# Understanding rigid-block equilibrium method by way of mathematical programming

Kao G. T. C., Iannuzzo A., Coros S., Van Mele T. and Block P.
Proceedings of the ICE - Engineering and Computational Mechanics
2021
doi: 10.1680/jencm.20.00036

This paper discusses and extends some main features of the rigid-block equilibrium (RBE) method. RBE is a numerical approach that frames the equilibrium problem (EP) of rigid-block assemblies as an optimisation problem to compute possible internal and equilibrated singular stress states. The contact between blocks is considered having a finite friction capacity and the unilateral behaviour is modelled through a penalty formulation. In particular, the penalty formulation widens the standard admissible solution space of compressive-only forces by allowing for tensile forces appearing on potentially unstable regions. The RBE objective function minimises the interface forces while the constraints are linear functions enforcing the static equilibrium of the whole assembly. In this paper, along with the original quadratic objective function, we propose a linear function to illustrate and explore the role played by both the nodal forces and the interface resultants. Moreover, we show how RBE can be used to explore different admissible internal stress states, for example, due to increasing, static, horizontal actions.

BibTeX

@article{Kao2021,
author  = "Kao, G. T. C. and Iannuzzo, A. and Coros, S. and Van Mele, T. and Block, P.",
title   = "Understanding rigid-block equilibrium method by way of mathematical programming",
journal = "Proceedings of the ICE - Engineering and Computational Mechanics",
year    = "2021",
volume  = "174",
number  = "4",
pages   = "178-192",
month   = "September",
doi     = "10.1680/jencm.20.00036",
note    = "",
}

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