DOI QR코드

DOI QR Code

Nonlinear large deflection buckling analysis of compression rod with different moduli

  • 투고 : 2014.04.19
  • 심사 : 2014.11.11
  • 발행 : 2015.06.10

초록

Many novel materials exhibit a property of different elastic moduli in tension and compression. One such material is graphene, a wonder material, which has the highest strength yet measured. Investigations on buckling problems for structures with different moduli are scarce. To address this new problem, firstly, the nondimensional expression of the relation between offset of neutral axis and deflection curve is derived based on the phased integration method, and then using the energy method, load-deflection relation of the rod is determined; Secondly, based on the improved constitutive model for different moduli, large deformation finite element formulations are developed and combined with the arc-length method, finite element iterative program for rods with different moduli is established to obtain buckling critical loads; Thirdly, material mechanical properties tests of graphite, which is the raw material of graphene, are performed to measure the tensile and compressive elastic moduli, moreover, buckling tests are also conducted to investigate the buckling behavior of this kind of graphite rod. By comparing the calculation results of the energy method and finite element method with those of laboratory tests, the analytical model and finite element numerical model are demonstrated to be accurate and reliable. The results show that it may lead to unsafe results if the classic theory was still adopted to determine the buckling loads of those rods composed of a material having different moduli. The proposed models could provide a novel approach for further investigation of non-linear mechanical behavior for other structures with different moduli.

키워드

과제정보

연구 과제 주관 기관 : Natural Science Foundation of China

참고문헌

  1. Ambartsumyan, S. A. (1986), Elasticity Theory of Different Modulus, China Railway Press, Bei Jing, China.
  2. Barak, M.M., Curry, J.D., Weiner, S. and Shahar, R. (2009), "Are tensile and compressive Young's moduli of compact bone different", J. Mech. Behav. Biomed. Mater., 2, 51-60. https://doi.org/10.1016/j.jmbbm.2008.03.004
  3. Bert, C.W. (1977), "Models for fibrous composites with different properties in tension and compression", ASME J. Eng. Mater. Technol., 99, 344-349. https://doi.org/10.1115/1.3443550
  4. Bert, C.W. and Ko, C.L. (1985), "Buckling of columns constructed of bimodular materials". Int. J. Eng. Sci., 23 (6), 641-657. https://doi.org/10.1016/0020-7225(85)90134-X
  5. Bruno, D., Lato, S. and Sacco, E. (1994), "Nonlinear analysis of bimodular composite plates under compression", Comput. Mech., 14, 28-37. https://doi.org/10.1007/BF00350155
  6. Crisfield, M.A. (2000), Nonlinear Finite Element Analysis of Solids and Structures, Volume 1: Essentials, Crisfield Imperial College of Science, Technology and Medicine, London, UK.
  7. Geim, A.K. (2009), "Graphene: status and prospects", Sci., 324, 1530-1534. https://doi.org/10.1126/science.1158877
  8. Gilbert, G. (1961), "Stress/strain properties of cast iron and Poisson's ratio in tension and compression", Brit. Cast Res. Assn. J., 9, 347-363.
  9. Gong, X.N., Wang, Q.T. and Luo, X. (1994), "Round hole expansion problem of bimodulus materials", J. Appl. Mech., 11(4), 127-132.
  10. Guo, Z.H. and Zhang, X.Q. (1987), "Investigation of complete Stree-deformation curves for concretes in tension", ACI Mater. J., 84 (4), 278-285.
  11. Haimson, B.C. and Tharp, T.M. (1974), "Stresses around borehole in bilinear elastic rock", Soc. Petrol. Engrs. J., 14, 145-151. https://doi.org/10.2118/4241-PA
  12. He, X.T., Chen, S.L. and Sun T.Y. (2007), "Applying the equivalent section method to solve beam subjected to lateral force and bend-compression column with different moduli", Int. J. Mech. Sci., 49, 919-924. https://doi.org/10.1016/j.ijmecsci.2006.11.004
  13. He, X.T., Zheng, Z.L., Sun, J.Y., Li, Y.M. and Chen, S.L. (2009), "Convergence analysis of a finite element method based on different moduli in tension and compression", Int. J. Solid. Struct., 46 (20), 3734-3740. https://doi.org/10.1016/j.ijsolstr.2009.07.003
  14. Jones, R.M. (1977), "Stress-strain relations for materials with different moduli in tension and compression", J. AIAA, 15, 16-23. https://doi.org/10.2514/3.7297
  15. Kratsh, K.M., Schutzler, J.C. and Eitman, D.S. (1972), "Carbon-carbon 3-D orthogonal material behavior", AIAA/ASME/SAE 13th Structures, Structural Dynamics and Material Conference, San Antonio, Texas, USA, April.
  16. Lan, T., Lin, P.D. and Chen, L.W. (2003), "Thermal buckling of bimodular sandwich beams", Compos. Struct., 25, 345-352.
  17. Leal, A. (2009), "Compressive strength analysis for high performance fibers with different modulus in tension and compression", J. Compos. Mater., 43(6), 661-674. https://doi.org/10.1177/0021998308088589
  18. Liu, X.B. and Zhang, Y.Z. (2000), "Modulus of elasticity in shear and accelerate convergence of different extension-compression elastic modulus finite element method", J. Dalian Univ. Tech., 40 (5), 526-530. (in Chinese)
  19. Patel, B.P. (2004), "Thermo-flexural analysis of thick laminates of bimodulus composite materials", Compos. Struct., 63(1), 11-20. https://doi.org/10.1016/S0263-8223(03)00120-X
  20. Patel, H.P., Turner, J.L. and Walter, J.D. (1976), "Radial tire cord-rubber composites", ASME Rub. Chem. Technol. Trans., 49, 1095-1110. https://doi.org/10.5254/1.3534991
  21. Qu, C. (2009), "Deformation of geocell with different tensile and compressive modulus", J. Geotech. Geoenviron., 14, 1-14.
  22. Raffaele, Z. and Fabrizio, G. (2001), "Damage evolution in bimodular laminated composites under cyclic loading", Compos. Struct., 53(4), 381-402. https://doi.org/10.1016/S0263-8223(01)00048-4
  23. Rigbi, Z. (1973), "The buckling of bimodular columns", Acta Mechanica, 18, 317-332. https://doi.org/10.1007/BF01178561
  24. Rizzi, E., Papa, E. and Corigliano, A. (2000), "Mechanical behavior of a syntactic foam: experiments and modeling", Int. J. Solid. Struct., 37, 5773-5794. https://doi.org/10.1016/S0020-7683(99)00264-4
  25. Rigbi, Z. and Shmolo, I. (1978), "Buckling and immediate post buckling behavior of bimodular columns", J. Struct. Mech., 6(2), 145-164. https://doi.org/10.1080/03601217808907333
  26. Tseng, Y.P. and Jiang, Y.C. (1998), "Stress analysis of bimodular laminates using hybrid stress plate element", Int. J. Solid. Struct., 35(17), 2025-2028. https://doi.org/10.1016/S0020-7683(97)00170-4
  27. Tsoukleri, G., Parthenios, J., Papagelis, K., Jalil, R., Ferrari, A., Geim, A., Novoselov, K. and Galiotis, C. (2009), "Subjecting a graphene monolayer to tension and compression", Small, 5, 2397-2402. https://doi.org/10.1002/smll.200900802
  28. Vijayakumar, K. and Ashoka, J.G. (1990), "A bilinear constitutive model for isotropic bimodulus materials", ASME J. Eng. Mater. Technol., 112, 372-379. https://doi.org/10.1115/1.2903341
  29. Yao, W.J. and Ye, Z. (2004), "Analytical solution of bending-compression column using different tension-compression modulus", Appl. Math. Mech., 25 (9), 901-909. (English Edition)
  30. Yao, W.J. and Ye, Z. (2004), "Analytical solution for bending beam subject to later force with different modulus", Appl. Math. Mech., 25(10), 1014-1022. (English Edition)
  31. Yao, W.J. and Ye, Z. (2006), "Internal forces for statically indeterminate structures having different moduli in tension and compression", ASCE J. Eng. Mech., 132(7), 739-746. https://doi.org/10.1061/(ASCE)0733-9399(2006)132:7(739)
  32. Yao, W.J., Zhang, C.H. and Jiang, X.F. (2006), "Nonlinear mechanical behavior of combined members with different moduli", Int. J. Nonlin. Sci. Numer. Simul., 7(2), 233-238. https://doi.org/10.1515/IJNSNS.2006.7.2.233
  33. Yang, H.T. and Wang, B. (2008), "An analysis of longitudinal vibration of bimodular rod via smoothing function approach", J. Sound Vib., 317, 419-431. https://doi.org/10.1016/j.jsv.2008.03.060
  34. Yang, H.T., Wu, R.F. and Yang, K.J. (1992), "Solution to problem of dual extension-compression elastic modulus with initial stress method", J. Dalian Univ. Tech., 32 (1), 35-39. (in Chinese)
  35. Yang, H.T., Yang, K.J. and Wu, R.F. (1999), "Solution of 3-D elastic dual extension-compression modulus problems using initial stress technique", J. Dalian Univ. Tech., 39 (4), 478-482. (in Chinese)
  36. Yang, H.T. and Zhu, Y.L. (2006), "Solving elasticity problems with bi-modulus via a smoothing technique", J. Comput, Mech., 23(1), 19-23.
  37. Ye, Z.M., Yu, H. and Yao, W.J. (2001), "A new elasticity and finite element formulation for different Young's modulus when tension and compression loading", J. Shanghai Univ., 5 (2), 89-92. (in Chinese) https://doi.org/10.1007/s11741-001-0001-0
  38. Zhang, Y.Z. and Wang, Z.F. (1989), "Algorithm for frames of bimodulus materials", J. Dalian Univ. Tech., 29(1), 23-32. (in Chinese)
  39. Zhang, Y.Z. and Wang, Z.F. (1989), "Finite element method of elasticity problem with different tension and compression moduli", Compu. Struct. Mech. Appl., 6 (1), 236-245. (in Chinese)

피인용 문헌

  1. Contact interaction of two rectangular plates made from different materials with an account of physical nonlinearity vol.91, pp.2, 2018, https://doi.org/10.1007/s11071-017-3939-6
  2. Analytical and numerical study of temperature stress in the bi-modulus thick cylinder vol.64, pp.1, 2015, https://doi.org/10.12989/sem.2017.64.1.081