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GEBT: convergence problem in analysis of an isotropic cantilever beam with tip bending moment

  1. Jaeseong Bae

    Hello,

    I am using GEBT to analyze an isotropic cantilever beam subject to a tip bending moment, a well-known problem in the geometrically nonlinear analysis of beams.

    The analysis conditions of the beam are given as follows.

    - Cross-section: width (b) = 0.1in., height (h) = 0.01in.

    - Beam length (L) = 10in.

    - Young's modulus (E) = 1x10^7psi

    - Poisson's ratio (nu) = 0.3

    - Reference frame : Global frame (a1: axial direction, a2: lag direction, a3: flap direction)

    - Tip bending moment: n x 2 x pi x EI_2 / L (The moment is acting about a2 axis, n is the loadfactor, EI_2 = b*h^3/12)

    - Shear flexiblities are suppressed to be zeros for the analysis under Euler-Bernoulli level.

    - GEBT (Rodriguez rotation parameters ver.) used for the analysis

     

    As already known, the beam should form a circle when n = 1. However, GEBT fails to find the converged solution under that loadfactor.

    For your information, I have posted my input file for this problem as follows.

     

    0 100 10 # analysis_flag, niter, nstep

    2 1 2 1 0 0 0 0 0 # nkp, nmemb, ncond_pt, nmate, nframe, ncond_mb, ndistrfun, ntimefun, ncurv

    1  0 0 0
    2 10 0 0

    1 1 2 1 1 0 10 0 # memb_no, kp1, kp2, mate1, mate2, frame_no, nelem, curv_no

    1
    1 2 3 4 5 6
    0 0 0 0 0 0
    0 0 0 0 0 0
    0 0 0 0 0 0

    2
    7 8 9 10 11 12
    0 0 0 0 5.23598776E-02 0
    0 0 0 0 0 0
    0 0 0 0 0 0

    1
    1.00000000E-04    0.00000000E+00    0.00000000E+00    0.00000000E+00    0.00000000E+00    0.00000000E+00
    0.00000000E+00    0.00000000E+00    0.00000000E+00    0.00000000E+00    0.00000000E+00    0.00000000E+00
    0.00000000E+00    0.00000000E+00    0.00000000E+00    0.00000000E+00    0.00000000E+00    0.00000000E+00
    0.00000000E+00    0.00000000E+00    0.00000000E+00    7.80000000E+00    0.00000000E+00    0.00000000E+00
    0.00000000E+00    0.00000000E+00    0.00000000E+00    0.00000000E+00    1.20000000E+01    0.00000000E+00
    0.00000000E+00    0.00000000E+00    0.00000000E+00    0.00000000E+00    0.00000000E+00    1.20000000E-01

    The input file for the problem is attached.

    I think I am missing something when making the input.

    It would be grateful if someone leaves me a reply.

    Thank you.

    Best regards,

    Jaeseong

    input-001.zip

    399 B Click to download

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