Latest revision as of 14:31, 30 November 2021

Abstract

A computational method is proposed for the lower-bound limit analysis of masonry arches with multiple failure sections. Main motivation is the observation that, not only the position, but also the orientation of the failure sections in an arch might not be known in advance in practical applications. The lower-bound limit analysis problem is formulated as a straightforward linear programming problem. Numerical simulations highlight the predicting capabilities of the proposed approach, enabling an accurate and safe prediction of the loading capacity of masonry arches.

Full document

References

[1] Gambarotta, L. and Lagomarsino, S. Damage models for the seismic response of brick masonry shear walls. Part I: the mortar joint model and its applications. Earthq. Eng.Struct. Dyn. (1997) 26(4):423-439.

[2] Oliveira, D.V. and Lourenço, P.B. Implementation and validation of a constitutive model for the cyclic behaviour of interface elements. Comput. Struct. (2004) 82(17-19):1451-1461.

[3] Milani, G. Simple homogenization model for the non-linear analysis of in-plane loaded masonry walls. Comput. Struct. (2011) 89(17-18):1586-1601.

[4] Addessi, D. and Sacco, E. A multi-scale enriched model for the analysis of masonry panels. Int. J. Solids Struct. (2012) 49(6):865-880.

[5] Petracca, M., Pelà, L., Rossi, R., Oller, S., Camata, G. and Spacone, E. Regularization of first order computational homogenization for multiscale analysis of masonry structures. Comput. Mech. (2016) 57(2):257-276.

[6] Braides, A. and Nodargi, N.A. Homogenization of cohesive fracture in masonry structures. Math. Mech. Solids (2020) 25(2):181-200.

[7] Pelà, L., Cervera, M. and Roca, P. Continuum damage model for orthotropic materials: Application to masonry. Comput. Meth. Appl. Mech. Eng. (2011) 200(912):917-930.

[8] Pelà, L., Cervera, M. and Roca, P. An orthotropic damage model for the analysis of masonry structures. Constr. Build. Mater. (2013) 41:957-967.

[9] Nodargi, N.A., Artioli, E., Caselli, F. and Bisegna, P. State update algorithm for associative elastic-plastic pressure-insensitive materials by incremental energy minimization. Fracture and Structural Integrity (2014) 29:111-127.

[10] Nodargi, N.A. and Bisegna, P. State update algorithm for isotropic elastoplasticity by incremental energy minimization. Int. J. Numer. Methods Eng. (2015) 105(3):163-196.

[11] Gatta, C., Addessi, D. and Vestroni, F. Static and dynamic nonlinear response of masonry walls. Int. J. Solids Struct. (2018) 155:291-303.

[12] Brasile, S., Casciaro, R. and Formica, G. Finite element formulation for nonlinear analysis of masonry walls. Comput. Struct. (2010) 88(3-4):135-143.

[13] Cervera, M., Chiumenti, M. and Codina, R. Mixed stabilized finite element methods in nonlinear solid mechanics. Part II: Strain localization. Comput. Meth. Appl. Mech. Eng. (2010) 199(37-40):2571-2589.

[14] Nodargi, N.A., Caselli, F., Artioli, E. and Bisegna, P. A mixed tetrahedral element with nodal rotations for large-displacement analysis of inelastic structures. Int. J. Numer. Methods Eng. (2016) 108(7):722-749.

[15] Nodargi, N.A. and Bisegna, P. A novel high-performance mixed membrane finite element for the analysis of inelastic structures. Comput. Struct. (2017) 182:337-353.

[16] Nodargi, N.A. An overview of mixed finite elements for the analysis of inelastic bidimensional structures. Arch. Comput. Method Eng. (2019) 26(4):1117-1151.

[17] Nodargi, N.A. and Bisegna, P. A mixed finite element for the nonlinear analysis of in-plane loaded masonry walls. Int. J. Numer. Methods Eng. (2019) 120(11):1227-1248.

[18] Nodargi, N.A. and Bisegna P. A mixed membrane finite element for masonry structures. In: Carcaterra A. et al. (Eds.): Proceedings of XXIV AIMETA Conference 2019. AIMETA 2019, Lecture Notes in Mechanical Engineering. Springer (2020), pp. 1167-1178.

[19] Heyman, J. The stone skeleton. Int. J. Solids Struct. (1966) 2(2):249-279.

[20] Como, M. Statics of historic masonry constructions. Springer-Verlag (2016).

[21] Roca, P., Cervera, M., Gariup, G. and Pelà, L. Structural analysis of masonry historical constructions. Classical and advanced approaches, Arch. Comput. Method Eng. (2010) 17(3):299-325.

[22] Tralli, A., Alessandri, C. and Milani, G. Computational methods for masonry vaults: a review of recent results, Open Civ. Eng. J. (2014) 8:272–282.

[23] Livesley, R.K. Limit analysis of structures formed from rigid blocks. Int. J. Numer. Methods Eng. (1978) 12(12):1853-1871.

[24] Portioli, F., Casapulla, C. and Cascini, L. An efficient solution procedure for crushing failure in 3D limit analysis of masonry block structures with non-associative frictional joints. Int. J. Solids Struct. (2015) 69-70: 252-266.

[25] Intrigila, C., Nodargi, N.A. and Bisegna P. Frictional behaviour of masonry interfaces: experimental investigation on two dry-jointed tuff blocks. In: Carcaterra A. et al. (Eds.): Proceedings of XXIV AIMETA Conference 2019. AIMETA 2019, Lecture Notes in Mechanical Engineering. Springer (2020), pp. 2032-2047.

[26] Baggio, C. and Trovalusci, P. Limit analysis for no-tension and frictional three- dimensional discrete systems. Mech. Based Des. Struct. Mach. (1998) 26(3):287-304.

[27] Ferris, M.C. and Tin-Loi, F. Limit analysis of frictional block assemblies as a mathematical program with complementarity constraints. Int. J. Mech. Sci. (2001) 43(1):209-224.

[28] Gilbert, M., Casapulla, C. and Ahmed, H.M. Limit analysis of masonry block structures with non-associative frictional joints using linear programming. Comput. Struct. (2006) 84(13-14):873-887.

[29] Nodargi, N.A., Intrigila, C. and Bisegna, P. A variational-based fixed-point algorithm for the limit analysis of dry-masonry block structures with non-associative Coulomb friction. Int. J. Mech. Sci. (2019) 161-162:105078.

[30] Portioli, F. and Cascini, L. Large displacement analysis of dry-jointed masonry structures subjected to settlements using rigid block modelling. Eng. Struct. (2017) 148:485-496.

[31] Intrigila, C., Nodargi, N.A. and Bisegna P. Square cross vaults on spreading supports. In: R. Aguilar et al. (Eds.): Structural Analysis of Historical Constructions, RILEM Bookseries 18 (2019), pp. 1045-1053.

[32] Block, P., Ciblac, T. and Ochsendorf, J. Real-time limit analysis of vaulted masonry buildings. Comput. Struct. (2006) 84(29-30):1841-1852.

[33] O'Dwyer, D.W. Funicular analysis of masonry vaults. Comput. Struct. (1999) 73(1-5):187-197.

[34] Marmo, F. and Rosati, L. Reformulation and extension of the thrust network analysis. Comput. Struct. (2017) 182:104-118.

[35] Nodargi, N.A. and Bisegna, P. Thrust line analysis revisited and applied to optimization of masonry arches. Int. J. Mech. Sci. (2020) 179:105690.

[36] Ricci, E., Fraddosio, A., Piccioni, M.D. and Sacco, E. A new numerical approach for determining optimal thrust curves of masonry arches. Eur. J. Mech. A-Solids (2019) 75: 426-442.

[37] Milankovitch, M. Theorie der druckkurven. Zeitschrift für Mathematik und Physik (1907) 55:1-27.

[38] Foce, F. Milankovitch's theorie der Druckkurven: Good mechanics for masonry architecture. Nexus Netw. J. (2007) 9(2):185-210.

[39] Alexakis, H. and Makris, N. Minimum thickness of elliptical masonry arches. Acta Mech. (2013) 224(12): 2977-2991.

[40] Alexakis, H. and Makris, N. Limit equilibrium analysis of masonry arches. Arch. Appl. Mech. 85(9-10): 1363-1381.

[41] Nodargi, N.A. and Bisegna, P. A unifying computational approach for the lower-bound analysis of systems of masonry arches and buttresses. Submitted (2020).

[42] Cavalagli, N., Gusella, V. and Severini, L. Lateral loads carrying capacity and minimum thickness of circular and pointed masonry arches. Int. J. Mech. Sci. (2016) 115-116:645-656.