Users:General FEM Analysis/Elements Reference/Membrane NURBS

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(Created page with "Coded and tested! === Example of a Complete Input Block === <pre> EL-PROP 1 : MEMRANE_NURBS MAT= EL-MAT 1 THICKNESS = 1.0 INT_TYPE_MEMBRANE_NURBS = USER !or FULL GAUS...")
 
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Coded and tested!
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== General Description ==
  
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=== Element Type ===
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* This membrane element is an isotropic plane stress element accounting for prestress
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* The membrane element neglects bending stiffness
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* The ratio of the thickness and the lengths in the other two directions is much smaller than one ( t/Lx << 1 and t/Ly << 1), the membrane is reduced to its mid-surface
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* The thickness is constant over the element
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An extensive description of the element can be found in <ref name="Phi16">B. Philipp, M. Breitenberger, I. D’Auria, R.Wüchner, and
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K.-U. Bletzinger. "Integrated design and analysis of structural
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membranes using the Isogeometric B-Rep Analysis." In: Computer
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Methods in AppliedMechanics and Engineering 303 (May 2016),
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pp. 312–340. DOI: 10.1016/j.cma.2016.02.003.</ref>
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 +
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== Input Parameters ==
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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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|Number for the used Material
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e.g. MAT=EL-MAT 1
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|-
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!THICKNESS
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|''real''
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|Thickness of the membrane
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|-
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!INT_TYPE_MEMBRANE_NURBS
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|FULL or USER
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|Type of numerical integration. With FULL the integration rule is automatically chosen, with USER it can manually be defined. For USER also the parameters GAUSS_U and GAUSS_V have to be defined.
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|-
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!GAUSS_U, GAUSS_V
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|''int''
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|Number of integration points in u and v-direction, respectively. In case of INT_TYPE_MEMBRANE_NURBS = FULL this specification is not required.
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|-
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!A_X, A_Y, A_Z
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B_X, B_Y, B_Z
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|
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|Definition of the principal directions of the surface to define the prestress directions, only applied with anisotropic prestress conditions. (see description of Membrane1-element)
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|-
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!SIG11
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SIG22
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SIG12
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|''reals''
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|Prestress state of the membrane. (see description of Membrane1-element)
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|-
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|}
  
 
=== Example of a Complete Input Block ===
 
=== Example of a Complete Input Block ===
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<!--
 
<pre>
 
<pre>
 
EL-PROP 1 : MEMRANE_NURBS   
 
EL-PROP 1 : MEMRANE_NURBS   
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   PRE_STRESS_G2 = 2
 
   PRE_STRESS_G2 = 2
 
</pre>
 
</pre>
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-->
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<pre>
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EL-PROP 1 : MEMBRANE_NURBS
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  MAT= EL-MAT 1
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  THICKNESS= 1.0
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  INT_TYPE_MEMBRANE_NURBS = FULL !or USER
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  PROJECTED_PRESTRESS=1 SIG11=400.0    SIG22=400.0      SIG12=0.0
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  A_X=1.0    A_Y=0.0    A_Z=0.0  !AREA FOR THE DEFINITION OF THE PRESTRESS
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  B_X=0.0    B_Y=1.0    B_Z=0.0  !VECTOR A AND VECTOR B DEFINE THE AREA
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</pre>
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The possibility for oriented anisotropic prestress fields is foreseen, yet no distortion control as for the classical FEM Membrane1-element is implemented.
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== Tests and Benchmarks ==
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The element Membrane_NURBS has successfully been applied in 3D in various geometrically non-linear static applications, as well as in form-finding.
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=== Benchmark examples ===
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* form-finding of a four-point sail with with B-Rep edge cables and elastic columns as supports: ..\examples\benchmark_examples\isogeometric\iga_formfinding_4point_with_trusses\cbm_4PointSailwTrusses.txt
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* static geometrically non-linear analysis of a prestressed single-patch membrane with fixed boundaries: ..\examples\benchmark_examples\isogeometric\iga_membrane_nln_1\cbm_iga_membrane_nln_1.txt
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== References ==
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<references/>

Latest revision as of 09:01, 13 January 2017

Contents

General Description

Element Type

  • This membrane element is an isotropic plane stress element accounting for prestress
  • The membrane element neglects bending stiffness
  • The ratio of the thickness and the lengths in the other two directions is much smaller than one ( t/Lx << 1 and t/Ly << 1), the membrane is reduced to its mid-surface
  • The thickness is constant over the element

An extensive description of the element can be found in [1]


Input Parameters

Parameter Description

Compulsory Parameters
Parameter Values, Default(*) Description
MAT EL-MAT int Number for the used Material

e.g. MAT=EL-MAT 1

THICKNESS real Thickness of the membrane
INT_TYPE_MEMBRANE_NURBS FULL or USER Type of numerical integration. With FULL the integration rule is automatically chosen, with USER it can manually be defined. For USER also the parameters GAUSS_U and GAUSS_V have to be defined.
GAUSS_U, GAUSS_V int Number of integration points in u and v-direction, respectively. In case of INT_TYPE_MEMBRANE_NURBS = FULL this specification is not required.
A_X, A_Y, A_Z

B_X, B_Y, B_Z

Definition of the principal directions of the surface to define the prestress directions, only applied with anisotropic prestress conditions. (see description of Membrane1-element)
SIG11

SIG22 SIG12

reals Prestress state of the membrane. (see description of Membrane1-element)

Example of a Complete Input Block 

EL-PROP 1 : MEMBRANE_NURBS
  MAT= EL-MAT 1
  THICKNESS= 1.0
  INT_TYPE_MEMBRANE_NURBS = FULL !or USER
  PROJECTED_PRESTRESS=1 SIG11=400.0     SIG22=400.0      SIG12=0.0
  A_X=1.0     A_Y=0.0    A_Z=0.0   !AREA FOR THE DEFINITION OF THE PRESTRESS
  B_X=0.0     B_Y=1.0    B_Z=0.0   !VECTOR A AND VECTOR B DEFINE THE AREA

The possibility for oriented anisotropic prestress fields is foreseen, yet no distortion control as for the classical FEM Membrane1-element is implemented.

Tests and Benchmarks

The element Membrane_NURBS has successfully been applied in 3D in various geometrically non-linear static applications, as well as in form-finding.

Benchmark examples

  • form-finding of a four-point sail with with B-Rep edge cables and elastic columns as supports: ..\examples\benchmark_examples\isogeometric\iga_formfinding_4point_with_trusses\cbm_4PointSailwTrusses.txt
  • static geometrically non-linear analysis of a prestressed single-patch membrane with fixed boundaries: ..\examples\benchmark_examples\isogeometric\iga_membrane_nln_1\cbm_iga_membrane_nln_1.txt

References

  1. ↑ B. Philipp, M. Breitenberger, I. D’Auria, R.Wüchner, and K.-U. Bletzinger. "Integrated design and analysis of structural membranes using the Isogeometric B-Rep Analysis." In: Computer Methods in AppliedMechanics and Engineering 303 (May 2016), pp. 312–340. DOI: 10.1016/j.cma.2016.02.003.




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