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On the Assumed Natural Strain method to alleviate locking in solid-shell NURBS-based finite elements

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Abstract

In isogeometric analysis (IGA), the functions used to describe the CAD geometry (such as NURBS) are also employed, in an isoparametric fashion, for the approximation of the unknown fields, leading to an exact geometry representation. Since the introduction of IGA, it has been shown that the high regularity properties of the employed functions lead in many cases to superior accuracy per degree of freedom with respect to standard FEM. However, as in Lagrangian elements, NURBS-based formulations can be negatively affected by the appearance of non-physical phenomena that “lock” the solution when constrained problems are considered. In order to alleviate such locking behaviors, the Assumed Natural Strain (ANS) method proposed for Lagrangian formulations is extended to NURBS-based elements in the present work, within the context of solid-shell formulations. The performance of the proposed methodology is assessed by means of a set of numerical examples. The results allow to conclude that the employment of the ANS method to quadratic NURBS-based elements successfully alleviates non-physical phenomena such as shear and membrane locking, significantly improving the element performance.

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Acknowledgments

The authors gratefully acknowledge the support given by the Ministrio da Educao e Cincia, Portugal, under the Grants SFRH/BD/70815/2010 and PTDC/EMS-TEC/0899/2012, as well as by the European Research Council through the Project ISOBIO No. 259229.

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Authors and Affiliations

  1. GRIDS Research Group, Centre for Mechanical Technology and Automation, University of Aveiro, Aveiro, Portugal

    J. F. Caseiro, R. A. F. Valente & R. J. Alves de Sousa

  2. Department of Civil Engineering and Architecture, Structural Mechanics Division, University of Pavia, Pavia, Italy

    A. Reali, J. Kiendl & F. Auricchio

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  1. J. F. Caseiro
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  2. R. A. F. Valente
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  6. R. J. Alves de Sousa
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Correspondence to J. F. Caseiro.

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Caseiro, J.F., Valente, R.A.F., Reali, A. et al. On the Assumed Natural Strain method to alleviate locking in solid-shell NURBS-based finite elements. Comput Mech 53, 1341–1353 (2014). https://doi.org/10.1007/s00466-014-0978-4

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  • DOI: https://doi.org/10.1007/s00466-014-0978-4

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