• Journal of information and communication convergence engineering
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• v.8 no.4
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• pp.457-460
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• 2010

we have analyzed tens of Giga pulse signal generation using sideband injection locking scheme. The numerical model for semiconductor lasers under the strong optical injection is based on the Lang's equation and has been extended in order to take into account the simultaneous injection of the multiple sidebands of the current-modulated laser. The numerical simulation results show that the unselected sidebands will affect the optical and RF-spectral characteristics even though the semiconductor laser is locked to the target sidebands.

• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.04a
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• pp.11-18
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• 1993

An Analytical study of shear locking is introduced for linear thick beam element. The appropriate sampling point which eliminate shear locking phenomenon was Proposed through this study. Reduced integration point is exactly same as the sampling point obtained from this study. Numerical example indicates how shear locking is serious. some solutions for shear locking are presented.

• Structural Engineering and Mechanics
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• v.59 no.3
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• pp.503-526
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• 2016

In-plane and out-of-plane free vibration analysis of Timoshenko curved beams is addressed based on the isogeometric method, and an effective scheme to avoid numerical locking in both of the two patterns is proposed in this paper. The isogeometric computational model takes into account the effects of shear deformation, rotary inertia and axis extensibility of curved beams, and is applicable for uniform circular beams, and more complicated variable curvature and cross-section beams as illustrated by numerical examples. Meanwhile, it is shown that, the $C^{p-1}$-continuous NURBS elements remarkably have higher accuracy than the finite elements with the same number of degrees of freedom. Nevertheless, for in-plane or out-of-plane vibration analysis of Timoshenko curved beams, the NURBS-based isogeometric method also exhibits locking effect to some extent. To eliminate numerical locking, the selective reduced one-point integration and $\bar{B}$ projection element based on stiffness ratio is devised to achieve locking free analysis for in-plane and out-of-plane models, respectively. The suggested integral schemes for moderately slender models obtain accurate results in both dominated and non-dominated regions of locking effect. Moreover, this strategy is effective for beam structures with different slenderness. Finally, the influence factors of structural parameters of curved beams on their natural frequency are scrutinized.

• Structural Engineering and Mechanics
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• v.37 no.6
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• pp.633-648
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• 2011

This paper investigates the aspect-ratio locking of the isoparametric 8-node quadrilateral (QUAD8) element. An important finding is that, if finite element solution is carried out with in exact arithmetic (i.e., with no truncation and round off errors), the locking tendency of the element is completely avoided even for aspect-ratios as high as 100000. The current finite element codes mostly use floating point arithmetic. Thus, they can only avoid this locking for aspect-ratios up to 100 or 1000. A novel method is proposed in the paper to avoid aspect-ratio locking in floating point computations. In this method, the offending terms of the strain-displacement matrix (i.e., $\mathbf{B}$-matrix) are multiplied by suitable scaling factors to avoid ill-conditioning of stiffness matrix. Numerical examples are presented to demonstrate the efficacy of the method. The examples reveal that aspect-ratio locking is avoided even for aspect-ratios as high as 100000.

• Computational Structural Engineering
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• v.9 no.4
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• pp.155-163
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• 1996

In the analysis of thin elastic structures such as beam-, arch-, plate- and shell-like bodies using standard finite element schemes, there may occur deterioration of approximation quality owing to shear and membrane lockings. Moreover, a recognition of this phenomenon in the computed numerical results is not easy without comparing with other available reference numerical data. This paper analyses briefly this phenomenon and introduces one inexpensive but reliable a posteriori locking detection method. Numerical examples are given supporting the theoretical results.

• Structural Engineering and Mechanics
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• v.11 no.2
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• pp.123-132
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• 2001

An improved version of the Element-free Galerkin method (EFGM) is presented here for addressing the problem of transverse shear locking in shear-deformable beams with a high length over thickness ratio. Based upon Timoshenko's theory of thick beams, it has been recognized that shear locking will be completely eliminated if the rotation field is constructed to match the field of slope, given by the first derivative of displacement. This criterion is applied directly to the most commonly implemented version of EFGM. However in the numerical process to integrate strain energy, the second derivative of the standard Moving Least Square (MLS) shape functions must be evaluated, thus requiring at least a $C^1$ continuity of MLS shape functions instead of $C^0$ continuity in the conventional EFGM. Yet this hindrance is overcome effortlessly by only using at least a $C^1$ weight function. One-dimensional quartic spline weight function with $C^2$ continuity is therefore adopted for this purpose. Various numerical results in this work indicate that the modified version of the EFGM does not exhibit transverse shear locking, reduces stress oscillations, produces fast convergence, and provides a surprisingly high degree of accuracy even with coarse domain discretizations.

• Proceedings of the IEEK Conference
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• 2008.06a
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• pp.607-608
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• 2008

Locking time of the DLL is the important design issue in case of clock gating for low power system. For precise analysis of the locking speed of the DLL, this paper analyzes the locking process of the DLL in time domain. Analysis result shows that the value of the DLL bandwidth over reference frequency should be limited to below 1 ($i.e.w_n/F_{REF}<1$) for the stable operation and relation between bandwidth and lock time is expressed by log function.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.445-454
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• 1991

In this thesis, Mindlin plate element with nine nodes and three degrees-of-freedom at each node is formulated and is employed in eigen-analysis of a rectangular plates in order to alleviate locking phenomenon of eigenvalues. Eigenvalues and their modes may be locked if conventional $C_{0}$-isoparametric element is used. In order to reduce stiffness locking phenomenon, two methods (1, the general reduced and selective integration, 2, the new element that use of modified shape function) are studied. Additionally in order to reduce the error due to mass matrix, two mass matrixes (1, Gauss-Legendre mass matrix, 2, Gauss-Lobatto mass matrix) are considered. The results of eigen-analysis for two models (the square plate with all edges simply-supported and all edges built-in), computed by two methods for stiffness matrix and by two mass matrixes are compared with theoretical solutions and conventional numerical solutions. These comparisons show that the performance of the two methods with Gauss-Lobatto mass matrix is better than that of the conventional plate element. But, by considering the spurious rigid body motions, the element which employs modified shape function with full integration and Gauss-Lobatto mass matrix can elevate the accuracy and convergence of numerical solutions.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1993.10a
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• pp.195-199
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• 1993

In the analysis of metal forming processes by the finite element method, there are many numerical instabilities such as element locking, hourglass mode, 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 elements and numerical integration 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. As a result, it has been shown that the finite element computation is stabilized from the viewpoint of computational time, convergency, and numerical instability.