Users:General FEM Analysis/Analyses Reference/Geodesic Lines

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== General Description ==
 
== General Description ==
  
Geodesic line generation determines geodesic lines on a surface between two given nodes/points.
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Geodesic line generation determines geodesic lines on a surface between two given nodes/points. A cable with a very high prestress is intorduced between the two endpoints. The out-of-plane forces are supressed as well as the forces at the two ends of the cable. Thus the cable finds the shortest distance in the membrane surface without altering it. By supressing the end-forces, the edge cables are not affected. <ref name="Dieringer"> Dieringer, F.: Numerical Methods for the Design and Analysis of Tensile Structures, Dissertation Lehrstuhl für Statik, 2014 </ref>
 
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=== Structure of Equation System ===
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A nonlinear problem is formulated by the equation '''r''' = '''f'''_int('''u''') where '''r''' specifies the residual vector and '''f'''_int defines the internal forces respectively. In general, the internal forces depend on the actual displacement field '''u'''. Thus, the equation is nonlinear with respect to the a priori unknown equilibrium displacements.
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At the equilibrium point the residual vector is equal to zero. The above specified nonlinear problem is linearized for the actual displacement state and solved e.g. by a Newton-Raphson scheme where the residual vector is used to compute incremental displacements by '''K'''_t '''u'''_inc = '''r'''.
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== Input Parameters ==
 
== Input Parameters ==
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== Example ==
 
== Example ==
  
The following simple example shows the geodesic line generation for a four-point sail, separating the geometry in 5 parts.  
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The following simple example shows the geodesic line generation for a four-point sail, separating the geometry in 6 parts (depicted by the differently coloured stripes). The separation into parts is done automatically. In a following step, these parts can be used for the [[Users:General_FEM_Analysis/Analyses_Reference/Cutting_Pattern|cutting pattern generation]]
 
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{|
 
|[[File:Geodesic_lines.png]]
 
|[[File:Geodesic_lines.png]]
 
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The cutting pattern of the two stripes is shown in the picture below.
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The formfound geometry with its separation into the different parts is shown in the picture below.
 
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{|
 
|[[File:Geodesic_lines_formfound.png]]  
 
|[[File:Geodesic_lines_formfound.png]]  
 
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== Benchmark Examples ==
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* Four point sail with three geodesic lines (not included in benchmarks due to amount of time but working!) ...benchmark_examples\analyses\geodesic_membrane1_I\x_cbm_4_point_geodesic.txt
  
 
== References ==
 
== References ==
  
 
<references/>
 
<references/>

Latest revision as of 13:15, 9 December 2016


Contents

General Description

Geodesic line generation determines geodesic lines on a surface between two given nodes/points. A cable with a very high prestress is intorduced between the two endpoints. The out-of-plane forces are supressed as well as the forces at the two ends of the cable. Thus the cable finds the shortest distance in the membrane surface without altering it. By supressing the end-forces, the edge cables are not affected. [1]

Input Parameters

Parameter Description

Compulsory Parameters
Parameter Values, Default(*) Description
PC-ANALYSIS int : FORMFINDING Keyword of analysis with analysis ID
SOLVER PC-SOLVER int Linking to a linear solver (direct or iterative)
OUTPUT PC-OUT int Linking to output objects (specifies the type of output format, e.g. GiD)
COMPCASE LD-COM int Linking to computation case object which specify the boundary conditions (loading and supports). Only a single computation case is allowed.
DOMAIN EL-DOMAIN int Linking to the domain the analysis should work on
MAX_ITER_EQUILIBRIUM int Maximum number of equilibrium iterations that are allowed.
EQUILIBRIUM_ACCURACY float Equilibrium accuracy that has to be reached for convergence. The convergence is checked with the L2 norm of the incremental displacements.
FORMFINDING_ELEMENTS PROP_ID int The parts which should be included in the analysis, separation with comma.
FORMFINDING_STEP int Definition of number of formfinding steps.
GEODESIC_LINES 0 or 1 0... FALSE. 1... TRUE
NUMGEO int NODE_I = int NODE_J = int Definition of start (NODE_I) and end (NODE_J) of geodesic line (nodes on the mesh)
Optional Parameters

Example of a Complete Input Block

PC-ANALYSIS 1: FORMFINDING
  DOMAIN = EL-DOMAIN 1
  OUTPUT = PC-OUT 1
  SOLVER = PC-SOLVER 1
  COMPCASE = LD-COM 1
  FORMFINDING_STEP = 20
  MAX_ITER_EQUILIBRIUM = 100
  EQUILIBRIUM_ACCURACY = 1e-06
  FORMFINDING_ELEMENTS = PROP_ID 101,201
  GEODESIC_LINES=1       ! 0=FALSE  1=TRUE
  NUMGEO 1 NODE_I=293   NODE_J=732
  NUMGEO 2 NODE_I=89    NODE_J=797
  NUMGEO 3 NODE_I=1     NODE_J=841
  NUMGEO 4 NODE_I=88    NODE_J=796
  NUMGEO 5 NODE_I=294   NODE_J=733

Example

The following simple example shows the geodesic line generation for a four-point sail, separating the geometry in 6 parts (depicted by the differently coloured stripes). The separation into parts is done automatically. In a following step, these parts can be used for the cutting pattern generation

Geodesic lines.png

The formfound geometry with its separation into the different parts is shown in the picture below.

Geodesic lines formfound.png

Benchmark Examples

  • Four point sail with three geodesic lines (not included in benchmarks due to amount of time but working!) ...benchmark_examples\analyses\geodesic_membrane1_I\x_cbm_4_point_geodesic.txt

References

  1. Dieringer, F.: Numerical Methods for the Design and Analysis of Tensile Structures, Dissertation Lehrstuhl für Statik, 2014




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