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Limit analysis formulation for frictional problems

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Abstract

The aim of this paper is to propose a limit analysis formulation concerning prescription of non-homogeneous velocities and unilateral conditions with friction at structures’ contact interfaces. This formulation is especially suitable for determining the limit state conditions in structures in which the external action is defined by prescribed velocities on boundaries, particularly if the contact interface is not planar and the force distribution is not known a priori. The requirement of body’s non-penetrability is attended by applying the unilateral conditions at normal direction and a sliding rule based on Coulomb friction law at tangential direction. Under limit state, if there is sliding between the contact surfaces, the external collapse power is consumed by plastic and friction dissipation. As applications, the influence of friction coefficient at tool–specimen interface at scratch test problem and the lateral resistance of a soil due to lateral movement of a partially embedded pipe are investigated.

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Acknowledgements

The authors would like to acknowledge the support of this research by their own institutions and by CAPES and CNPq.

Funding This study was funded by CNPq (141627 / 2009.3) and CAPES (PNPD 31001017030D4).

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Authors and Affiliations

  1. UFRJ - Federal University of Rio de Janeiro, Av. Horácio Macedo 2030, bl. G, sl. 202, Rio de Janeiro, RJ, 21945-970, Brazil

    Fabio C. Figueiredo & Lavinia A. Borges

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  1. Fabio C. Figueiredo
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  2. Lavinia A. Borges
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Correspondence to Fabio C. Figueiredo.

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Figueiredo, F.C., Borges, L.A. Limit analysis formulation for frictional problems. Arch Appl Mech 87, 1965–1977 (2017). https://doi.org/10.1007/s00419-017-1304-3

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