Issue 51

E. Mousavian et alii, Frattura ed Integrità Strutturale, 51 (2020) 336-355; DOI: 10.3221/IGF-ESIS.51.25 353 1 2 0 1 2 0 μ  sin cos      μ  sin m k n t i i t i m k t i i t n i g f f b k f q q g f b k f f q                      (35) In the future, the proposed convex model including the heuristic method for sliding resistance of the interlocking interfaces will be introduced to the revised membrane approach to find the thinnest hemispheric domes with interlocking blocks. C ONCLUSION he paper presented two contributions to develop a limit analysis method for hemispherical domes composed of interlocking blocks. First the revision to an existing limit analysis approach using the membrane theory to find the thinnest hemispherical dome is presented. The dome is composed of blocks with isotropic sliding properties governed by the Coulomb’s friction law and it is only subjected to its own weight. The base thrust-line was constructed by a number of control points whose coordinates are the optimization variables. The optimization was constrained to meet the developed equilibrium conditions and sliding resistances. The results were obtained for (1) the finite tensile hoop stresses allowed by friction between the blocks assembled by running bond pattern; and for (2) no tensile hoop stresses which occurs in case of assembling the dome using stacked bond pattern. The outcomes showed that the revised formulations provided better results when compared to the other existing methods to find the minimum thickness of a structurally feasible dome, rather than the original formulation in [1]. The paper also demonstrated how the discrete network of forces can be constructed using the meridional thrust-line. The second issue addressed was the development of a heuristic method to find the orthotropic sliding resistance of the interlocking interface. First, a modelling procedure was proposed to abstract the interface and formulate the geometric properties on the interlocking interface affecting the sliding resistance. Then, adopting the convex contact model, the constraints for the internal forces tangential to the block interfaces within the hemispherical dome were defined. In further work, the developed constraints will be applied to find the thinnest dome composed of interlocking blocks and the revised limit analysis approach will also be extended to find the minimum thickness of shells with various basic geometries and non-isotropic interfaces. A CKNOWLEDGEMENTS This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 791235. REFERENCES [1] D’Ayala, D. and Casapulla, C. (2001). Limit state analysis of hemispherical domes with finite friction, Proc. III International Seminar on Structural Analysis of Historical Constructions (SAHC01), Guimarães (Portugal), pp. 617- 626. [2] Casapulla, C., Mousavian, E. and Zarghani, M. (2019). A digital tool to design structurally feasible semi-circular masonry arches composed of interlocking blocks, Comput. Struct., 221, pp. 111-126. DOI: 10.1016/j.compstruc.2019.05.001 [3] Livesley, R.K. (1978). Limit analysis of structures formed from rigid blocks, Int. J. Numer. Meth. Eng., 12(12), pp. 1853-1871. DOI: 10.1002/nme.1620121207 [4] Block, P.P.C.V. (2009). Thrust network analysis: exploring three-dimensional equilibrium, Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge (USA). [5] O’Dwyer, D. (1999). Funicular analysis of masonry vaults, Comput. Struct., 73(1-5), pp. 187-197. T