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

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Coded and tested.
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== General Description ==
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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].  
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Documentation will be coming soon!
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=== 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   
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   MAT= EL-MAT 1
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   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
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! 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)
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   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
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! GAUSS_U = 4                                         !# of quadratur points in u-dir in case of INT_TYPE = USER
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! GAUSS_V = 4                                         !# of quadratur points in u-dir in case of INT_TYPE = USER
 
</pre>
 
</pre>
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=== Element Type ===
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* The element formulation is well tested for static and dynamic linear and nonlinear analysis.
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* Stresses for nonlinear case need to be corrected.
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* Can be used for thin shell structures
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=== Degrees of Freedom ===
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The element uses three translatoric degrees of freedom (''Disp_X'', ''Disp_Y'', ''Disp_Z'')  at each control point.
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=== Parameter Description ===
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{| 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(*)
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!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_SHELL_NURBS_KL
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|FULL, USER, OPTIMAL
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|Control of integration type.
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* FULL: p+1 and q+1 quadrature points are used (p and q are the polynomial degrees of the NURBS patch)
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* USER: the optional parameters GAUSS_U and GAUSS_V define the number of quadrature points
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* OPTIMAL: uses in the interior of the patch less quadrature points (some tests required for higher polynomial degrees >3
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|-
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!THICKNESS
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| ''float''
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| Thickness of the shell
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|-
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|-
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!NEJA
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| NURBS, DIP, FULL
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| Integration technique for trimmed elements
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*NURBS: trimmed elements are parametrized with untrimmed NURBS within the parameter space
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* DIP: ''Discrete Integration procedure'' does not work properly, requires improvement (quadrature points must fullfill the moment fitting equations)
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* FULL: Full integration of trimmed elements (not recommended)
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|-
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|colspan="3" style="background:#efefef;"| Optional Parameters
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|-
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!Parameter
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!Values, Default(*)
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!Description
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|-
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!GAUSS_U
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|GAUSS_U = ''int''
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|Number of quadrature points in u-direction. Requires  INT_TYPE_SHELL_NURBS_KL= USER
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|-
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|-
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!GAUSS_V
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|GAUSS_V = ''int''
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||Number of quadrature points in v-direction. Requires  INT_TYPE_SHELL_NURBS_KL= USER
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|-
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|-
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!COUPLING
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| EL-PROP= ''int''
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||BRep coupling element to handle C^0 continuity inside the patch
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|-
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|-
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!STABILIZATION
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| EL-PROP= ''int''
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||Stabilization element for improving condition number (requires some tests, no optimal solution)
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|-
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!PRESTRESS_CRV
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| PRESTRESS_CRV = AUTO
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||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
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|-
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!PRESTRESS_CL_A1
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| PRESTRESS_CL_A1 = AUTO
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||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.
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|-
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!PRESTRESS_CL_A2
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| PRESTRESS_CL_A2 = AUTO
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||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.
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|-
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|}
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== Element Loading ==
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The KL shell element is able to handle 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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== Benchmarks ==
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The main benchmark file in the ''Carat++''-repository is
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* '../examples/benchmark_examples/isogeometric/KL_shell_trim_plate_hole/cbm_plate_with_hole.txt'.
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It is further used in:
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* '../examples/benchmark_examples/isogeometric/isogeometric_trim_non_linear/cbm_PlateHoleLineSupHighAcc.txt.txt'
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== 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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