PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

A numerical upper bound formulation with sensibly-arranged velocity discontinuities and orthotropic material strength behaviour

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Numerical limit analysis allows for fast estimates of the collapse load of structures exhibiting ideal plastic material behaviour. In numerical upper bound formulations, the description of the unknown velocity field can be extended by introducing velocity discontinuities between finite elements. Through these additional degrees of freedom, localised failure modes may be approximated more accurately and better upper bounds can be obtained. In the existing formulations, such discontinuities are typically introduced between all elements and the description is restricted to isotropic failure behaviour. In this work, a general 3D upper bound formulation is briefly proposed, allowing the consideration of both isotropic and orthotropic yield functions within finite elements as well as at velocity discontinuities. The concept of “projecting” a stress-based orthotropic yield function onto a certain discontinuity is presented, giving a traction-based yield function which allows for a consistent description of the material strength behaviour across the interface. The formulation is verified by means of two classical examples, the rigid strip footing and the block with asymmetric holes. Furthermore, based on the computation of potential orientations of plastic flow localisation, a simple concept for a sensible arrangement of velocity discontinuities is proposed. It is shown that this concept performs very well for isotropic as well as anisotropic material strength behaviour. A feature of the present work is that, velocity jumps are allowed only across the prescribed finite element interfaces determined from the sensible discontinuity arrangement. Good upper bounds similar to those in the existing works are obtained with far fewer degrees of freedom.
Rocznik
Strony
417--433
Opis fizyczny
Bibliogr. 37 poz., rys.
Twórcy
autor
  • Vienna University of Technology, Vienna, Austria
autor
  • Vienna University of Technology, Vienna, Austria
autor
  • Vienna University of Technology, Vienna, Austria
  • Vienna University of Technology, Vienna, Austria
autor
  • University of Oxford, Oxford, UK
Bibliografia
  • 1. Anderheggen E., Knopfel H., 1972, Finite element limit analysis using linear programming, International Journal of Solids and Structures, 8, 12, 1413-1431
  • 2. Andersen E.D., Roos C., Terlaky T., 2003, On implementing a primal-dual interior-point method for conic quadratic optimization, Mathematical Programming, 95, 2, 249-277
  • 3. Belytschko T., Hodge P.G., 1970, Plane stress limit analysis by finite elements, Journal of the Engineering Mechanics Division, 96, 6, 931-944
  • 4. Bottero A., Negre R., Pastor J., Turgeman S., 1980, Finite element method and limit analysis theory for soil mechanics problems, Computer Methods in Applied Mechanics and Engineering, 22, 1, 131-149
  • 5. Chen J., Yin J.-H., Lee C.F., 2003, Upper bound limit analysis of slope stability using rigid finite elements and nonlinear programming, Canadian Geotechnical Journal, 40, 742-752
  • 6. Ciria H., Peraire J., 2004, Computation of upper and lower bounds in limit analysis using second-order cone programming and mesh adaptivity, 9th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability
  • 7. Ciria H., Peraire J., Bonet J., 2008, Mesh adaptive computation of upper and lower bounds in limit analysis, International Journal for Numerical Methods in Engineering, 75, 8, 899-944
  • 8. Dorn M., 2012, Investigations on the Serviceability Limit State of Dowel-Type Timber Connections, PhD Thesis, Vienna University of Technology
  • 9. Drucker D.C., Greenberg H.J., Prager W., 1951, The safety factor of an elastic-plastic body in plane strain, Journal of Applied Mechanics, 18, 371-378
  • 10. Drucker D.C., Prager W., Greenberg H.J., 1952, Extended limit design theorems for continuous media, Quarterly of Applied Mathematics, 9, 381-389
  • 11. Fussl J., Lackner R., Eberhardsteiner J., Mang H.A. , 2008, Failure modes and effective strength of two-phase materials determined by means of numerical limit analysis, Acta Mechanica, 1-4, 195, 185-202
  • 12. Fussl J., Li M., Lukacevic M., Eberhardsteiner J., Martin C.M. , 2017, Comparison of unit cell-based computational methods for predicting the strength of wood, Engineering Structures, 141, 427-443
  • 13. Hawksbee S., Smith C., Gilbert M., 2013, Application of discontinuity layout optimization to three-dimensional plasticity problems, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 469, 2155
  • 14. Hochreiner G., Fussl J., Eberhardsteiner J. , 2013, Cross-laminated timber plates subjected to concentrated loading – experimental identification of failure mechanisms, Strain, 50, 1, 68-81
  • 15. Hochreiner G., Fussl J., Serrano E., Eberhardsteiner J. , 2014, Influence of wooden board strength class on the performance of cross-laminated timber plates investigated by means of full-field deformation measurements, Strain, 50, 2, 161-173
  • 16. Krabbenhøft K., Lyamin A.V., Hjiaj M., Sloan S.W., 2005, A new discontinuous upper bound limit analysis formulation, International Journal for Numerical Methods in Engineering, 63, 7, 1069-1088
  • 17. Le C.V., Askes H., Gilbert M., 2019, Adaptive element-free Galerkin method applied to the limit analysis of plates, Computer Methods in Applied Mechanics and Engineering, 199, 37, 2487-2496
  • 18. Li M., Fussl J., Lukacevic M., Eberhardsteiner J., Martin C.M. , 2018, Strength predictions of clear wood at multiple scales using numerical limit analysis approaches, Computers and Structures, 196, 200-216
  • 19. Liu F., Zhao J., 2013, Upper bound limit analysis using radial point interpolation meshless method and nonlinear programming, International Journal of Mechanical Sciences, 70, 26-38
  • 20. Lukacevic M., Fussl J. , 2016, Application of a multisurface discrete crack model for clear wood taking into account the inherent microstructural characteristics of wood cells, Holzforschung, 70, 9, 845-853
  • 21. Lukacevic M., Fussl J., Lampert R. , 2014, Failure mechanisms of clear wood identified at wood cell level by an approach based on the extended finite element method, Engineering Fracture Mechanics, 144, 158-175
  • 22. Lyamin A.V., Sloan S.W., 2002a, Lower bound limit analysis using non-linear programming, International Journal for Numerical Methods in Engineering, 55, 5, 573-611
  • 23. Lyamin A.V., Sloan S.W., 2002b, Upper bound limit analysis using linear finite elements and non-linear programming, International Journal for Numerical and Analytical Methods in Geomechanics, 26, 2, 181-216
  • 24. Lysmer J., 1970, Limit analysis of plane problems in soil mechanics, Journal of the Soil Mechanics and Foundations Division, 96, 4, 1311-1334
  • 25. Maier G., Zavelani-Rossi A., Benedetti D., 1972, A finite element approach to optimal design of plastic structures in plane stress, International Journal for Numerical Methods in Engineering, 4, 4, 455-473
  • 26. Makrodimopoulos A., Martin C.M., 2006, Lower bound limit analysis of cohesive-frictional materials using second-order cone programming, International Journal for Numerical Methods in Engineering, 66, 4, 604-634
  • 27. Makrodimopoulos A., Martin C.M., 2007, Upper bound limit analysis using simplex strain elements and second-order cone programming, International Journal for Numerical and Analytical Methods in Geomechanics, 31, 6, 835-865
  • 28. Makrodimopoulos A., Martin C.M., 2008, Upper bound limit analysis using discontinuous quadratic displacement fields, Communications in Numerical Methods in Engineering, 24, 11, 911-927
  • 29. Martin C., Makrodimopoulos A., 2008, Finite-element limit analysis of Mohr-Coulomb materials in 3D using semidefinite programming, Journal of Engineering Mechanics, 134, 4, 339-347
  • 30. Milani G., Lourenc¸o P.B., 2009, A discontinuous quasi-upper bound limit analysis approach with sequential linear programming mesh adaptation, International Journal of Mechanical Sciences, 51, 89-104
  • 31. MOSEK ApS, 2014, The MOSEK optimization tools version 7.0, User’s Manual and Reference, http://www.mosek.com
  • 32. Prandtl L., 1920, Uber die H¨arte plastischer Korper, Nachrichten von der Gesellschaft der Wissenschaften zu G¨ottingen, Mathematisch-Physikalische Klasse, 12, 74-85
  • 33. Sloan S.W., Kleeman P.W., 1995, Upper bound limit analysis using discontinuous velocity fields, Computer Methods in Applied Mechanics and Engineering, 127, 14, 293-314
  • 34. Smith C., Gilbert M., 2007, Application of discontinuity layout optimization to plane plasticity problems, Proceedings of the Royal Society A, 463, 2461-2484
  • 35. Wu J.-Y., Cervera M., 2014, On the equivalence between traction- and stress-based approaches for the modeling of localized failure in solids, Journal of the Mechanics and Physics of Solids, 82, 137-163
  • 36. Yu S., Zhang X., Sloan S.W., 2016, A 3D upper bound limit analysis using radial point interpolation meshless method and second-order cone programming, International Journal for Numerical Methods in Engineering, 108, 13, 1686-1704
  • 37. Zouain N., Borges L., Silveira J.L., 2002, An algorithm for shakedown analysis with nonlinear yield functions, Computer Methods in Applied Mechanics and Engineering, 191, 23, 2463-2481
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c8355ea6-e715-4c17-a872-7d55e6bd1812
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.