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

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== General Description ==
 
== General Description ==
−
This element is based on the [https://mediatum.ub.tum.de/node?id=1002634 Phd Thesis of J.Kiendl]. This 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 Kiendl et al. 2009 <ref>J. Kiendl, K.-U. Bletzinger, J. Linhard, and R.Wüchner. “Isogeometric shell analysis with Kirchhoff–Love elements.” In: ComputerMethods in AppliedMechanics and Engineering 198.49-52 (2009), pp. 3902–3914. DOI: 10.1016/j.cma.2009.08.013 </ref> and  [https://mediatum.ub.tum.de/node?id=1002634 Phd Thesis of J.Kiendl].  
  
 
=== Example of a Complete Input Block ===
 
=== Example of a Complete Input Block ===
Line 8: Line 8:
 
   THICKNESS = 1.0
 
   THICKNESS = 1.0
 
   COUPLING = EL-PROP 6                      !BRep coupling element to handle C^0 continuity inside the patch
 
   COUPLING = EL-PROP 6                      !BRep coupling element to handle C^0 continuity inside the patch
−
! STABILIZATION = EL-PROP 7               !Stabilization element for improving condition number
+
! STABILIZATION = EL-PROP 7               !Stabilization element for improving condition number (requires some tests, no optimal solution)
−
   NEJA = NURBS !DIP or FULL                   !Method for handling the integration for trimmed elements(use NURBS)
+
   NEJA = NURBS !DIP or FULL                 !Method for handling the integration for trimmed elements(use NURBS)
 
   INT_TYPE_SHELL_NURBS_KL = USER !or FULL or OPTIMAL  !FULL means p+1 and q+1;OPTIML uses in the interior of the patch less quadrature points (some tests required for higher polynomial degrees >3
 
   INT_TYPE_SHELL_NURBS_KL = USER !or FULL or OPTIMAL  !FULL means p+1 and q+1;OPTIML uses in the interior of the patch less quadrature points (some tests required for higher polynomial degrees >3
−
! GAUSS_U = 4                                         !# of quadratur points in u-dir in case of INT_TYPE = USER
+
! GAUSS_U = 4                                         !# of quadratur points in u-dir in case of INT_TYPE = USER
 
! GAUSS_V = 4                                          !# of quadratur points in u-dir in case of INT_TYPE = USER
 
! GAUSS_V = 4                                          !# of quadratur points in u-dir in case of INT_TYPE = USER
 
</pre>
 
</pre>
Line 18: Line 18:
 
=== Element Type ===
 
=== 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>.
+
* The element formulation is well tested for static and dynamic linear and nonlinear analysis.  
−
* Torsion without warping is included
+
* Stresses for nonlinear case need to be corrected.
−
* The element formulation can handle arbitrary orientations of the cross section along the beam.
+
* Can be used for thin shell structures
  
 
=== Degrees of Freedom ===
 
=== 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.  
+
The element uses three translatoric degrees of freedom (''Disp_X'', ''Disp_Y'', ''Disp_Z'') at each control point.  
  
 
=== Parameter Description ===
 
=== Parameter Description ===
Line 39: Line 39:
 
|Linking to a material input block
 
|Linking to a material input block
 
|-
 
|-
−
!INT_TYPE_BEAM_3D_NURBS_KLRod
+
!INT_TYPE_SHELL_NURBS_KL
−
|FULL, USER
+
|FULL, USER, OPTIMAL
 
|Control of integration type.  
 
|Control of integration type.  
−
* FULL: p+1 Gauss points are used (p = polynomial degree of the NURBS patch)  
+
* FULL: p+1 and q+1 quadrature points are used (p and q are the polynomial degrees of the NURBS patch)  
−
* USER: the optional Parameter GAUSS_U defines the number of Gauss points
+
* USER: the optional parameters GAUSS_U and GAUSS_V define the number of quadrature points
 +
* OPTIMAL: uses in the interior of the patch less quadrature points (some tests required for higher polynomial degrees >3
 
|-
 
|-
−
!rowspan="3" | CROSS SECTION
+
!THICKNESS
−
|DIAMETER = ''float''  
+
| ''float''
−
|circular cross section defined ba the diameter. A = d^2π/4, Iy = Iz = d^4π/32, It= d^4π/32
+
| Thickness of the shell
−
|-
+
−
|HEIGHT = ''float'' <br> 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'' <br> IY = ''float'' <br> IZ = ''float'' <br> IT = ''float''
+
−
|cross section defined directly
+
 
|-
 
|-
−
!AXIS
+
|-
−
|AXIS ''float1'' ''float2'' ''float3'' ''float4''
+
!NEJA
−
|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.
+
| NURBS, DIP, FULL
 +
| Integration technique for trimmed elements
 +
*NURBS: trimmed elements are parametrized with untrimmed NURBS within the parameter space
 +
* DIP: ''Discrete Integration procedure'' does not work properly, requires improvement (quadrature points must fullfill the moment fitting equations)
 +
* FULL: Full integration of trimmed elements (not recommended)
 
|-
 
|-
 
|colspan="3" style="background:#efefef;"| Optional Parameters
 
|colspan="3" style="background:#efefef;"| Optional Parameters
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!GAUSS_U
 
!GAUSS_U
 
|GAUSS_U = ''int''
 
|GAUSS_U = ''int''
−
|Number of Gauss point per element. Must only to be defined when INT_TYPE_BEAM_3D_NURBS_KLRod = USER
+
|Number of quadrature points in u-direction. Requires  INT_TYPE_SHELL_NURBS_KL= USER
 +
|-
 +
|-
 +
!GAUSS_V
 +
|GAUSS_V = ''int''
 +
||Number of quadrature points in v-direction. Requires  INT_TYPE_SHELL_NURBS_KL= USER
 +
|-
 +
|-
 +
!COUPLING
 +
| EL-PROP= ''int''
 +
||BRep coupling element to handle C^0 continuity inside the patch
 +
|-
 +
|-
 +
!STABILIZATION
 +
| EL-PROP= ''int''
 +
||Stabilization element for improving condition number (requires some tests, no optimal solution)
 +
|-
 +
!PRESTRESS_CRV
 +
| PRESTRESS_CRV = AUTO
 +
||All curvature terms (b_ref) are set to zero in stiff_mat_el_nln(). This is equal to having a flat patch as reference patch
 +
|-
 +
!PRESTRESS_CL_A1
 +
| PRESTRESS_CL_A1 = AUTO
 +
||covariant metric for reference configuration (gab_ref[0] and gab_ref[2]) is set to the one of the center line (v_mid=const) in stiff_mat_el_nln(). This is only valid for special case of pre-bent lamellas.
 +
|-
 +
!PRESTRESS_CL_A2
 +
| PRESTRESS_CL_A2 = AUTO
 +
||covariant metric for reference configuration (gab_ref[1] and gab_ref[2]) is set to the one of the center line (u_mid=const) in stiff_mat_el_nln(). This is only valid for special case of pre-bent lamellas.
 
|-
 
|-
 
|}
 
|}
−
 
−
 
−
=== Example of a Complete Input Block ===
 
−
<pre>
 
−
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
 
−
</pre>
 
  
 
== Element Loading ==
 
== Element Loading ==
  
−
The Beam_3D_NURBS_KLRod element is able to carry the following loads:
+
The KL shell element is able to handle the following loads:
 
* dead load
 
* dead load
 
* snow load
 
* snow load
 
* pressure load
 
* pressure load
−
* moment
 
  
 
== Benchmarks ==
 
== Benchmarks ==
  
 
The main benchmark file in the ''Carat++''-repository is  
 
The main benchmark file in the ''Carat++''-repository is  
−
* '../examples/benchmark_examples/isogeometric/iga_kl_rod_nln/cbm_iga_kl_rod_nln.txt'.
+
* '../examples/benchmark_examples/isogeometric/KL_shell_trim_plate_hole/cbm_plate_with_hole.txt'.
 
It is further used in:  
 
It is further used in:  
−
* '../examples/benchmark_examples/isogeometric/iga_formfinding_4point_with_trusses/cbm_4PointSailwTrusses.txt'
+
* '../examples/benchmark_examples/isogeometric/isogeometric_trim_non_linear/cbm_PlateHoleLineSupHighAcc.txt.txt'
  
 
== References ==
 
== References ==
  
 
<references/>
 
<references/>

Latest revision as of 09:56, 19 December 2018

Contents

General Description

This element is based on Kiendl et al. 2009 [1] and Phd Thesis of J.Kiendl.

Example of a Complete Input Block 

EL-PROP 1 : SHELL_NURBS_KL  
  MAT= EL-MAT 1                                      !material property
  THICKNESS = 1.0
  COUPLING = EL-PROP 6                       !BRep coupling element to handle C^0 continuity inside the patch
! STABILIZATION = EL-PROP 7               !Stabilization element for improving condition number (requires some tests, no optimal solution)
  NEJA = NURBS !DIP or FULL                 !Method for handling the integration for trimmed elements(use NURBS)
  INT_TYPE_SHELL_NURBS_KL = USER !or FULL or OPTIMAL   !FULL means p+1 and q+1;OPTIML uses in the interior of the patch less quadrature points (some tests required for higher polynomial degrees >3
! GAUSS_U = 4                                          !# of quadratur points in u-dir in case of INT_TYPE = USER
! GAUSS_V = 4                                          !# of quadratur points in u-dir in case of INT_TYPE = USER


Element Type

  • The element formulation is well tested for static and dynamic linear and nonlinear analysis.
  • Stresses for nonlinear case need to be corrected.
  • Can be used for thin shell structures

Degrees of Freedom

The element uses three translatoric degrees of freedom (Disp_X, Disp_Y, Disp_Z) at each control point.

Parameter Description

Compulsory Parameters
Parameter Values, Default(*) Description
MAT EL-MAT int Linking to a material input block
INT_TYPE_SHELL_NURBS_KL FULL, USER, OPTIMAL Control of integration type.
  • FULL: p+1 and q+1 quadrature points are used (p and q are the polynomial degrees of the NURBS patch)
  • USER: the optional parameters GAUSS_U and GAUSS_V define the number of quadrature points
  • OPTIMAL: uses in the interior of the patch less quadrature points (some tests required for higher polynomial degrees >3
THICKNESS float Thickness of the shell
NEJA NURBS, DIP, FULL Integration technique for trimmed elements
  • NURBS: trimmed elements are parametrized with untrimmed NURBS within the parameter space
  • DIP: Discrete Integration procedure does not work properly, requires improvement (quadrature points must fullfill the moment fitting equations)
  • FULL: Full integration of trimmed elements (not recommended)
Optional Parameters
Parameter Values, Default(*) Description
GAUSS_U GAUSS_U = int Number of quadrature points in u-direction. Requires INT_TYPE_SHELL_NURBS_KL= USER
GAUSS_V GAUSS_V = int Number of quadrature points in v-direction. Requires INT_TYPE_SHELL_NURBS_KL= USER
COUPLING EL-PROP= int BRep coupling element to handle C^0 continuity inside the patch
STABILIZATION EL-PROP= int Stabilization element for improving condition number (requires some tests, no optimal solution)
PRESTRESS_CRV PRESTRESS_CRV = AUTO All curvature terms (b_ref) are set to zero in stiff_mat_el_nln(). This is equal to having a flat patch as reference patch
PRESTRESS_CL_A1 PRESTRESS_CL_A1 = AUTO covariant metric for reference configuration (gab_ref[0] and gab_ref[2]) is set to the one of the center line (v_mid=const) in stiff_mat_el_nln(). This is only valid for special case of pre-bent lamellas.
PRESTRESS_CL_A2 PRESTRESS_CL_A2 = AUTO covariant metric for reference configuration (gab_ref[1] and gab_ref[2]) is set to the one of the center line (u_mid=const) in stiff_mat_el_nln(). This is only valid for special case of pre-bent lamellas.

Element Loading

The KL shell element is able to handle the following loads:

  • dead load
  • snow load
  • pressure load

Benchmarks

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

  • '../examples/benchmark_examples/isogeometric/KL_shell_trim_plate_hole/cbm_plate_with_hole.txt'.

It is further used in:

  • '../examples/benchmark_examples/isogeometric/isogeometric_trim_non_linear/cbm_PlateHoleLineSupHighAcc.txt.txt'

References

  1. ↑ J. Kiendl, K.-U. Bletzinger, J. Linhard, and R.Wüchner. “Isogeometric shell analysis with Kirchhoff–Love elements.” In: ComputerMethods in AppliedMechanics and Engineering 198.49-52 (2009), pp. 3902–3914. DOI: 10.1016/j.cma.2009.08.013




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