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      Static Analysis of Timoshenko Beams using Isogeometric Approach

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      https://www.riss.kr/link?id=A104646685

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      다국어 초록 (Multilingual Abstract)

      A study on the static analysis of Timoshenko beams is presented. A beam element is developed by using isogeometric approach based on Timoshenko beam theory which allows the transverse shear deformation. The identification of transverse shear locking i...

      A study on the static analysis of Timoshenko beams is presented. A beam element is developed by using isogeometric approach based on Timoshenko beam theory which allows the transverse shear deformation. The identification of transverse shear locking is conducted by three refinement schemes such as h-, p- and k-refinement and compared to other reference solutions. From numerical examples, the present beam element does not produce any shear locking in very thin beam situations even with full Gauss integration rule. Finally, the benchmark tests described in this study is provided as future reference solutions for Timoshenko beam problems based on isogeometric approach.

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      참고문헌 (Reference)

      1 Kapur, K. K., "Vibrations of a Timoshenko beam using finite element approach" 40 : 1058-1063, 1966

      2 Lee, S.J., "Vibrations of Timoshenko beams with isogeometric approach" 37 : 9174-9190, 2013

      3 Timoshenko, S.P., "Theory of Elasticity" McGraw Hill 1970

      4 Zienkiewicz, O.C., "The finite element method" McGraw-Hill 1989

      5 Prathap, G., "Reduced integration and the shear-flexible beam element" 18 : 195-210, 1982

      6 Timoshenko, S.P., "On the correction for shear of the differential equation for transverse vibrations of prismatic bars" 41 : 744-746, 1921

      7 Reddy, J.N., "On locking shear deformable beam finite elements" 149 : 113-132, 1997

      8 Hughes, T. J. R., "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement" 194 : 4135-4195, 2005

      9 Hughes, T.J.R., "Isogeometric analysis" The Institute of Computational Engineering and Science, University of Texas 2010

      10 Cottrell, J. A., "Isogeometric Analysis: Towards Integration of CAD and FEA" Wiley 2009

      1 Kapur, K. K., "Vibrations of a Timoshenko beam using finite element approach" 40 : 1058-1063, 1966

      2 Lee, S.J., "Vibrations of Timoshenko beams with isogeometric approach" 37 : 9174-9190, 2013

      3 Timoshenko, S.P., "Theory of Elasticity" McGraw Hill 1970

      4 Zienkiewicz, O.C., "The finite element method" McGraw-Hill 1989

      5 Prathap, G., "Reduced integration and the shear-flexible beam element" 18 : 195-210, 1982

      6 Timoshenko, S.P., "On the correction for shear of the differential equation for transverse vibrations of prismatic bars" 41 : 744-746, 1921

      7 Reddy, J.N., "On locking shear deformable beam finite elements" 149 : 113-132, 1997

      8 Hughes, T. J. R., "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement" 194 : 4135-4195, 2005

      9 Hughes, T.J.R., "Isogeometric analysis" The Institute of Computational Engineering and Science, University of Texas 2010

      10 Cottrell, J. A., "Isogeometric Analysis: Towards Integration of CAD and FEA" Wiley 2009

      11 Hughes, T. J. R., "Duality and unified analysis of discrete approximations in structural dynamics and wave propagation: Comparison of p-method finite elements with k-method NURBS" 197 : 4104-4124, 2008

      12 Nickel, R.E., "Convergence of consistently derived Timoshenko beam finite elements" 5 : 243-252, 1972

      13 Lee, S.J., "Analytical study of shear locking" 1993

      14 Lee, S. J., "Analysis and optimization of shells" University of Wales, Swansea 1998

      15 Rogers, D.F., "An introduction to NURBS: With Historical Perspective" Morgan Kaufmann 2000

      16 Kosmatka, J. B., "An improved two-node finite element for stability and natural frequencies of axial-loaded Timoshenko beams" 57 : 141-149, 1995

      17 Levinson, M., "A new rectangular beam theory" 74 : 81-87, 1981

      18 Heyliger, P.R., "A higher order beam finite element for bending and vibration problems" 126 : 309-326, 1988

      19 Dawe, D. J., "A finite element for the vibration analysis of Timoshenko beams" 60 : 11-20, 1978

      20 De Boor, C., "A Practical Guide to Splines" Springer 2001

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