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

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== General Description ==
 
This element is based on the [https://mediatum.ub.tum.de/node?id=1002634 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.
 
This element is based on the [https://mediatum.ub.tum.de/node?id=1002634 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.
  
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   GAUSS_V = 4
 
   GAUSS_V = 4
 
</pre>
 
</pre>
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 +
 +
=== Element Type ===
 +
 +
* This element provides a geometrically nonlinear, isogeometric spatial Bernoulli beam<ref> 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 </ref>.
 +
* 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 ===
 +
 +
{| border="1" cellpadding="3" cellspacing="0"
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|colspan="3" style="background:#efefef;"| Compulsory Parameters
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|-
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!Parameter
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!Values, Default(*)
 +
!Description
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|-
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!MAT
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|EL-MAT ''int''
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|Linking to a material input block
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|-
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!INT_TYPE_BEAM_3D_NURBS_KLRod
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|FULL, USER
 +
|Control of integration type.
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* FULL: p+1 Gauss points are used (p = polynomial degree of the NURBS patch)
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* USER: the optional Parameter GAUSS_U defines the number of Gauss points
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|-
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!rowspan="3" | CROSS SECTION
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|DIAMETER = ''float''
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|circular cross section defined ba the diameter. A = d^2π/4, Iy = Iz = d^4π/32, It= d^4π/32
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|-
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|HEIGHT = ''float'' <br> WIDTH = ''float''
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|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
 +
|-
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| AREA = ''float'' <br> IY = ''float'' <br> IZ = ''float'' <br> IT = ''float''
 +
|cross section defined directly
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|-
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!AXIS
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|AXIS ''float1'' ''float2'' ''float3'' ''float4''
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|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.
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|-
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|colspan="3" style="background:#efefef;"| Optional Parameters
 +
|-
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!Parameter
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!Values, Default(*)
 +
!Description
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|-
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!GAUSS_U
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|GAUSS_U = ''int''
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|Number of Gauss point per element. Must only to be defined when INT_TYPE_BEAM_3D_NURBS_KLRod = USER
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|-
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|}
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 +
 +
=== Example of a Complete Input Block ===
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<pre>
 +
EL-PROP 1 : BEAM_3D_NURBS_KLRod
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  MAT= EL-MAT 1 
 +
 
 +
  DIAMETER=1.0
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  !or:
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  HEIGHT=1.0
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  WIDTH=1.0
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  or:
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  AREA=1.0000e+008
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  IY=1.0000e+008
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  IZ=1.0000e+008
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  IT=1.0000e+008
 +
 
 +
  INT_TYPE_BEAM_3D_NURBS_KLRod = FULL
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  !or:
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  INT_TYPE_BEAM_3D_NURBS_KLRod = USER
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  GAUSS_U = 3
 +
 
 +
  !  U     n1 n2 n3
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  AXIS 0.000000e+000 0.000000e+000 1.000000e+000 0.000000e+000
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  AXIS 1.000000e+000 0.000000e+000 1.000000e+000 0.000000e+000
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</pre>
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 +
== Element Loading ==
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 +
The Beam_3D_NURBS_KLRod element is able to carry the following loads:
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* dead load
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* snow load
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* pressure load
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* moment
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 +
== Benchmarks ==
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 +
The main benchmark file in the ''Carat++''-repository is
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* '../examples/benchmark_examples/isogeometric/iga_kl_rod_nln/cbm_iga_kl_rod_nln.txt'.
 +
It is further used in:
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* '../examples/benchmark_examples/isogeometric/iga_formfinding_4point_with_trusses/cbm_4PointSailwTrusses.txt'
 +
 +
== References ==
 +
 +
<references/>

Revision as of 16:49, 8 December 2016

Contents

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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