• 대한기계학회논문집
• /
• 제17권7호
• /
• pp.1719-1730
• /
• 1993

This paper presents the theoretical natural frequencies of out-of-plane deformable ring based on the variables such as out-of-plane deflection, torsional rotation and shear rotation. Based on the same variables, a finite element eigen analysis is carried out by using the $C^0$-continuous, isoparametric element which has three nodes per element and three degrees-of-freedom at each node. Numerical experiments are peformed to find the integration scheme which produces accurate natural frequencies, natural modes and correct rigid body motion. The uniformly reduced integration and the selective reduced integration give more accurate numerical frequencies than the uniformly full integration, but the uniformly reduced integration produces incorrect rigid body motion while selective reduced integration does correct one. Therefore, the ring element based on the three variables which employes selective reduced integration is recommended to avoid spurious modes, to alleviate the error due to shear locking and to produce correct rigid body motion, simultaneously.

• Structural Engineering and Mechanics
• /
• 제21권5호
• /
• pp.539-551
• /
• 2005

Finite elements based on isoparametric formulation are known to suffer spurious stiffness properties and corresponding stress oscillations, even when care is taken to ensure that completeness and continuity requirements are enforced. This occurs frequently when the physics of the problem requires multiple strain components to be defined. This kind of error, commonly known as locking, can be circumvented by using reduced integration techniques to evaluate the element stiffness matrices instead of the full integration that is mathematically prescribed. However, the reduced integration technique itself can have a further drawback - rank deficiency, which physically implies that spurious energy modes (e.g., hourglass modes) are introduced because of reduced integration. Such instability in an existing stiffness matrix is generally detected by means of an eigenvalue test. In this paper we show that a knowledge of the dimension of the solution space spanned by the column vectors of the strain-displacement matrix can be used to identify the instabilities arising in an element due to reduced/selective integration techniques a priori, without having to complete the element stiffness matrix formulation and then test for zero eigenvalues.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2004년도 추계학술대회
• /
• pp.453-458
• /
• 2004

This study proposes a new two-level condensation scheme for the construction of a reduced system. In the first step, the candidate area is selected for the construction of the reduced system by energy estimation in element-level. In the second step, primary degrees of freedom are selected by sequential elimination from the candidate degrees of freedom linked to the selected elements. Numerical examples demonstrate that the proposed method saves the computational cost effectively and provides a reduced system which predicts the eigenvalues accurately. Moreover, the well-constructed reduced system can present the reliable behavior of the structure under arbitrary dynamic loads comparing to that of global system. Time integration in a reduced system can save the computing time remarkably. Through a few numerical examples, the efficiency and reliability of the proposed scheme are verified.

• 마이크로전자및패키징학회지
• /
• 제20권1호
• /
• pp.1-5
• /
• 2013

3D integration 기술 특히 W2W integration 기술은 전자산업의 디바이스 scaling 문제를 해결하고 고성능화 소형화 추세에 맞춘 가장 핵심적인 기술 방향이다. 그러나 W2W integration 기술은 현재 가격과 생산수율의 장애를 가지고 있고, 이를 해결하기 위해서 웨이퍼 매칭, 리던던시, 다이 면적 축소, 배선 층 수 축소와 같은 디자인 연구들이 진행되고 있다. W2W integration 기술이 대량생산으로 연결되기 위해서는 우선적으로 웨이퍼 본딩, 실리콘연삭, TSV 배선 공정의 최적화가 이루어져야 하겠지만, 가격을 포함한 생산수율을 높이기 위해서는 반드시 디자인 연구가 선행되어야 하겠다.

• 대한기계학회논문집A
• /
• 제20권12호
• /
• pp.3792-3803
• /
• 1996

Since the skew beam element has two curvatures which are a curvature and a torsion, spatial behavior of curved beam which cannot be included in one plane can be anlayzed by emploting the skew beam element. The $C^{0}$-continuous skew beam element shows the stiffness locking phenomenon when full integration is employed. The locking phenomenpn is characterized by two typical phenomena ; one is the much smaller displacement thant the exact one and theother is the undelation phenomenon is stress distribution. In this paper, we examine how unmatched coefficient in the constrained energy brings about the locking by Reduced Minimization theory. We perform the numerical ones. These comparisons show that uniformly full integration(UFI), which employs full integration for the constrained energy, entails the locking phenomenon. But the use of uniformly reduced integration(URI) of selectively reduced integration(SRI), which employs reduced integration for constrained energy, does not produce the significant errors of displacements of the undulation phenomenon in stress distribution since they do not entails the locking, Additionally, the error due to the approximated parameters for describing the geometry of skew beam is examined.d.

• 한국정밀공학회지
• /
• 제12권3호
• /
• pp.32-41
• /
• 1995

In the analysis of metal forming processes by the finite element method, there are many numerical instabilities such as element locking, hourglass mode and shear locking. These instabilities may have a bad effect upon accuracy and convergence. The present work is concerned with improvement of stability and efficiency in two-dimensional rigid-plastic finite element method using various type of elemenmts and numerical intergration schemes. As metal forming examples, upsetting and backward extrusion are taken for comparison among the methods: various element types and numerical integration schemes. Comparison is made in terms of stability and efficiency in element behavior and computational efficiency and a new scheme of adaptive directional reduced integration is introduced. As a result, the finite element computation has been stabilized from the viewpoint of computational time, convergency, and numerical instability.

• 마이크로전자및패키징학회지
• /
• 제17권4호
• /
• pp.1-9
• /
• 2010

삼차원 집적화기술의 현황과 과제 및 향후에 요구되어질 새로운 삼차원 집적화기술의 필요성에 대해 논의를 하였다. Super-chip 기술이라 불리우는 자기조직화 웨이퍼집적화 기술 및 삼차원 헤테로집적화 기술에 대해 소개를 하였다. 액체의 표면장력을 이용하여지지 기반위에 다수의 KGD를 일괄 실장하는 새로운 집적화 기술을 적용하여, KGD만으로 구성된 자기조직화 웨이퍼를 다층으로 적층함으로써 크기가 다른 칩들을 적층하는 것에 성공을 하였다. 또한 삼차원 헤테로집적화 기술을 이용하여 CMOS LSI, MEMS 센서들의 전기소자들과 PD, VC-SEL등의 광학소자 및 micro-fluidic 등의 이종소자들을 삼차원으로 집적하여 시스템화하는데 성공하였다. 이러한 기술은 향후 TSV의 실용화 및 궁극의 3-D IC인 super-chip을 구현하는데 필요한 핵심기술이다.

• 소성∙가공
• /
• 제4권4호
• /
• pp.365-374
• /
• 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.

• Structural Engineering and Mechanics
• /
• 제8권6호
• /
• pp.591-605
• /
• 1999

An accurate and efficient shell element is presented. The stiffness of the shell element is decomposed into two parts with one part corresponding to stretching and bending deformation and the other part corresponding to shear deformation of the shell. Both parts of the stiffness are calculated with reduced integration rules, thereby improving computational efficiency. Shear strains are averaged on the reference surface such that neither locking phenomena nor any zero energy mode can occur. The satisfactory behaviour of the element is demonstrated in several numerical examples.

• Structural Engineering and Mechanics
• /
• 제85권1호
• /
• pp.89-104
• /
• 2023

This work presents a proposal for employing reduced numerical integration in the formulation of the 4-node quadrilateral solid finite element. The use of these low-order integration rules leads to numerical instabilities such as those producing the hourglass effect. The proposed procedure allows evaluating a given constitutive model only in one integration point, achieving an attractive computational cost reduction and, also, successfully controls the hourglass effect. A validation of the proposal is included and discussed throughout the paper. To show the efficiency of the proposal, several application examples of masonry structures are studied and discussed. To represent the non-linear mechanical behaviour of masonry a plastic-damage model is implemented within the application of this sub-integration scheme. Also, in order to have a full and computationally efficient strategy to determine the behaviour of masonry structures, involving its evolution to collapse, a homogenization technique with a macro-modeling approach is used. The methodology discussed throughout this paper demonstrates a substantial computational cost reduction and an improved approximation of the non-linear problem evidenced by a reduction of up to 85% of the computational time for some cases.