• 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.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.4
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• pp.255-262
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• 2013

In this paper, a shape design sensitivity analysis(DSA) method is presented for Mindlin plates using an isogeometric approach. The isogeometric method possesses desirable advantages; the representation of exact geometry and the higher order inter-element continuity, which lead to the fast convergence of solution as well as accurate sensitivity results. Unlike the finite element methods using linear shape functions, the isogeometric method considers the exact normal vector and curvature of the CAD geometry, taking advantages of higher order NURBS basis functions. A selective reduced integration(SRI) technique is incorporated to overcome the difficulty of 'shear locking' phenomenon. This simple technique is surprisingly helpful for the accuracy of the isogeometric shape sensitivity without complicated formulation. Through the numerical examples of plate bending problems, the accuracy of the proposed isogeometric analysis method is compared with that of finite element one. Also, the isogeometric shape sensitivity turns out to be very accurate when compared with finite difference sensitivity.

• Journal of Power Electronics
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• v.16 no.4
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• pp.1306-1315
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• 2016

Modern power systems driven by high-power converters have become inevitable in view of the ever increasing demand for electric power. The total power loss can be reduced by limiting the switching losses in such power converters; increased power efficiency can thus be achieved. A reduced switching frequency that is less than a few hundreds of hertz is applied to power converters that produce output waveforms with high distortion. Selective harmonic elimination pulse width modulation (SHEPWM) is an optimized low switching frequency pulse width modulation method that is based on offline estimation. This method can pre-program the harmonic profile of the output waveform over a range of modulation indices to eliminate low-order harmonics. In this paper, a SHEPWM scheme for three-phase three-leg neutral point clamped inverter is proposed. Aside from eliminating the selected harmonics, the DC capacitor voltages at the DC bus are also balanced because of the symmetrical pulse pattern over a quarter cycle of the period. The technique utilized in the estimation of switching angles involves the firefly algorithm (FA). Compared with other techniques, FA is more robust and entails less computation time. Simulation in the MATLAB/SIMULINK environment and experimental verification in the very large scale integration platform with Spartan 6A DSP are performed to prove the validity of the proposed technique.

• Structural Engineering and Mechanics
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• v.6 no.1
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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.

• 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 Computational Structural Engineering Institute Conference
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• 1995.04a
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• pp.17-27
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• 1995

For the post-buckling and elasto-plastic analysis of shell structures, the total Lagrangian formulation is presented based upon the degenerated shell element. Geometrically correct formulation is developed by updating the direction of normal vectors in the iteration process and evaluating the total Green-Lagrange stain corresponding U total displacements. In the calculation of the stiffness matrix, the element formulation takes into account the effect of finite rotation increments by retaining second order rotation terms in the incremental displacement field. The selective or reduced integration scheme using the heterosis element is applied in order to overcome both shear locking phenomena and the zero energy mode. The load/displacement incremental scheme is adopted for geometric non-linear F .E. analysis. Based on such methodology, the computer program is developed and numerical examples to demonstrate the accuracy and the effectiveness of the proposed shell element are presented and compared with references's results.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.8 no.2
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• pp.25-32
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• 1988

A formulation of an isoparametric quadrilateral higher-order plate bending finite element is presented. The 8-noded 28-d.o.f. plate element has been degenerated from the three-dimensional continuum by introducing the plate assumptions and considering higher-order in-plane displacement profile. The element characteristics have been derived by the Galerkin's weighted residual method and computed by using the selective reduced integration technique to avoid shear-locking phenomenon. Several numerical examples are given to demonstrate the accuracy and versatility of the proposed quadrilateral higher-order plate bending element over the other existing plate finite elements in both static and dynamic analyses.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.27-34
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• 1998

A versatile flat shell element has been developed by combining a membrane element with drilling degree-of-freedom and a plate bending element. This element is formulated by the enhanced displacement field with the additional non-conforming displacement modes. Thus the element possesses six degrees-of-freedom (DOF) per node which permits an easy connection to other six DOF elements as well as the improvement of the element behavior. In plate bending part, this element is established by the combined use of the addition of non-conforming modes, the reduced (or selective) integration scheme, and the construction of the substitute shear strain fields. The achieved improvement may be attributable to the fact that the merits of these individual techniques are merged into the new element in a complementary manner. In membrane part, this element shows better membrane behavior as the nonconforming displacement mode is added to drilling mode.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.60-67
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• 1998

This paper deals with the development of a variable-node element and its application to the adaptive h-version mesh refinement-recovery for the incompressible viscous flow analysis. The element which has variable mid-side nodes can be used in generating the transition zone between the refined and unrefined elements and efficiently used for construction of a refined mesh without generating distorted elements. A modified Gaussian quadrature is needed to evaluate the element matrices due to the discontinuity of derivatives of the shape functions used for the element. The penalty function method which can reduce the number of independent variables is adopted for the purpose of computational efficiency and the selective reduced integration is carried out for the convection and pressure terms to preserve the stability of solution. For the economical analysis of transient problems, not only the mesh refinement but also the mesh recovery is needed. The numerical examples show that the optimal mesh for the finite element analysis of a wind around the structures can be obtained automatically by the proposed scheme.