• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.7 s.94
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• pp.1719-1730
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• 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
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• v.21 no.5
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• pp.539-551
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• 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.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.453-458
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• 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.

• Journal of the Microelectronics and Packaging Society
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• v.20 no.1
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• pp.1-5
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• 2013

Wafer-to-Wafer (W2W) integration technology is an emerging technology promising many benefits, such as reduced size, improved performance, reduced power, lower cost, and divergent integration. As the maturity of W2W technology progresses, new applications will become more viable. However, at present the cost for W2W integration is still very high and both manufacturing yield and reliability issues have not been resolved yet for high volume manufacturing (HVM). Especially for WTW integration resolving compound yield issue can be a key factor for HVM. To have the full benefits of WTW integration technology more than simple wafer stacking technologies are necessary. In this paper, the manufacturing yield for W2W integration is described and the challenges of WTW integration will be discussed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.12
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• pp.3792-3803
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• 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.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.3
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• pp.32-41
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• 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.

• Journal of the Microelectronics and Packaging Society
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• v.17 no.4
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• pp.1-9
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• 2010

Three-dimensional (3-D) integration is an emerging technology, which vertically stacks and interconnects multiple materials, technologies, and functional components such as processor, memory, sensors, logic, analog, and power ICs into one stacked chip to form highly integrated micro-nano systems. Since CMOS device scaling has stalled, 3D integration technology allows extending Moore's law to ever high density, higher functionality, higher performance, and more diversed materials and devices to be integrated with lower cost. The potential benefits of 3D integration can vary depending on approach; increased multifunctionality, increased performance, increased data bandwidth, reduced power, small form factor, reduced packaging volume, increased yield and reliability, flexible heterogeneous integration, and reduced overall costs. It is expected that the semiconductor industry's paradiam will be shift to a new industry-fusing technology era that will offer tremendous global opportunities for expanded use of 3D based technologies in highly integrated systems. Anticipated applications start with memory, handheld devices, and high-performance computers and extend to high-density multifunctional heterogeneous integration of IT-NT-BT systems. This paper attempts to introduce new 3D integration technologies of the chip self-assembling stacking and 3D heterogeneous opto-electronics integration for realizng the super-chip.

• Transactions of Materials Processing
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• v.4 no.4
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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.

• Structural Engineering and Mechanics
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• v.8 no.6
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• pp.591-605
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• 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
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• v.85 no.1
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• pp.89-104
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• 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.