• Journal of the Computational Structural Engineering Institute of Korea
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• v.16 no.2
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• pp.165-172
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• 2003

In this study, a new and efficient harmonic axisymmetric shell element for static and dynamic analysis Is proposed. The present element considering shear strain is based on a modified mixed variational principle in which the independent unknowns are only the Quantities prescribable at the shell edges. Unlike existing hybrid-mixed axisymmetric shell elements, the present element introduces additional nodeless degrees for displacement field Interpolation In order to enhance the numerical performance. The stress parameters are eliminated by the stationary condition and the nodeless degrees are condensed out by the Guyan reduction. Through several numerical examples, the hybrid-miked shell element with the additional nodeless degrees and the consistent stress parameters is shown to be efficient and yield very accurate results for static and vibration analysis.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.1 s.244
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• pp.18-25
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• 2006

The purpose of this research work is to demonstrate a successful application of hybrid-mixed formulation and nodeless degrees of freedom in developing a very accurate in-plane curved beam element for free vibration analysis. To resolve the numerical difficulties due to the spurious constraints, the present element, based on the Hellinger-Reissner variational principle and considering the effect of shear deformation, employed consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees. The stress parameters were eliminated by the stationary condition, and the nodeless degrees were condensed by Guyan Reduction. Several numerical examples indicated that the property of the mass matrix as well as that of the stiffness matrix have a great effect on the numerical performance. The element with consistent mass matrix produced best results on convergence and accuracy in the numerical analysis of Eigenvalue problems. Also, the higher-order mixed curved beam element showed a superior numerical behavior for the free vibration analyses.

• Journal of Mechanical Science and Technology
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• v.19 no.3
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• pp.811-819
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• 2005

In this study, we present a new efficient hybrid-mixed composite laminated curved beam element. The present element, which is based on the Hellinger-Reissner variational principle and the first-order shear deformation lamination theory, employs consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees in order to resolve the numerical difficulties due to the spurious constraints. The stress parameters are eliminated and the nodeless degrees are condensed out to obtain the ($6{\times}6$) element stiffness matrix. The present study also incorporates the straightforward prediction of interlaminar stresses from equilibrium equations. Several numerical examples confirm the superior behavior of the present composite laminated curved beam element.

• Journal of Mechanical Science and Technology
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• v.18 no.10
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• pp.1747-1754
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• 2004

In this study, a new harmonic axisymmetric thick shell element for static and dynamic analyses is proposed. The newly proposed element considering shear strain is based on a modified Hellinger-Reissner variational principle, and introduces additional nodeless degrees for displacement field interpolation in order to enhance numerical performance. The stress parameters selected via the field-consistency concept. are very important in formulating a trouble-free hybrid-mixed elements. For computational efficiency, the stress parameters are eliminated by the stationary condition and then the nodeless degrees are condensed out by the dynamic reduction. Several numerical examples confirm that the present element shows improved efficiency and yields very accurate results for static and vibration analyses.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.4
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• pp.559-566
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• 2003

In this study, we present a new highly accurate two-dimensional curved composite beam element. The present element, which is based on the Hellinger-Reissner variational principle and classical lamination theory, employs consistent stress parameters corresponding to cubic displacement polynomials with additional nodeless degrees to resolve the numerical difficulties due to the spurious constraints. The stress parameters are eliminated and the nodeless degrees are condensed out to obtain the (9x9) element stiffness matrix. It should be noted that the stacking sequences without transverse deformation to the load plane makes a two dimensional analysis of curved composite beams practically useful . Several numerical examples confirm the superior locking-free behavior of the present higher-order laminated curved beam element.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.2 s.72
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• pp.151-160
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• 2006

In this study, we propose a new efficient 2-noded hybrid-mixed element for curved beam vibrationshaving a uniform and non-uniform cross section. The present element considering transverse shear strain is based on Hellinger-Reissner variational principle and introduces additional nodeless degrees for displacement field interpolation in order to enhance the numerical performance. The stress parameters are eliminated by the stationary condition and then the nodeless degrees are condensed out by the Guyan reduction. In the performance evaluation process of the present field-consistent higher-order element, we carefully examine the effects of field consistency and the role of higher-order interpolation functions on the hybrid-mixed formulation. Several benchmark tests confirm e superior behavior of the present hybrid-mixed element for curved beam vibrations.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.6
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• pp.615-626
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• 2010

The discrete-layer model is proposed to analyze the edge-effect problem of laminates under extension and flexure. Based on three-dimensional elasticity theory, the displacement fields of each layer in a laminate have been treated discretely in terms of three displacement components across the thickness. The displacement fields at bottom and top surfaces within a layer are approximated by two-dimensional shape functions. Then two surfaces are connected by one-dimensional high order shape functions. Thus the p-convergent refinement on approximated one- and two-dimensional shape functions can be implemented independently of each other. The quality of present model is mostly determined by polynomial degrees of shape functions for given displacement fields. For nodal modes with physical meaning, the linear Lagrangian polynomials are considered. Additional modes without physical meaning, which are created by increasing nodeless degrees of shape functions, are derived from integrals of Legendre polynomials which have an orthogonality property. Also, it is assumed that mapping functions are linear in the light of shape of laminated plates. The results obtained by this proposed model are compared with those available in literatures. Especially, three-dimensional out-of-plane stresses in the interior and near the free edges are evaluated and convergence performance of the present model is established with the stress results.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.12
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• pp.3003-3009
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• 2000

In this paper, we propose a new efficient hybrid-mixed C(sup)0 curved beam element with the optimal interpolation functions determined from numerical tests, which gives very accurate locking-free two-node curved beam element. In the element level, the stress parameters are eliminated from the stationary condition and the nodeless degrees of freedom are also removed by static condensation so that a standard six-by-six stiffness matrix is finally obtained. The numeri cal benchmark problems show that the element with cubic displacement functions and quadratic stress functions is the most efficient.