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^{7}psi

- 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.

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

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

0 10000 100 # 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 1 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

It would be grateful if someone leave me a reply.

Thank you.

Best regards,

Jaeseong

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Wenbin Yu@ onPlease ask this type of questions at https://cdmhub.org/groups/yugroup/forum instead to get a quick answer. Thanks a lot!

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Jaeseong Bae@ onThanks at lot for the reply. Do I need to get a membership to post this question in that page?

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Wenbin Yu@ onYes.

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Wenbin Yu@ onYes. You just request it. It is free.

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Qi Wang@ onHi Jaeseong,

GEBT uses vector parameterization for rotations. There will be a singular point by using this kind of rotation representation, usually at pi (180 degree) or 2pi (360 degree). For GEBT, the singular point is at 2pi, that's the reason your case failed to form a circle. You may try load factor 0.9, 0.98 etc so that you can see it is very close to a full circle. More details can be found in this paper:

https://aip.scitation.org/doi/abs/10.1063/1.4985091

Qi

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