Abstract
This paper presents the formulation of a tri-dimensional (3D) beam-column finite element (FE) with cross-section warping, based on a corotational approach for the analysis of damaging structures including material and geometric nonlinear effects. The model derives from an extended Hu–Washizu formulation and is an enhancement of a previously proposed beam FE formulation originally adopted for steel and reinforced concreted structures under linear geometry. The warping of the cross-sections is described by introducing additional degrees of freedom to those standard for a classic 3D beam FE and interpolating the corresponding displacement field with polynomial shape functions. The effects of large displacements are modeled through a corotational approach also including the axial-torsion interaction due to the Wagner effect. A 3D plastic-damage model is introduced to reproduce the degrading phenomena typical of many structural elements. This is used to simulate both damage occurring in ductile materials under large deformations and the non-symmetric tensile-compressive damage of brittle-like materials. The paper concludes with some numerical studies to validate the proposed FE and investigate the performances of the adopted corotational approach.
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References
Crisfield MA (1990) A consistent co-rotational formulation for non-linear, three-dimensional, beam-elements. Comput Method Appl Mech Eng 81(2):131–150
Nour-Omid B, Rankin CC (1991) Finite rotation analysis and consistent linearization using projectors. Comput Method Appl Mech Eng 93(3):353–384
Crisfield MA, Moita GF (1996) A unified co-rotational for solids, shells and beams. Int J Solids Struct 81(20–22):2969–2992
Wempner G (1969) Finite elements, finite rotations and small strains of flexible shells. Int J Solids Struct 5(2):117–153
Belytschko T, Hsieh BJ (1973) Nonlinear transient finite element analysis with convected coordinates. Int J Numer Meth Eng 7(3):255–271
Felippa CA, Haugen B (2005) A unified formulation of small-strain corotational finite elements: I. Theory. Comput Method Appl Mech Eng 194(21):2285–2335
Rankin CC, Nour-Omid B (1988) The use of projectors to improve finite element performance. Comput Struct 30(1–2):257–267
De Souza RM (2000) Force-based finite element for large displacement inelastic analysis of frames. Ph.D. thesis, University of California, Berkeley, CA, USA
Battini JM, Pacoste C (2002) Co-rotational beam elements with warping effects in instability problems. Comput Method Appl Mech Eng 191(17):1755–1789
Battini JM (2007) A modified corotational framework for triangular shell elements. Comput Method Appl Mech Eng 196(13):1905–1914
Battini JM (2007) A non-linear corotational 4-node plane element. Mech Res Commun 35(6):408–413
Battini JM (2008) Large rotations and nodal moments in corotational elements. Comput Model Eng Sci CMES 33(1):1–15
Nukala PKV, White DW (2004) A mixed finite element for three-dimensional nonlinear analysis of steel frames. Comput Method Appl Mech Eng 193(23):2507–2545
Alsafadie R, Hjiaj M, Battini JM (2010) Corotational mixed finite element formulation for thin-walled beams with generic cross-section. Comput Method Appl Mech Eng 199(49):3197–3212
Camotim D, Basaglia C, Silvestre N (2010) GBT buckling analysis of thin-walled steel frames: a state-of-the-art report. Thin Wall Struct 48(10):726–743
Alsafadie R, Hjiaj M, Battini JM (2011) Three-dimensional formulation of a mixed corotational thin-walled beam element incorporating shear and warping deformation. Thin Wall Struct 49(4):523–533
Garcea G, Madeo A, Casciaro R (2012) The implicit corotational method and its use in the derivation of nonlinear structural models for beams and plates. J Mech Mater Struct 7(6):509–538
Le TN, Battini JM, Hjiaj M (2014) A consistent 3D corotational beam element for nonlinear dynamic analysis of flexible structures. Comput Method Appl Mech Eng 269:538–565
Genoese A, Genoese A, Bilotta A, Garcea G (2014) Buckling analysis through a generalized beam model including section distortions. Thin Wall Struct 85:125–141
Gabriele S, Rizzi N, Varano V (2016) A 1D nonlinear TWB model accounting for in plane cross-section deformation. Int J Solids Struct 94:170–178
Le Corvec V (2012) Nonlinear 3d frame element with multi-axial coupling under consideration of local effects. Ph.D. thesis, University of California, Berkeley, CA, USA
Di Re P, Addessi D, Filippou FC (2016) 3D beam-column finite element under non-uniform shear stress distribution due to shear and torsion. In: ECCOMAS congress 2016, VII European congress on computational methods in applied sciences and engineering
Di Re P (2017) 3D beam-column finite elements under tri-axial stress–strain states: non-uniform shear stress distribution and warping. Ph.D. thesis, Sapienza University of Rome, http://hdl.handle.net/11573/937922
Di Re P, Addessi D, Filippou FC (Revised) A mixed 3D beam element with damage plasticity for the analysis of RC members under warping torsion. J Struct Eng ASCE
Pi YL, Bradford MA, Uy B (2005) A spatially curved beam element with warping and Wagner effects. Ibt J Numer Meth Eng 63(9):1342–1369
Timoshenko S, Gere JM (1961) Theory of elastic stability, 2nd edn. McGraw-Hill, New York
Ciampi V, Carlesimo L (1986) A nonlinear beam element for seismic analysis of structures. In: Proceedings of the 8th European conference on earthquake engineering
Spacone E, Filippou FC, Taucer FF (2012) Fibre beam-column model for non-linear analysis of R/C frames: Part I. Formulation. Earthq Eng Struct 25(7):711–726
Addessi D, Ciampi V (2007) A regularized force-based beam element with a damage-plastic section constitutive law. Int J Numer Meth Eng 70(5):610–629
Neuenhofer A, Filippou FC (1997) Evaluation of nonlinear frame finite-element models. J Struct Eng ASCE 123(7):958–966
Haugen B (1994) Buckling and stability problems for thin shell structures using high performance finite elements. Ph.D. thesis, University of Colorado, Boulder, USA
Taylor RL, Filippou FC, Saritas A, Auricchio F (2003) A mixed finite element method for beam and frame problems. Comput Mech 31(1):192–203
Vlasov VZ (1984) Thin-walled elastic beams. National Technical Information Service, Washington
Addessi D, Marfia S, Sacco E (2002) A plastic nonlocal damage model. Comput Method Appl Mech Eng 191(13):1291–1310
Drucker DC, Prager W (1952) Soil mechanics and plastic analysis or limit design. Q Appl Math 10(2):157–165
Rezaiee-Pajand M, Sharifian M, Sharifian M (2011) Accurate and approximate integrations of DruckerPrager plasticity with linear isotropic and kinematic hardening. Eur J Mech A Solid 30(3):345–361
Öztekin E, Pul S, Hüsem M (2016) Experimental determination of Drucker–Prager yield criterion parameters for normal and high strength concretes under triaxial compression. Constr Build Mater 112(1):725–732
Filippou FC, Constantinides M (2004) Fedeaslab getting started guide and simulation examples. Technical Report 22, NEESgrid
Rizzi N, Varano V, Gabriele S (2013) Initial postbuckling behavior of thin-walled frames under mode interaction. Thin Wall Struct 68:124–134
Pi YL, Trahair NS (1995) Inelastic torsion of steel I-beams. J Struct Eng ASCE 121(4):609–620
Kostic SM, Filippou FC (2011) Section discretization of fiber beam-column elements for cyclic inelastic response. J Struct Eng ASCE 138(5):592–601
Zhou SJ (2010) Finite beam element considering shear-lag effect in box girder. J Eng Mech ASCE 136(9):1115–1122
Légeron F, Paultre P (2000) Behavior of high-strength concrete columns under cyclic flexure and constant axial load. ACI Struct J 97(4):591–601
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Di Re, P., Addessi, D. A mixed 3D corotational beam with cross-section warping for the analysis of damaging structures under large displacements. Meccanica 53, 1313–1332 (2018). https://doi.org/10.1007/s11012-017-0749-3
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DOI: https://doi.org/10.1007/s11012-017-0749-3