Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Large deflection analysis of edge cracked simple supported beams

  • Received : 2014.01.01
  • Accepted : 2014.11.06
  • Published : 2015.05.10
⟨ Previous Next ⟩

Abstract

This paper focuses on large deflection static behavior of edge cracked simple supported beams subjected to a non-follower transversal point load at the midpoint of the beam by using the total Lagrangian Timoshenko beam element approximation. The cross section of the beam is circular. The cracked beam is modeled as an assembly of two sub-beams connected through a massless elastic rotational spring. It is known that large deflection problems are geometrically nonlinear problems. The considered highly nonlinear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of Aluminum. In the study, the effects of the location of crack and the depth of the crack on the non-linear static response of the beam are investigated in detail. The relationships between deflections, end rotational angles, end constraint forces, deflection configuration, Cauchy stresses of the edge-cracked beams and load rising are illustrated in detail in nonlinear case. Also, the difference between the geometrically linear and nonlinear analysis of edge-cracked beam is investigated in detail.

Keywords

Acknowledgement

Supported by : Bursa Technical University

References

  1. Akbas, S.D. (2013), "Geometrically nonlinear static analysis of edge cracked Timoshenko beams composed of functionally graded material", Math. Prob. Eng., Article ID 871815, 14.
  2. Akbas, S.D. (2014a), "Wave propagation analysis of edge cracked circular beams under impact force", Plos. One, 9(6), e100496. https://doi.org/10.1371/journal.pone.0100496
  3. Akbas, S.D. (2014b), "Wave propagation analysis of edge cracked beams resting on elastic foundation", Int. J. Eng. Appl. Sci., 6(1), 40-52.
  4. Akbas, S.D. (2014c), "Wave propagation in edge cracked functionally graded beams under impact force", J. Vib. Control, Doi: 10.1177/1077546314547531.
  5. Andreasus, U. and Baragatti, P. (2012), "Experimental damage detection of cracked beams by using nonlinear characteristics of forced response", Mech. Syst. Signal Pr., 31, 382-404. https://doi.org/10.1016/j.ymssp.2012.04.007
  6. Anifantis, N. and Dimarogonas, A. (1984), "Post buckling behavior of transverse cracked columns", Comput. Struct., 18(2), 351-356. https://doi.org/10.1016/0045-7949(84)90134-2
  7. Banik, A.K. (2011), "Nonlinear dynamics of cracked RC beams under harmonic excitation", World Acad. Sci. Eng. Tech., 75, 144-149.
  8. Broek, D. (1986), Elementary engineering fracture mechanics, Martinus Nijhoff Publishers, Dordrecht.
  9. Chartterjee, A. (2011), "Nonlinear dynamics and damage assessment of a cantilever beam with breathing edge crack", J. Vib. Acoust. Trans. ASME, 133(5), 051004. https://doi.org/10.1115/1.4003934
  10. Chen, G., Yang, X., Ying, X. and Nanni, A. (2006), "Damage detection of concrete beams using nonlinear features of forced vibration", Struct. Hlth. Monit., 5(2), 125-141. https://doi.org/10.1177/1475921706057985
  11. Douka, E., Zacharias, K.A., Hadjileintiadis, L.J. and Trochidis, A. (2010), "Non-linear vibration technique for carck detection in beam structures using frequency mixing", Acta Acustica Unites With Acustica, 96(5), 977-980. https://doi.org/10.3813/AAA.918357
  12. Dutta, D., Sohn, H., Harries, K.A. and Rizzo, P. (2009), "A nonlinear acoustic technique for crack detection in metallic structures", Struct. Hlth. Monit., 8(3), 251-262. https://doi.org/10.1177/1475921709102105
  13. Felippa, C.A. (2013), Notes on nonlinear finite element methods, http://www.colorado.edu/engineering/cas/courses.d/NFEM.d/NFEM.Ch10.d/NFEM.Ch10.pdf, Retrieved December 2013.
  14. Giannini, O., Casini, P. and Vestroni, F. (2013), "Nonlinear harmonic identification of breathing cracks in beams", Comput. Struct., 129, 166-177. https://doi.org/10.1016/j.compstruc.2013.05.002
  15. Ke, L.L., Yang, J. and Kitipornchai, S. (2009), "Postbuckling analysis of edge cracked functionally graded Timoshenko beams under end shortening", Compos. Struct., 90(2), 152-160. https://doi.org/10.1016/j.compstruct.2009.03.003
  16. Kitipornchai, S., Ke, L.L., Yang, J. and Xiang, Y. (2009), "Nonlinear vibration edge cracked functionally graded Timoshenko beams", J. Sound Vib., 324(3-5), 962-982. https://doi.org/10.1016/j.jsv.2009.02.023
  17. Kocaturk, T. and Akbas, S.D. (2010), "Geometrically non-linear static analysis of a simply supported beam made of hyperelastic material", Struct. Eng. Mech., 35(6), 677-697. https://doi.org/10.12989/sem.2010.35.6.677
  18. Mendelsohn, D.A., Vedacalam, S., Pecorari, C. and Mokasji, P.S. (2008), "Nonlinear vibration of an edgecracked beam with a cohesive zone, 2: Perturbation analysis of Euler-Bernoulli beam vibration using a nonlinear spring for damage represantation", J. Mech. Mater. Struct., 3(8), 1589-1604. https://doi.org/10.2140/jomms.2008.3.1589
  19. Mokasji, P.S. and Mendelsohn, D.A. (2008), "Nonlinear vibration of an edge-cracked beam with a cohesive zone, 1: Nonlinear bending load-displacement relations for a linear softening cohesive law", J. Mech. Mater. Struct., 3(8), 1573-1588. https://doi.org/10.2140/jomms.2008.3.1573
  20. Peng, Z.K., Lang, Z. and Chu, F.L. (2008), "Numerical analysis of cracked beams using nonlinear output frequency responses functions", Comput. Struct., 86(17-18), 1809-1818. https://doi.org/10.1016/j.compstruc.2008.01.011
  21. Sundermeyer, J.N. and Weaver, R.L. (1995), "On crack identification and characterization in a beam by nonlinear vibration analysis", J. Sound Vib., 183(5), 857-871. https://doi.org/10.1006/jsvi.1995.0290
  22. Tada, H., Paris, P.C. and Irwin, G.R. (1985), The Stress Analysis of Cracks Handbook, Paris Production Incorporated and Del Research Corporation.
  23. Yan, T., Yang, J. and Kitipornchai, S. (2012), "Nonlinear dynamics response of an edge-cracked functionally graded Timoshenko beam under parametric excitation", Nonlin. Dyn., 67(1), 527-540. https://doi.org/10.1007/s11071-011-0003-9
  24. Younesian, D., Marjani, S.R. and Esmailzadeh, E. (2013), "Nonlinear vibration analysis of harmonically excites cracked beams on viscoelastic foundations", Nonlin. Dyn., 71(1-2), 109-120. https://doi.org/10.1007/s11071-012-0644-3
  25. Wei, K.X., Ye, L., Ning, L.W. and Liu, Y.C. (2013), "Nonlinear dynamics response of a cracked beam under multi-frequency excitation", Adv. Vib. Eng., 12(5), 431-446.
  26. Zienkiewichz, O.C. and Taylor, R.L. (2000), The Finite Element Method, Fifth Edition, Volume 2: Solid Mechanics, Butterworth-Heinemann, Oxford.

Cited by

  1. Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM vol.59, pp.3, 2016, https://doi.org/10.12989/sem.2016.59.3.431
  2. Using co-rotational method for cracked frame analysis 2017, https://doi.org/10.1007/s11012-017-0796-9
  3. Force-based curved beam elements with open radial edge cracks pp.1537-6532, 2018, https://doi.org/10.1080/15376494.2018.1472326
  4. Deformation of multi-storey flat slabs, a site investigation vol.5, pp.1, 2015, https://doi.org/10.12989/acc.2017.5.1.49
  5. Geometrically nonlinear analysis of a laminated composite beam vol.66, pp.1, 2015, https://doi.org/10.12989/sem.2018.66.1.027
  6. Large deflection analysis of a fiber reinforced composite beam vol.27, pp.5, 2015, https://doi.org/10.12989/scs.2018.27.5.567
  7. Geometrically nonlinear analysis of functionally graded porous beams vol.27, pp.1, 2015, https://doi.org/10.12989/was.2018.27.1.059
  8. Thermal post-buckling analysis of a laminated composite beam vol.67, pp.4, 2018, https://doi.org/10.12989/sem.2018.67.4.337
  9. Nonlinear behavior of fiber reinforced cracked composite beams vol.30, pp.4, 2019, https://doi.org/10.12989/scs.2019.30.4.327
  10. A Force-Based Rectangular Cracked Element vol.13, pp.4, 2015, https://doi.org/10.1142/s1758825121500472