3.1.10.6. Geometrically Exact Frame Element

Fig. 3.1.10.2 Fig. 1: Torsional instability captured by the ExactFrame formulation and rendered with sees.

The ExactFrame element is a geometrically exact beam element based on Simo’s parameterization [1] of Antman’s Special Cosserat Rod [2]. This element is formulated without any geometric simplifications, and consequently, is capable of modeling highly nonlinear geometric phenomena with extreme accuracy. The implementation closely follows the treatment by Perez and Filippou (2024) [3].

TclPython (RT)

element ExactFrame $tag $iNode $jNode $sect $tran

The required arguments are:

Argument	Type	Description
tag	integer	unique element object tag
iNode jNode	integer	end nodes
sect	integer	section tag
tran	integer	identifier for previously-defined coordinate-transformation

Geometrically exact elements often exhibit undesirable features. These are rectified as follows:

• Path Dependence The geometrically exact Cosserat rod theory is posed over a non-vectorial configuration space, and consequently may exhibit minor path-dependence.

3.1.10.6.1. References

[1]

Simo, J.C. (1985) ‘A finite strain beam formulation. The three-dimensional dynamic problem. Part I’, Computer Methods in Applied Mechanics and Engineering, 49(1), pp. 55–70. Available at: https://doi.org/10.1016/0045-7825(85)90050-7.

[2]

Antman, S.S. (2005) Nonlinear problems of elasticity. 2nd ed. New York: Springer (Applied mathematical sciences, v. 107).

[3]

Perez, C.M. and Filippou, F.C. (2024) ‘On nonlinear geometric transformations of finite elements’, International Journal for Numerical Methods in Engineering, p. e7506. Available at: https://doi.org/10.1002/nme.7506.

Code developed by: Claudio M. Perez (University of California, Berkeley).