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

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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.
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== General Description ==
 +
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 ===
 
<pre>
 
<pre>
 
EL-PROP 1 : SHELL_NURBS_KL   
 
EL-PROP 1 : SHELL_NURBS_KL   
−
   MAT= EL-MAT 1
+
   MAT= EL-MAT 1                                     !material property
 
   THICKNESS = 1.0
 
   THICKNESS = 1.0
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   INT_TYPE_SHELL_NURBS_KL = USER !or FULL
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  COUPLING = EL-PROP 6                      !BRep coupling element to handle C^0 continuity inside the patch
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   GAUSS_U = 4
+
! STABILIZATION = EL-PROP 7              !Stabilization element for improving condition number (requires some tests, no optimal solution)
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  GAUSS_V = 4
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  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
 
</pre>
 
</pre>
 +
 +
 +
=== 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 ===
 +
 +
{| border="1" cellpadding="3" cellspacing="0"
 +
|colspan="3" style="background:#efefef;"| 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)
 +
|-
 +
|colspan="3" style="background:#efefef;"| 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 ==
 +
 +
<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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