Users:General FEM Analysis/Elements Reference/Shell NURBS KL

Contents 1 General Description 1.1 Example of a Complete Input Block 1.2 Element Type 1.3 Degrees of Freedom 1.4 Parameter Description 1.5 Example of a Complete Input Block 2 Element Loading 3 Benchmarks 4 References

General Description

This element is based on the Phd Thesis of J.Kiendl. The element formulation is well tested for static and dynamic linear and nonlinear analysis. Stresses for nonlinear case need to be corrected.

Example of a Complete Input Block

EL-PROP 1 : SHELL_NURBS_KL  
  MAT= EL-MAT 1
  THICKNESS = 1.0
  INT_TYPE_SHELL_NURBS_KL = USER !or FULL
  GAUSS_U = 4
  GAUSS_V = 4

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

EL-PROP 1 : BEAM_3D_NURBS_KLRod
  MAT= EL-MAT 1  
  
  DIAMETER=1.0
  !or:
  HEIGHT=1.0
  WIDTH=1.0
  or:
  AREA=1.0000e+008
  IY=1.0000e+008
  IZ=1.0000e+008
  IT=1.0000e+008
  
  INT_TYPE_BEAM_3D_NURBS_KLRod = FULL
  !or:
  INT_TYPE_BEAM_3D_NURBS_KLRod = USER
  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

Benchmarks

The main benchmark file in the Carat++-repository is

• '../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'

References

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 http://dx.doi.org/10.1016/j.cma.2015.12.027

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