, Volume 53, Issue 7, pp 1875–1898 | Cite as

A fast and general upper-bound limit analysis approach for out-of-plane loaded masonry walls

  • Andrea Chiozzi
  • Gabriele Milani
  • Nicola Grillanda
  • Antonio Tralli
New Trends in Mechanics of Masonry


A new general approach for the limit analysis of out-of-plane loaded masonry walls based on an upper bound formulation is presented. A given masonry wall of generic form presenting openings of arbitrary shape is described through its Non-Uniform Rational B-Spline (NURBS) representation in the three-dimensional Euclidean space. A lattice of nodes is defined in the parameters space together with possible fracture lines. An initial set of rigid elements initially subdividing the original wall geometry is identified accordingly. A homogenized upper bound limit analysis formulation, which takes into account the main characteristics of masonry material such as very low resistance in traction and anisotropic behavior is deduced. Moreover the effect of vertical loads and membrane stresses is considered, assuming internal dissipation allowed exclusively along element edges. A number of technically meaningful examples prove that a good estimate of the collapse load multiplier is obtained, provided that the initial net of yield lines is suitably adjusted by means of a meta-heuristic approach (i.e. a Genetic Algorithm, GA) in order to enforce that element edges accurately represent the actual failure mechanism.


Limit analysis Masonry Masonry walls NURBS 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Department of EngineeringUniversity of FerraraFerraraItaly
  2. 2.Department of Architecture, Built Environment and Construction Engineering (A.B.C.)Technical University of MilanMilanItaly

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