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Restraining approach for the spurious kinematic modes in hybrid equilibrium element

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Abstract

The present paper proposes a rigorous approach for the elimination of spurious kinematic modes in hybrid equilibrium elements, for three well known mesh patches. The approach is based on the identification of the dependent equations in the set of inter-element and boundary equilibrium equations of the sides involved in the spurious kinematic mode. Then the kinematic variables related to the dependent equations are reciprocally constrained and, by application of master slave elimination method, the set of inter-element equilibrium equations is reduced to full rank. The elastic solutions produced by means of the proposed approach verify the homogeneous, the inter-element and the boundary equilibrium equations. Hybrid stress formulation is developed in a rigorous mathematical setting. The results of linear elastic analysis obtained by the proposed approach and by classical displacement based method are compared for some structural examples.

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Notes

  1. change of sign in left hand side is due to the fact that tangential stresses in standard notation (see Fig. 4) are convergent or divergent from the same corner, but not in side local reference (see Fig. 3a).

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Acknowledgments

A grant from MIUR for PRIN09, 2009XWLFKW project Multi-scale modelling of materials and structures is acknowledged.

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  1. DICAM - Università di Palermo, viale delle Scienze, 90100 , Palermo, Italy

    F. Parrinello

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  1. F. Parrinello
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Parrinello, F. Restraining approach for the spurious kinematic modes in hybrid equilibrium element. Comput Mech 52, 885–901 (2013). https://doi.org/10.1007/s00466-013-0851-x

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