Abstract
This aim of this paper is to present the application of the combined finite–discrete element method (FDEM) in structural mechanics. FDEM is an innovative numerical technique, which has been intensively used in the past several decades in various engineering simulations. FDEM combines the advantages of both the finite and the discrete elements and enables the simulation of initiation and propagation of cracks, as well as interaction of a large number of discrete elements. The examples presented in this paper show the advantages of FDEM in the analysis of structural mechanics issues including dry-joint masonry structures, concrete and reinforced concrete structures, masonry structures with mortar joints and confined masonry structures, cable and truss structures, membrane structures, and plate and shell structures.
Similar content being viewed by others
References
Munjiza A (2004) The combined finite-discrete element method. Wiley, London
Munjiza A, Andrews KRF (1998) NBS contact detection algorithm for bodies of similar size. Int J Numer Meth Eng 43(1):131–149. https://doi.org/10.1002/(SICI)1097-0207(19980915)43:1%3C131:AID-NME447%3E3.0.CO;2-S
Munjiza A, Andrews KRF (2000) Penalty function method for combined finite-discrete element system comprising large number of separate bodies. Int J Numer Meth Eng 49(11):1377–1396. https://doi.org/10.1002/1097-0207(20001220)49:113.3.CO;2-2
Smoljanović H, Živaljić N, Nikolić Ž, Munjiza A (2018) Numerical analysis of 3D dry-stone masonry structures by combined finite-discrete element method. Int J Sol Struct 136–137:150–167. https://doi.org/10.1016/j.ijsolstr.2017.12.012
Munjiza A, Andrews KRF, White JK (1998) Combined single and smeared crack model in combined finite-discrete element method. Int J Numer Meth Eng 44(1):41–57. https://doi.org/10.1002/(SICI)1097-0207(19990110)44:1%3c41:AID-NME487%3e3.0.CO;2-A
Munjiza A, John NWM (2002) Mesh size sensitivity of the combined FEM/DEM fracture and fragmentation algorithms. Eng Fract Mech 69:281–295. https://doi.org/10.1016/S0013-7944(01)00090-X
Munjiza A, Knight EE, Rouiger E (2012) Computational mechanics of discontinua. Wiley, London
Munjiza A, Owen DRJ, Bicanic N (1995) A combined finite-discrete element method in transient dynamics of fracturing solids. Eng Comput 12:145–174. https://doi.org/10.1108/02644409510799532
Divić V (2014) Simulations of ultimate limit states under wind loading by combined finite discrete element method. Dissertation (in Croatian), University of Split, Croatia
Smoljanović H, Uzelac I, Trogrlić B, Živaljić N, Munjiza A (2018) A computationally efficient numerical model for a dynamic analysis of beam type structures based on the combined finite discrete element method. MatWerk 49(5):651–665. https://doi.org/10.1002/mawe.201700277
Divić V, Uzelac I, Peroš B (2014) Multiplicative decomposition based fdem model for membrane structures. Trans FAMENA 38:1–12
Uzelac I, Smoljanović H, Peroš B (2015) A computationally efficient numerical model for a dynamic analysis of thin plates based on the combined finite–discrete element method. Eng Struct 101:509–517. https://doi.org/10.1016/j.engstruct.2015.07.054
Uzelac Glavinić I, Smoljanović H, Galić M, Munjiza A, Mihanović A (2018) Computational aspects of the combined finite- discrete element method in static and dynamic analysis of shell structures. MatWerk 49(5):635–651. https://doi.org/10.1002/mawe.201700276
Uzelac I, Smoljanovic H, Batinic M, Peroš B, Munjiza A (2018) A model for thin shells in the combined finite- discrete element method. Eng Comput 35(1):377–394. https://doi.org/10.1108/EC-09-2016-0338
Živaljić N, Smoljanović H, Nikolić Ž (2013) A combined finite-discrete element model for RC structures under dynamic loading. Eng Comput 30(7):982–1010. https://doi.org/10.1108/EC-03-2012-0066
Živaljić N, Nikolić Ž, Smoljanović H (2014) Computational aspects of the combined finite—discrete element method in modelling of plane reinforced concrete structures. Eng Fract Mech 131:669–686. https://doi.org/10.1016/j.engfracmech.2014.10.017
Nikolić Ž, Živaljić N, Smoljanović H, Balić I (2017) Numerical modelling of reinforced-concrete structures under seismic loading based on the finite element method with discrete inter-element cracks. Earth Eng Struct Dyn 46(1):159–178. https://doi.org/10.1002/eqe.2780
Maekawa K, Pimanmas A, Okamura, H (2003), Nonlinear mechanics of reinforced concrete, London
Kato B (1979) Mechanical properties of steel under load cycles idealizing seismic action. In: Bulletin D’Information 131, CEB, AICAP-CEB symposium, Rome pp 7–27
Smoljanović H, Nikolić Ž, Živaljić N (2015) A combined finite-discrete numerical model for analysis of masonry structures. Eng Fract Mech 136:1–14. https://doi.org/10.1016/j.engfracmech.2015.02.006
Van der Pluijm R (1992) Material properties of masonry and its components under tension and shear. In Neis VV (ed) Canadian masonry symposium: proceedings of the 6th Canadian masonry symposium, Saskatoon, Saskatchewan pp 675–686
Van der Pluijm R (1993) Shear behaviour of bed joints. In: Hanid AA, Harris HG (ed) North American masonry conference: proceedings of the 6th North American Masonry Conference, Philadelphia, Pennsylvania, pp 125–136
Gopalaratnam VS, Shah SP (1985) Softening response of plain concrete in direct tension. ACI J 82:310–323. https://doi.org/10.14359/10338
Atkinson RH, Amadei BP, Saeb S, Sture S (1989) Response of masonry bed joints in direct shear. J Struct Eng 115(9):2276–2296
Miyamura T (2000) Wrinkling on stretched circular membrane under in-plane torsion: bifurcation analyses and experiments. Eng Struct 22(11):1407–1425
Raijmakers TMJ, Vermeltfoort AT (1992) Deformation controlled tests in masonry shear walls. Delft, TNO-Bouw, Report No. B-92-1156
Smoljanović H, Živaljić N, Nikolić Ž (2013) A combined finite-discrete element analysis of dry stone masonry structures. Eng Struct 52:89–100. https://doi.org/10.1016/j.engstruct.2013.02.010
Balić I, Živaljić N, Smoljanović H, Trogrlić B (2016) Seismic resistance of dry stone arches under in-plane seismic loading. Struct Eng Mech 58(2):243–257. https://doi.org/10.12989/sem.2016.58.2.243
Smoljanović H, Nikolić Ž, Živaljić N (2015) A finite-discrete element model for dry stone masonry structures strengthened with steel clamps and bolts. Eng Struct 90:117–129. https://doi.org/10.1016/j.engstruct.2015.02.004
Bui T, Limam A, Sarhosis V, Hjiaj M (2017) Discrete element modelling of the in-plane and out-of-plane behaviour of dry-joint masonry wall constructions. Eng Struct 136(1):277–294. https://doi.org/10.1016/j.engstruct.2017.01.020
Acknowledgements
This paper is supported by the Croatian Science Foundation under the project Development of numerical models for reinforced-concrete and stone masonry structures under seismic loading based on discrete cracks (IP-2014-09-2319) and by the Croatian Government and the European Union through the European Regional Development Fund—the Competitiveness and Cohesion Operational Programme under the Project KK.01.1.1.02.0027.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Munjiza, A., Smoljanović, H., Živaljić, N. et al. Structural applications of the combined finite–discrete element method. Comp. Part. Mech. 7, 1029–1046 (2020). https://doi.org/10.1007/s40571-019-00286-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40571-019-00286-5