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A new locking-free shear deformable finite element based on absolute nodal coordinates

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Abstract

The absolute nodal coordinate formulation has been recently extended to shear deformable beam or plate elements. This has been accomplished, in practice, by parameterizing the complete volume of the elements instead of a line or surface in the element kinematics description. In the absolute nodal coordinate formulation, the position of any point of the element volume is defined employing independent slope coordinates. The use of a large number of slope coordinates leads to unusual kinematic features that must be accounted for in order to avoid the element locking. This study demonstrates that the shear deformable element based on the absolute nodal coordinate formulation suffers from curvature thickness locking and shear locking in addition to the previously reported Poisson’s locking. Due to the tendency of locking, the use of the absolute nodal coordinate formulation can lead to elements with weak performance. In order to eliminate locking problems, this study introduces a new absolute nodal coordinate-based finite element. The introduced element uses redefined polynomial expansion together with a reduced integration procedure. The performance of the introduced element is studied by means of certain dynamic problems. The element exhibits a competent convergence rate and it does not suffer from the previously mentioned locking effects.

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Authors and Affiliations

  1. Department of Mechanical and Materials Engineering, University of Seville, Camino de los descubrimientos S/N, 41092, Seville, Spain

    Daniel García-Vallejo & José Luis Escalona

  2. Department of Mechanical Engineering, Institute of Mechatronics and Virtual Engineering, Lappeenranta University of Technology, P.O. Box 20, 53851, Lappeenranta, Finland

    Aki M. Mikkola

Authors
  1. Daniel García-Vallejo
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  2. Aki M. Mikkola
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  3. José Luis Escalona
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Correspondence to Daniel García-Vallejo.

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García-Vallejo, D., Mikkola, A.M. & Escalona, J.L. A new locking-free shear deformable finite element based on absolute nodal coordinates. Nonlinear Dyn 50, 249–264 (2007). https://doi.org/10.1007/s11071-006-9155-4

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  • DOI: https://doi.org/10.1007/s11071-006-9155-4

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