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A numerical model for masonry implemented in the framework of a discrete formulation

  • Nappi, A. (Department of Civil Engineering, University of Trieste) ;
  • Tin-Loi, F. (School of Civil and Environmental Engineering, The University of New South Wales)
  • Published : 2001.02.25

Abstract

A direct discrete formulation suitable for the nonlinear analysis of masonry structures is presented. The numerical approach requires a pair of dual meshes, one for describing displacement fields, one for imposing equilibrium. Forces and displacements are directly used (instead of having to resort to a model derived from a set of differential equations). Associated and nonassociated flow laws are dealt with within a complementarity framework. The main features of the method and of the relevant computer code are discussed. Numerical examples are presented, showing that the numerical approach is able to describe plastic strains, damage effects and crack patterns in masonry structures.

Keywords

References

  1. Bazant, Z.P. and Cedolin, L. (1979), "Blunt crack band propagation in finite element analysis", ASCE J. of Eng. Mech., 105, 297-315.
  2. Bolzon, G., Maier, G. and Novati, G. (1994), "Some aspects of quasi-brittle fracture analysis as a linear complementarity problem", Fracture and Damage in Quasibrittle Structures, Eds Z.P. Bazant, Z. Bittnar, M. Jirasek, J. Mazars, E&FN Spon, London, 159-174.
  3. Cottle, R.W., Pang, J.S. and Stone, R.E. (1992), The Linear Complementarity Problem, Academic Press.
  4. Benedetti, D. and Benzoni, G.M. (1984), "A numerical model for the seismic analysis of masonry buildings: Experimental correlations", Earth. Eng. and Struct. Dyn., 12, 817-831. https://doi.org/10.1002/eqe.4290120608
  5. Dhanasekar, M., Kleeman, P.W. and Page, A.W. (1985), "Non-linear biaxial stress-strain relations for brick masonry", ASCE J. of Struct. Div., 111(5), 1085-1100. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:5(1085)
  6. Gambarotta, L. and Lagomarsino, S. (1997), "Damage models for the seismic response of brick masonry shear walls. Part II: The continuum model and its applications", Earth. Eng. and Struct. Dyn., 26(4), 441-462. https://doi.org/10.1002/(SICI)1096-9845(199704)26:4<441::AID-EQE651>3.0.CO;2-0
  7. Lofti, H.R. and Shing, P.B. (1991), "An appraisal of smeared crack models for masonry shear wall analysis", Comput. Struct., 41, 413-425. https://doi.org/10.1016/0045-7949(91)90134-8
  8. Lourenco, P.B. (1996), Computational Strategies for Masonry Structures, Delft University Press, Delft, The Netherlands.
  9. Lourenço, P.B., Rots, J.G. and Blaauwendraad, J. (1998), "Continuum model for masonry: Parameter estimation and validation", ASCE J. of Struct. Engineering, 124(6), 642-652. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:6(642)
  10. Maier, G. (1970), "A matrix structural theory of piecewise-linear plasticity with interacting yield planes", Meccanica, 5(1), 55-66.
  11. Maier, G. and Nappi, A. (1985), "A theory of perfectly no-tension discretized structural systems", Engineering Structures, 12, 227-234.
  12. Maier, G., Nappi, A. and Papa, E. (1991), "Damage models for masonry as a composiste material: a numerical and experimental analysis", Constitutive Laws for Engineering Materials, Ed. by C.S. Desai, E. Krempl, G. Frantziskonis and H. Saadatmanesh, ASME Press, New York, 427-432.
  13. G. Maier, E. Papa and A. Nappi (1991), "On damage and failure of brick masonry", Experimental and Numerical Methods in Earthquake Engineering, Ed. by J. Donea and P.M. Jones, ECSC, Brussels, 223-245.
  14. Molins, C. and Roca, P. (1998), "Capacity of masonry arches and spatial frames", ASCE J. of Struct. Engineering, 124(6), 653-663. https://doi.org/10.1061/(ASCE)0733-9445(1998)124:6(653)
  15. Nappi, A., Facchin, G. and Marcuzzi, C. (1997), "Structural dynamics: Convergence properties in the presence of damage and applications to masonry structures", Structural Engineering and Mechanics, 5(5), 587-598. https://doi.org/10.12989/sem.1997.5.5.587
  16. Page, A.W. (1978), "Finite element model for masonry", ASCE J. of Struct. Div., 104, 1267-1285.
  17. Pande, G.N., Liang, J.X. and Middleton, J. (1989), "Equivalent elastic moduli for brick masonry", Computer and Geotechnics, 8, 243-265. https://doi.org/10.1016/0266-352X(89)90045-1
  18. Panzeca, T. and Polizzotto, C. (1988), "Constitutive equations for no-tension materials", Meccanica, 23, 88-93. https://doi.org/10.1007/BF01556706
  19. Papa, E. (1996), "A unilateral damage model for masonry based on a homogenization procedure", Mechanics of Cohesive-Frictional Materials, 1, 349-366. https://doi.org/10.1002/(SICI)1099-1484(199610)1:4<349::AID-CFM18>3.0.CO;2-M
  20. Papa, E. and Nappi, A. (1997), "Numerical modelling of masonry: A material model accounting for damage effects and plastic strains", Applied Mathematical Modelling, 21(6), 319-335. https://doi.org/10.1016/S0307-904X(97)00011-5
  21. Tin-Loi, F. and Ferris, M.C. (1997), "Holonomic analysis of quasibrittle fracture with nonlinear softening", Fracture Research, Ed. by B.L. Karihaloo, Y.W. Mai, M.I. Ripley and R.O. Ritchie, Pergamon, 2183-2190.
  22. Tin-Loi, F. and Xia, S.H. (2000), "Nonholonomic elastoplastic analysis involving unilateral frictionless contact as a mixed complementarity problem", Computer Methods in Applied Mechanics and Engineering, to appear.
  23. Tomazevic, M. and Weiss, P. (1994), "Seismic behavior of plain and reiforced-masonry buildings", ASCE J. of Struct. Engineering, 120, 2, 323-338. https://doi.org/10.1061/(ASCE)0733-9445(1994)120:2(323)
  24. Tonti, E. (2000A), "A finite formulation for the wave equation", Journal of Computational Acoustics, to appear.
  25. Tonti, E. (2000B), "Finite formulation of electromagnetic field", Journal of Electromagnetic Waves and Applications, to appear.

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