DOI QR코드

DOI QR Code

A numerical method for the limit analysis of masonry structures

  • Degl'Innocenti, Silvia (Istituto di Scienza e Tecnologie dell'Informazione, 'Alessandro Faedo', ISTI-CNR Area della Ricerca CNR) ;
  • Padovani, Cristina (Istituto di Scienza e Tecnologie dell'Informazione, 'Alessandro Faedo', ISTI-CNR Area della Ricerca CNR)
  • 투고 : 2003.03.03
  • 심사 : 2004.01.27
  • 발행 : 2004.07.25

초록

The paper presents a numerical method for the limit analysis of structures made of a rigid no-tension material. Firstly, we formulate the constrained minimum problem resulting from the application of the kinematic theorem, which characterizes the collapse multiplier as the minimum of all kinematically admissible multipliers. Subsequently, by using the finite element method, we derive the corresponding discrete minimum problem in which the objective function is linear and the inequality constraints are linear as well as quadratic. The method is then applied to some examples for which the collapse multiplier and a collapse mechanism are explicitly known. Lastly, the solution to the minimum problem calculated via numerical codes for quadratic programming problems, is compared to the exact solution.

키워드

참고문헌

  1. Bennati, S. and Padovani, C. (1997), "Some non-linear elastic solutions for masonry solids", Mech. Struct. Mach., 25(2), 243-266. https://doi.org/10.1080/08905459708905289
  2. Capsoni, A. and Corradi, L. (1997), "A finite element formulation of the rigid-plastic limit analysis problem", Int. J. Numer. Meth. Eng., 40, 2063-2086. https://doi.org/10.1002/(SICI)1097-0207(19970615)40:11<2063::AID-NME159>3.0.CO;2-#
  3. Cea, J. (1978), Lectures on Optimization - Theory and Algorithms, Springer Verlag.
  4. Czyzyk, J., Mesnier, M. and Moré, J. (1998), "The NEOS Server", IEEE J. Comput. Sci. Eng., 5, 68-75.
  5. Del Piero, G. (1989), "Constitutive equation and compatibility of the external loads for linear elastic masonrylike materials", Meccanica, 24, 150-162. https://doi.org/10.1007/BF01559418
  6. Del Piero, G. (1998), "Limit analysis and no-tension materials", Int. J. Plasticity, 14, 259-271. https://doi.org/10.1016/S0749-6419(97)00055-7
  7. Dolan, E. (2001), The NEOS Server 4.0 Administrative Guide, Technical Memorandum ANL/MCS-TM-250, Mathematics and Computer Science Division, Argonne National Laboratory.
  8. Drucker, D.C., Prager, W. and Greenberg, H.J. (1952), "Extended limit design theorems for continuous media", Quart. Appl. Math., 9, 381-389. https://doi.org/10.1090/qam/45573
  9. Gropp, W. and Moré, J. (1997), "Optimization Environments and the NEOS Server", Approximation Theory and Optimization, M.D. Buhmann and A. Iserles, Eds., 167-182, Cambridge University Press.
  10. Heyman, J. (1966), "The stone skeleton", Int. J. Solids Struct., 2, 249-279. https://doi.org/10.1016/0020-7683(66)90018-7
  11. Hinton, E. and Owen, D.R.J. (1977), Finite Element Programming, Academic Press, London.
  12. Kooharian, A. (1952), "Limit analysis of voussoir and concrete arches", J. Amer. Concrete Inst., 24, 317-328.
  13. Lucchesi, M. and Zani, N. (2001), "No tension materials and pressureless gases, an analogy", Proc. Strumas V, Computer Methods in Structural Masonry - 5, Roma 18-21 September 2001, 231-238.
  14. Lucchesi, M., Padovani, C., Pasquinelli, G. and Zani, N. (1997), "On the collapse of masonry arches", Meccanica, 32, 327-346. https://doi.org/10.1023/A:1004275223879
  15. Lucchesi, M., Padovani, C., Pagni, A., Pasquinelli, G. and Zani, N. (2000), COMES-NOSA a Finite Element Code for Non-linear Structural Analysis, Report CNUCE-B4-2000-003.
  16. Lucchesi, M., Padovani, C., Pasquinelli, G. and Zani, N. (1999), "The maximum modulus eccentricities surface for masonry vaults and limit analysis", Math. Mech. Solids, 4, 71-87. https://doi.org/10.1177/108128659900400105