the MLS approximation, in an integration domain, have a single type of a rational function, which reduces the difficulty of numerical integration to evaluate the weak form. The present method is very useful in an adaptive calculation, because the secondary nodes can be easily added and moved without an additional mesh. Several numerical examples are presented to illustrate the effectiveness of the present method.

• 소성∙가공
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• 제4권4호
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• pp.365-374
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• 1995

Numerical simulation of blade forming is carried out as stretch forming by an elasto-plastic finite element method. The method adopts a Lagrangian formulation, which incorporates large deformation and rotation, with a penalty method to treat the contact boundary condition. Numerical integration is done with a directional reduced integration scheme to avoid shear locking. The numerical results demonstrates various final shapes of blades which depend on the variation of the stretching force. The strain distributions in deformed blades are also obtained with the variation of the stretching force.

• 한국산업융합학회 논문집
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• 제12권3호
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• pp.149-155
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• 2009

A new finite element equation is derived by applying quadratic and cubic time integration scheme to the variational formulation in time-integral for the analysis of the transient elastodynamic problems to increase the numerical accuracy and stability. Emphasis is focused on methodology for cubic time integration scheme procedure which are never presented before. In this semidiscrete approximations of the field variables, the time axis is divided equally and quadratic and cubic time variation is assumed in those intervals, and space is approximated by the usual finite element discretization technique. It is found that unconditionally stable numerical results are obtained in case of the cubic time variation. Some numerical examples are given to show the versatility of the presented formulation.

• 한국자동차공학회논문집
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• 제2권1호
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• pp.106-115
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• 1994

A parallel integration approach is proposed for real-time simulation of controlled mechanical systems. The proposed approach, which employs the dual-rate integration method in a parallel computing environment, is developed to deal with stiffness and high frequency characteristics of the controlled mechanical systems effectively. Numerical experiments are performed to demonstrate the effectiveness of the approach in shared memory multiprocessors, Alliant FX/8 and Alliant FX/80.

• Structural Engineering and Mechanics
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• 제28권5호
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• pp.549-570
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• 2008

Numerical integration is an efficient approach for nonlinear dynamic analysis. In this paper, general category of the implicit integration errors will be discussed. In order to decrease the errors, Dynamic Relaxation method with modified time step (MFT) will be used. This procedure leads to an alternative algorithm which is very general and can be utilized with any implicit integration scheme. For numerical verification of the proposed technique, some single and multi degrees of freedom nonlinear dynamic systems will be analyzed. Moreover, results are compared with both exact and other available solutions. Suitable accuracy, high efficiency, simplicity, vector operations and automatic procedures are the main merits of the new algorithm in solving nonlinear dynamic problems.

• 한국정밀공학회지
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• 제13권2호
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• pp.185-193
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• 1996

Errors included in solutions obtained by the boundary element method are generally larger than those by the finite element method in the case that the number of discreted elements is small. One of the reasons is supposed to be attributed to the error which will be produced in the numerical integration of the singular functions in two dimensional elastic problem. Then, treatment of analytical integration to reduce computing time and to decrease errors of boundary element method are proposed.