• Structural Engineering and Mechanics
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• 제5권4호
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• pp.471-490
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• 1997

In this paper, the classical Irons' patch tests which have been generally accepted for the convergence proof of a finite element are performed for Mindlin plate bending elements with a special emphasis on the nonconforming elements. The elements considered are 4-node and 8-node quadrilateral isoparametric elements which have been dominantly used for the analyses of plate bending problems. It was recognized from the patch tests that some nonconforming Mindlin plate elements pass all the cases of patch tests even though nonconforming elements do not preserve conformity. Then, the clues for the Mindlin plate element to pass the Irons' patch tests are investigated. Also, the convergent characteristics of some nonconforming Mindlin plate elements that do not pass the Irons' patch tests are examined by weak patch tests. The convergence tests are performed on the benchmark numerical problems for both nonconforming elements which pass the patch tests and which do not. Some conclusions on the relationship between the patch test and convergence of nonconforming Mindlin plate elements are drawn.

• Structural Engineering and Mechanics
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• 제6권1호
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• pp.41-61
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• 1998

A state-of-the-art report on the new finite elements formulated by the addition of nonconforming displacement modes has been presented. The development of a series improved nonconforming finite elements for the analysis of plate and shell structures is described in the first part of this paper. These new plate and shell finite elements are established by the combined use of different improvement schemes such as; the addition of nonconforming modes, the reduced (or selective) integration, and the construction of the substitute shear strain fields. The improvement achieved may be attributable to the fact that the merits of these improvement techniques are merged into the formation of the new elements in a complementary manner. It is shown that the results obtained by the new elements give significantly improved solutions without any serious defects such as; the shear locking, spurious zero energy mode for the linear as well as nonlinear benchmark problems. Recent developments in the transition elements that have a variable number of mid-side nodes and can be effectively used in the adaptive mesh refinement are presented in the second part. Finally, the nonconforming transition flat shell elements with drilling degrees of freedom are also presented.

• Industrial Engineering and Management Systems
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• 제8권2호
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• pp.72-79
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• 2009

The ultimate goal of inventory management is to decide the timing and the quantity of ordering in response to uncertain demands. Recently, some researchers have focused upon an impact of distortions in the information, e.g., customer order cancellation, on an economical inventory policy. The customer order cancellation is considered a kind of distortions in demands, because a demand that is eventually cancelled is equivalent to a phony demand. Also, there are some additional distortions in the inventory information. For instance, the procurement of suppliers may include some nonconforming items as a result of imperfect production and inspection by the suppliers, and/or damage in transit. The nonconforming item should be considered a kind of distortions in the inventory information, because the nonconforming item is equivalent to a phony stock. In this article, we consider an inventory model under the situation that customers can cancel their orders and the procurement of suppliers may include some nonconforming items. Then, we introduce the customer order reservation into the inventory model for the purpose of avoiding the costly backlogs, because the customer order reservation gives retailers a period to fulfill customer's requests. We formulate a periodic review (s, S) inventory model and investigate the economical operation under the situation mentioned above. Further, through the sensitivity analysis, we show the impact of these distortions and the effect of the customer order reservation on the inventory policy.

• 한국전산구조공학회논문집
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• 제13권4호
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• pp.475-484
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• 2000

본 연구에서는 찌그러진 요소에서의 휨거동 개선을 위한 추가적인 비적합변위형과 효율적인 비적합변위형의 수정방법의 개발을 통하여 기존 비적합 입체요소의 개선을 시도하였으며, 회전자유도가 독립변수로 존재하는 범함수를 이용하여 매개변수의 값에 따라 회전자유도의 도입유무가 결정되도록하는 입체요소를 개발하였다. 제시된 요소에서는 변위장과 회전장에 동일한 형상함수를 적용하였으며, 비적합변위형은 변위장에만 적용하였다. 다양한 예제를 통한 수치실험결과 개발된 요소는 양호한 거동을 보여주었으며, 특히 휨거동에 있어서 개선된 거동을 보였다.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.761-781
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• 2014

An exponentially accurate nonconforming spectral element method for elasticity systems with discontinuities in the coefficients and the flux across the interface is proposed in this paper. The method is least-squares spectral element method. The jump in the flux across the interface is incorporated (in appropriate Sobolev norm) in the functional to be minimized. The interface is resolved exactly using blending elements. The solution is obtained by the preconditioned conjugate gradient method. The numerical solution for different examples with discontinuous coefficients and non-homogeneous jump in the flux across the interface are presented to show the efficiency of the proposed method.

• 대한수학회보
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• 제51권6호
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• pp.1655-1668
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• 2014

In this article, we propose and analyze a new nonconforming primal mixed finite element method for the stationary Stokes equations. The approximation is based on the pseudostress-velocity formulation. The incompressibility condition is used to eliminate the pressure variable in terms of trace-free pseudostress. The pressure is then computed from a simple post-processing technique. Unique solvability and optimal convergence are proved. Numerical examples are given to illustrate the performance of the method.

• 품질경영학회지
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• 제27권1호
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• pp.18-34
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• 1999

This paper is a brief review of the different procedures that are available for fitting theoretical distributions to data. The use of each technique Is illustrated by reference to a distribution system which including the Pearson, Johnson and Burr functions. These functions can be used to calculate percent out of specification. Therefore, in this paper a new method for estimating a measure of process capability for Gamma distributed variable data proposed using the percentage nonconforming. Process capability indices combines with the percentage nonconforming Information can be used to evaluate more accurately process capability.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제1권1호
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• pp.105-125
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• 1997

In this paper we consider multigrid algorithms for solving elasticity problems by using Wilson's nonconforming finite element method. We consider two types of intergrid transfer operators which is needed to define the multigrid algorithm and prove convergence of $\mathcal{W}$-cycle mutigrid algorithm and uniform condition number estimates for the variable $\mathcal{V}$-cycle multigrid preconditioner.

• 품질경영학회지
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• 제25권3호
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• pp.74-85
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• 1997

In this paper we calculate the subgroup size necessary for detecting the change of percent defective with several detection probabilities for orginal population fraction nonconforming p, changed population fraction nonconforming $p^*$, and the ratio k=$p^*$/p in the usage of p control charts. From our calculation we can know the error level of normal a, pp.oximation in detection probability calculation and recommend the subgroup size with lower error levels of normal a, pp.oximation, and then we show the reasonable subgroup size necessary for p, $p^*$, k, and the detection probability of the change of fraction nonconforming in a process. The information that we here show in tables will be useful when p control chart users decide the subgroup size in the p control chart users decide the subgroup size in the p control chart.

• 대한기계학회논문집A
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• 제36권10호
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• pp.1139-1146
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• 2012

P1 비순응 요소를 이용하여 정상 비압축성 Navier-Stokes 유동의 위상최적화 문제를 푸는 방법을 제시한다. 본 연구는 Stokes 유동의 위상최적화 문제에 P1 비순응 요소를 적용하여 그 수치적 효용성을 보인바 있는 이전 연구에 대한 후속 연구이다. 비압축성 물질 해석에서 잠김현상이 발생하지 않으며 선형형상함수를 가지는 P1 비순응 요소의 장점이 관성항을 가지는 유체 문제의 해석과 설계에도 유효한 지를 파악하고자 한다. 일반적으로 사용되는 혼합정식화법과 비교하여 P1 비순응 요소의 사용은 벌칙 함수를 이용하여 연속 방정식을 따로 사용하지 않고 운동방정식에 부과할 수 있기 때문에 자유도의 개수를 감소시킬 수 있다. 벌칙 파라미터가 해의 정확도에 주는 영향과 적정 범위는 수치적으로 검토하도록 한다. 또한 보통의 사각 비순응 요소들이 요소면의 중앙에 절점을 가지고 고차의 형상함수를 지니는데 비하여, 본 연구에서 제시하는 P1 비순응 요소는 요소의 꼭지점에 절점을 가지고 {1, x, y}의 P1 형상함수로 구성됨으로써 수치적인 구현의 용이함이 일반 선형 사절점 요소와 동일하다. 제안한 방법의 효용성을 다양한 레이놀즈수에 따른 유동최적화 문제들을 살펴봄으로써 검증하도록 한다.