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http://dx.doi.org/10.12989/gae.2016.11.1.095

Nonlinear FEA of higher order beam resting on a tensionless foundation with friction  

He, Guanghui (School of Maritime and Civil Engineering, Zhejiang Ocean University)
Li, Xiaowei (Songjiang Campus of Shanghai Open University)
Lou, Rong (School of Maritime and Civil Engineering, Zhejiang Ocean University)
Publication Information
Geomechanics and Engineering / v.11, no.1, 2016 , pp. 95-116 More about this Journal
Abstract
A novel higher order shear-deformable beam model, which provides linear variation of transversal normal strain and quadratic variation of shearing strain, is proposed to describe the beam resting on foundation. Then, the traditional two-parameter Pasternak foundation model is modified to capture the effects of the axial deformation of beam. The Masing's friction law is incorporated to deal with nonlinear interaction between the foundation and the beam bottom, and the nonlinear properties of the beam material are also considered. To solve the mathematical problem, a displacement-based finite element is formulated, and the reliability of the proposed model is verified. Finally, numerical examples are presented to study the effects of the interfacial friction between the beam and foundation, and the mechanical behavior due to the tensionless characteristics of the foundation is also examined. Numerical results indicate that the effects of tensionless characteristics of foundation and the interfacial friction have significant influences on the mechanical behavior of the beam-foundation system.
Keywords
nonlinear quasi-static analysis; Pasternak foundation; Masing's friction law; higher order beam model; finite element method;
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1 Al-Bender, F., Lampaert, V. and Swevers, J. (2005), "The generalized Maxwell-slip model: a novel model for friction simulation and compensation", IEEE T. Automat. Control, 50(11), 1883-1887.   DOI
2 Ayoub, A. (2003), "Mixed formulation of nonlinear beam on foundation elements", Comput. Struct., 81(7), 411-421.   DOI
3 Batoz, J.L. and Dhatt, G. (1979), "Incremental displacement algorithms for nonlinear problems", Int. J. Numer. Meth. Eng., 14(8), 1262-1267.   DOI
4 Berger, E.J. (2002), "Friction modeling for dynamic system simulation", App. Mech. Rev., 55(6), 535-577.   DOI
5 Chen, W.Q., Lv, C.F. and Bian, Z.G. (2004), "A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation", Appl. Math. Model., 28(10), 877-890.   DOI
6 Comodromos, E.M. and Bareka, S.V. (2005), "Evaluation of negative skin friction effects in pile foundations using 3D nonlinear analysis", Comput. Geotech., 32(3), 210-221.   DOI
7 Comodromos, E. M. and Papadopoulou, M.C. (2013), "Explicit extension of the p-y method to pile groups in cohesive soils", Comput. Geotech., 47(1), 28-41.   DOI
8 Dall'Asta, A. and Zona, A. (2004), "Slip locking in finite elements for composite beams with deformable shear connection", Finite Elem. Anal. Des., 40(13-14), 1907-1930.   DOI
9 Dash, S.R., Govindaraju, L. and Bhattacharya, S. (2009), "A case study of damages of the Kandla Port and Customs Office tower supported on a mat-pile foundation in liquefied soils under the 2001 Bhuj earthquake", Soil Dyn. Earthq. Eng., 29(2), 333-346.   DOI
10 Dutta, S.C. and Roy, R. (2002), "A critical review on idealization and modeling for interaction among soilfoundation-structure system", Comput. Struct., 80(20), 1579-1594.   DOI
11 Feng, Z. and Cook, R.D. (1983), "Beam elements on two-parameter elastic foundation", J. Eng. Mech., ASCE, 109(6), 1390-1402.   DOI
12 Georgiadis, K. and Georgiadis, M. (2012), "Development of p-y curves for undrained response of piles near slopes", Comput. Geotech., 40(3), 53-61.   DOI
13 Han, S.M., Benaroya, H. and Wei, T. (1999), "Dynamics of transversely vibrating beams using four engineering theoroes", J. Sound Vib., 225(5), 935-988.   DOI
14 Jones, R. and Xenophontos, J. (1977), "The vlasov foundation model", Int. J. Mech. Sci., 19(6), 317-323.   DOI
15 Masing, G. (1923), Zur Heyn'schen Theorie der Verfestigung der Metalle durch verborgen elastische Spannungen, Springer.
16 Mullapudi, R. and Ayoub, A. (2010), "Nonlinear finite element modeling of beams on two-parameter foundations", Comput. Geotech., 37(3), 334-342.   DOI
17 Nobili, A. (2013), "Superposition principle for the tensionless contact of a beam resting on a Winkler or a Pasternak foundation", J. Eng. Mech., ASCE, 139(10), 1470-1478.   DOI
18 Sapountzakis, E.J. and Kampitsis, A.E. (2011a), "Nonlinear analysis of shear deformable beam-columns partially supported on tensionless three-parameter foundation", Arch. Appl. Mech., 81(12), 1833-1851.   DOI
19 Nogami, T. and O'Neill, M.W. (1985), "Beam on generalized two-parameter foundation", J. Eng. Mech., ASCE, 111(5), 664-679.   DOI
20 Popp, K., Panning, L. and Sextro, W. (2003), "Vibration damping by friction forces: Theory and applications", J. Vib. Control, 9(3-4), 419-448.   DOI
21 Sapountzakis, E.J. and Kampitsis, A.E. (2011b), "Nonlinear response of shear deformable beams on tensionless nonlinear viscoelastic foundation under moving loads", J. Sound Vib., 330(22), 5410-5426.   DOI
22 Sapountzakis, E.J. and Kampitsis, A.E. (2013), "Inelastic analysis of beams on two-parameter tensionless elastoplastic foundation", Eng. Struct., 48, 389-401.   DOI
23 Shirima, L.M. and Giger, M.W. (1992), "Timoshenko beam element resting on two-parameter elastic foundation", J. Eng. Mech., ASCE, 118(2), 280-295.   DOI
24 Winkler, E. (1867), Theory of Elasticity and Strength, Dominicus Prague.
25 Zhang, Y. and Murphy, K.D. (2013), "Tensionless contact of a finite beam: Concentrated load inside and outside the contact zone", Acta Mech. Sinica, 29(6), 836-839.   DOI
26 Zhou, H., Luo, S. and Sun, D. (2011), "The bending analysis of a beam on elastic foundation with large deflection including the effects of horizontal friction", Eng. Mech., 28(1), 43-54.
27 Zienkiewicz, O.C. and Taylor, R.L. (2000), The Finite Element Method, (Fifth Edition), Volume 2: Solid Mechanics, Butterworth-Heinemann.