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Manuscript ID : JSM-2007-1623 (R1) Visit : 235 Page: 118 - 130

10.22034/jsm.2020.1904760.1623

20.1001.1.20083505.2022.14.2.1.3

Article Type: Original Research

On Validity of Analytical Method in Cracked Column Post-Buckling Analysis Using Empirical and Numerical Investigations

Subject Areas : Computational Mechanics

K Salmalian 1 , A Alijani 2 , H Ramezannejad Azarboni 3

1 - Department of Mechanical Engineering, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali, Iran
2 - Department of Mechanical Engineering, Bandar Anzali Branch, Islamic Azad University, Bandar Anzali, Iran
3 - Department of Mechanical Engineering, Ramsar Branch, Islamic Azad University, Ramsar, Iran

Received: 2022-01-18 Accepted : 2022-03-23 Published : 2022-06-01

Keywords: Cracked column, Experimental method, Nonlinear buckling, Finite Element Method, analytical method,

Abstract :

The three analytical, finite element and experimental methods are applied to study the nonlinear buckling of cracked columns. The original aim of this research is to investigate the validity of the common analytical method in an analogy with the experimental method and the finite element method of MATLAB programming-based. The literature review shows that papers applied this analytical method without considering its drawbacks to determine the post-buckling results. Results in the linear part of the analytical method are in close accordance with the two others, while a clear difference in the nonlinear part of the analytical method is observed with the actual results obtained from the experimental tests and numerical results of the finite element method. An in-depth discussion is represented to find out the main reasons of this difference. The conversion matrix technique in the finite element method and dividing the column into two segments in the analytical method are used to include the crack parameters in relations according to the continuity conditions in the crack tip. An investigation is performed to study the effect of the crack depth and position on the critical buckling load and the post-buckling path.

References:


  1.  Irwin G.R., 1957, Analysis of stresses and strains near the end of a crack traversing a plate, Journal of Applied Mechanics 24: 361-364.
    2.
  2.  Alijani A., Abadi M.M., Darvizeh A., Abadi M.K., 2018, Theoretical approaches for bending analysis of founded Euler–Bernoulli cracked beams, Archive of Applied Mechanics88(6): 875-895.
    3.
  3.  Ricci P., Viola E., 2006, Stress intensity factors for cracked T-sections and dynamic behaviour of T-beams, Engineering Fracture Mechanics73(1): 91-111.
    4.
  4.  Yokoyama T., Chen M.C., 1998, Vibration analysis of edge-cracked beams using a line-spring model, Engineering Fracture Mechanics59(3): 403-409.
    5.
  5.  Okamura H., Liu H.W., Chu C.S., Liebowitz H., 1969, A cracked column under compression, Engineering Fracture Mechanics1(3): 547-564.
    6.
  6.  Skrinar M., 2019, On the application of the simplified crack model in the bending, free vibration and buckling analysis of beams with linear variation of widths, Periodica Polytechnica Civil Engineering63(2): 423-431.
    7.
  7.  Biondi B., Caddemi S., 2005, Closed form solutions of Euler–Bernoulli beams with singularities, International Journal of Solids and Structures42(9-10): 3027-3044.
    8.
  8.  Biondi B., Caddemi S., 2007, Euler–Bernoulli beams with multiple singularities in the flexural stiffness, European Journal of Mechanics-A/Solids26(5): 789-809.
    9.
  9. Al-Shayea N.AR., Baluch M.H., Azad A.K., 1987, Influence of non-propagating cracks on conservative buckling of columns, Transactions of the Canadian Society for Mechanical Engineering 11(4): 215-220.
    10.
  10.  Alijani A., Abadi M.K., Razzaghi J., Jamali A., 2019, Numerical analysis of natural frequency and stress intensity factor in Euler–Bernoulli cracked beam, Acta Mechanica230(12): 4391-4415.
    11.
  11.  Mottaghian F., Darvizeh A., Alijani A., 2018, Extended finite element method for statics and vibration analyses on cracked bars and beams, Journal of Solid Mechanics10(4): 902-928.
    12.
  12.  Khoei A.R., 2014, Extended Finite Element Method: Theory and Applications, John Wiley & Sons.
    13.
  13.  Rabczuk T., Bordas S.P.A., Askes H., 2010, Meshfree Discretization Methods for Solid Mechanics, in Encyclopedia of Aerospace Engineering, Chichester, UK, John Wiley & Sons.
    14.
  14.  Shirazizadeh M.R., Shahverdi H., 2015, An extended finite element model for structural analysis of cracked beam-columns with arbitrary cross-section, International Journal of Mechanical Sciences99: 1-9.
    15.
  15.  Jia L.J., Ge H., 2019, Ultra-low-Cycle Fatigue Failure of Metal Structures Under Strong Earthquakes, Springer Nature Singapore Pte Ltd.
    16.
  16.  Turvey G.J., Zhang Y., 2006, A computational and experimental analysis of the buckling, postbuckling and initial failure of pultruded GRP columns, Computers & Structures84(22-23): 1527-1537.
    17.
  17.  Debski H., Teter A., Kubiak T., Samborski S., 2016, Local buckling, post-buckling and collapse of thin-walled channel section composite columns subjected to quasi-static compression, Composite Structures136: 593-601.
    18.
  18.  Mazaheri H., Rahami H., Kheyroddin A., 2018, Static and dynamic analysis of cracked concrete beams using experimental study and finite element analysis, Periodica Polytechnica Civil Engineering62(2): 337-345.
    19.
  19.  Anifantis N., Dimarogonas A., 1984, Post buckling behavior of transverse cracked columns, Computers & Structures18(2): 351-356.
    20.
  20.  Anifantis N., Dimarogonas A., 1983, Imperfection post-buckling analysis of cracked columns, Engineering Fracture Mechanics 18(3): 693-702.
    21.
  21.  Ke L.L., Yang J., Kitipornchai S., Xiang Y., 2009, Flexural vibration and elastic buckling of a cracked Timoshenko beam made of functionally graded materials, Mechanics of Advanced Materials and Structures16(6): 488-502.
    22.
  22.  Bouboulas A., Anifantis N., 2016, Three-dimensional finite element modeling for post-buckling analysis of cracked columns, International Journal of Structural Integrity 7(3): 397-411.
    23.
  23.  Akbaş Ş.D., 2016, Post-buckling analysis of edge cracked columns under axial compression loads, International Journal of Applied Mechanics8(08): 1650086.
    24.
  24. Akbaş Ş.D., 2019, Post-buckling analysis of a fiber reinforced composite beam with crack, Engineering Fracture Mechanics212: 70-80.
    25.
  25.  Akbaş Ş.D., 2015, Post-buckling analysis of axially functionally graded three-dimensional beams, International Journal of Applied Mechanics7(03): 1550047.
    26.
  26.  Yang G., Bradford M.A., 2015, Thermoelastic buckling and post-buckling of weakened columns, Structures 1: 12-19.
    27.
  27.  Kamocka M., Mania R.J., 2019, Post-buckling response of FML column with delamination, Composite Structures230: 111511.
    28.
  28.  Ke L.L., Yang J., Kitipornchai S., 2009, Postbuckling analysis of edge cracked functionally graded Timoshenko beams under end shortening, Composite Structures90(2): 152-160.
    29.
  29.  Shariati M., Majd Sabeti A.M., Gharooni H., 2014, A numerical and experimental study on buckling and post-buckling of cracked plates under axial compression load, Journal of Computational & Applied Research in Mechanical Engineering4(1): 43-54.
    30.
  30.  Yang J., Chen Y., 2008, Free vibration and buckling analyses of functionally graded beams with edge cracks, Composite Structures83(1): 48-60.
    31.
  31.  Nayfeh A.H., Emam S.A., 2008, Exact solution and stability of postbuckling configurations of beams, Nonlinear Dynamics54(4): 395-408.
    32.
  32.  Ma L.S., Lee D.W., 2012, Exact solutions for nonlinear static responses of a shear deformable FGM beam under an in-plane thermal loading, European Journal of Mechanics-A/Solids31(1): 13-20.
    33.
  33.  Emam S.A., Nayfeh A.H., 2009, Postbuckling and free vibrations of composite beams, Composite Structures88(4): 636-642.
    34.
  34.  Yaghoobi H., Torabi M., 2013, An analytical approach to large amplitude vibration and post-buckling of functionally graded beams rest on non-linear elastic foundation, Journal of Theoretical and Applied Mechanics51(1): 39-52.
    35.
  35.  Nasirzadeh R., Behjat B., Kharazi M., 2018, Finite element study on thermal buckling of functionally graded piezoelectric beams considering inverse effects, Journal of Theoretical and Applied Mechanics56(4): 1097-1108.
    36.
  36.  Santos H.A.F.A., Gao D.Y., 2012, Canonical dual finite element method for solving post-buckling problems of a large deformation elastic beam, International Journal of Non-Linear Mechanics47(2): 240-247.
    37.
  37.  Cai K., Gao D.Y., Qin Q.H., 2014, Postbuckling analysis of a nonlinear beam with axial functionally graded material, Journal of Engineering Mathematics88(1): 121-136.
    38.
  38.  Amara K., Bouazza M., Fouad B., 2016, Postbuckling analysis of functionally graded beams using nonlinear model, Periodica Polytechnica Mechanical Engineering60(2): 121-128.
    39.
  39.  Correia J.R., Branco F.A., Silva N.M.F., Camotim D., Silvestre N., 2011, First-order, buckling and post-buckling behaviour of GFRP pultruded beams, Part 1: Experimental study, Computers & Structures89(21-22): 2052-2064.
    40.
  40.  Ghavanloo E., 2020, Semi-analytical solution for post-buckling analysis of simply-supported multi-stepped columns, Structures 27: 1086-1092.
    41.
  41.  Gürel M.A., Kisa M., 2005, Buckling of slender prismatic columns with a single edge crack under concentric vertical loads, Turkish Journal of Engineering and Environmental Sciences29(3): 185-193.
    42.
  42. Wood R.D., Schrefler B., 1978, Geometrically non‐linear analysis—A correlation of finite element notations,International Journal for Numerical Methods in Engineering 12(4): 635-642.
    43.

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