Users:General FEM Analysis/Elements Reference/Beam 3D NURBS KLRod

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General Description

Element Type

  • This element provides a geometrically nonlinear, isogeometric spatial Bernoulli beam[1].
  • Torsion without warping is included
  • The element formulation can handle arbitrary orientations of the cross section along the beam.

Degrees of Freedom

The element uses three translatoric degrees of freedom (Disp_X, Disp_Y, Disp_Z) and a rotational degree of freedom (Rot_Tan) at each control point.

Parameter Description

Compulsory Parameters
Parameter Values, Default(*) Description
MAT EL-MAT int Linking to a material input block
INT_TYPE_BEAM_3D_NURBS_KLRod FULL, USER Control of integration type.
  • FULL: p+1 Gauss points are used (p = polynomial degree of the NURBS patch)
  • USER: the optional Parameter GAUSS_U defines the number of Gauss points
CROSS SECTION DIAMETER = float circular cross section defined ba the diameter. A = d^2π/4, Iy = Iz = d^4π/32, It= d^4π/32
HEIGHT = float
WIDTH = float
rectangular cross section defined by height and width. A = h*w, Iy = h^3*w/12 Iz = h*w^3/12 It= min(h,w)^3*max(h,w)/3
AREA = float
IY = float
IZ = float
IT = float
cross section defined directly
AXIS AXIS float1 float2 float3 float4 Definition of the cross sectional principal axis. Second axis is perpendicual to first and tangent of the curve. float1 is the position on the curve and float - float4 the direction (x,y,z). Base vectors are normalized and linearly interpolated for postions inbetween the defined ones. Axes for start and end knot of the NURBS curve are mandatory.
Optional Parameters
Parameter Values, Default(*) Description
GAUSS_U GAUSS_U = int Number of Gauss point per element. Must only to be defined when INT_TYPE_BEAM_3D_NURBS_KLRod = USER

Example of a Complete Input Block

  MAT= EL-MAT 1  
  GAUSS_U = 3
  !  	U	    	n1		n2 		n3
  AXIS	0.000000e+000	0.000000e+000	1.000000e+000	0.000000e+000
  AXIS	1.000000e+000	0.000000e+000	1.000000e+000	0.000000e+000

Element Loading

The Beam_3D_NURBS_KLRod element is able to carry the following loads:

  • dead load
  • snow load
  • pressure load
  • moment


The main benchmark files in the Carat++-repository are

  • '../examples/benchmark_examples/isogeometric/iga_kl_rod_lin/cbm_beam3D_nurbs_csa.txt'.
  • '../examples/benchmark_examples/isogeometric/iga_kl_rod_nln/cbm_iga_kl_rod_nln.txt'.

It is further used in:

  • '../examples/benchmark_examples/isogeometric/iga_formfinding_4point_with_trusses/cbm_4PointSailwTrusses.txt'


  1. A. M. Bauer, M. Breitenberger, B. Philipp, R. Wüchner, K.-U. Bletzinger: „Nonlinear isogeometric spatial Bernoulli beam“, in „Computer methods in applied mechanics and engineering“, Vol. 303, 2016, Seiten 101-127

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