Users:Form Finding/Form Finding with CARAT++

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To beform an analysis for ''form finding'' with CARAT++ the related analysis type have to be defined. The following table shows all important commands to define a  
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The following table shows the important commands to define a ''form finding'' analysis in CARAT++ and gives an explanation for each parameter.
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''form finding'' analysis in CARAT++. This tabel gives an explanation for each paramter due to that no futher describtion of the paramters will be given.
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{| border="1" cellpadding="3" cellspacing="0"
 
{| border="1" cellpadding="3" cellspacing="0"
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!DOMAIN  
 
!DOMAIN  
 
|EL-DOMAIN ''int''
 
|EL-DOMAIN ''int''
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|Domain which should be calculated. The Parameter EL-DOMAIN should be defined in the Element Block of the Inputfile
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|Domain which should be calculated. The parameter EL-DOMAIN should be defined in the Element Block of the Inputfile
 
|-
 
|-
 
!OUTPUT  
 
!OUTPUT  
 
|PC-OUT ''int''
 
|PC-OUT ''int''
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|Definition of the Output object. The Parameter PC-OUT should be defined in the PC-Problem Block of the Inputfile
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|Definition of the [[Users:General FEM Analysis/Data Output|Output object]]. The Parameter PC-OUT should be defined in the PC-Problem Block of the Inputfile
 
|-
 
|-
 
!SOLVER  
 
!SOLVER  
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!COMPCASE
 
!COMPCASE
 
|LD-COM ''int''
 
|LD-COM ''int''
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|Definition of the Computation Case. The Parameter LD-COM  should be Block of the Inputfile
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|Definition of the Computation Case. The Parameter LD-COM  should defined in the Load-Block of the Inputfile
 
|-                                             
 
|-                                             
 
!FORMFINDING_STEP
 
!FORMFINDING_STEP
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|-                       
 
|-                       
 
!EQUILIBRIUM_ACCURACY
 
!EQUILIBRIUM_ACCURACY
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|''int''
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|''real''
 
|Equilibrium accuracy
 
|Equilibrium accuracy
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|-
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!FORMFINDING_ELEMENTS
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|PROP_ID ''ints''
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|elements that have to be formfound (i.e. that have no material contribution, but only geometrical stiffness), identified through their property ID             
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|-
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|colspan="3" style="background:#efefef;"| Optional parameters for full URS
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|-
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!HOMOTOPY_CURVE
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|LD-CURVE ''int'' 
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|Defines the homotopy factor (has to be between 0 and 1) for the different form-finding steps in a separate curve. If not used, the homotopy factor is set to 0, i.e. the reference problem is solved.
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|-
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|colspan="3" style="background:#efefef;"| Optional parameters for stress adaption / distortion control
 
|-
 
|-
 
!STRESS_ADAPTION
 
!STRESS_ADAPTION
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|''int''/0  
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|PROP_ID ''ints''   
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|Defines for which elements the distortion control is active (0=false; 1=true)
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|Defines for which elements the distortion control is active through their property ID
 
|-                       
 
|-                       
 
!LAMBDA_MAX  
 
!LAMBDA_MAX  
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|''int''
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|''real''
 
|Maximum allowable element distortion in case of stress adaption
 
|Maximum allowable element distortion in case of stress adaption
 
|-                       
 
|-                       
 
!MUE_RELAX
 
!MUE_RELAX
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|''int''
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|''real''
 
|Relaxation of the element distortion (Values between 0 and 1 are valid)
 
|Relaxation of the element distortion (Values between 0 and 1 are valid)
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|-
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|colspan="3" style="background:#efefef;"| Optional parameters for restart file
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|-
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!ELASTIC_RESTART_METHOD
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|''string'' 
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|Defines the update of elastic members for the restart file (NONE = everything is updated and results set to 0, FORCE = geometry is updated, results set to 0 and inital stresses added, DISPLACEMENT = geometry of elastic members is not updated, initial displacement is added and nodes with different neighbouring elements are doubled)
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|-
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|colspan="3" style="background:#efefef;"| Optional parameters for eXtended URS
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|-
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!X_URS
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|''bool'' 
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|Defines whether or not the xURS shall be applied to the computation resp. to the Membrane1 properties; Default is FALSE, leading to normal URS
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|-                     
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!X_URS_STEP
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|''int''
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|Defines the form-finding step from which on xURS is applied
 
|}       
 
|}       
  
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=== Example of an Input Block ===
 
=== Example of an Input Block ===
  
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The below shown input block defines a formfinding analysis with the ID 1. It uses for the element domain, the output, the solver and the compcase fields which have the ID 1. The analysis perform 20 formfinding steps and stops the computation after 100 steps if no convergence is reached. The accuracy of the analysis is defined as 10<sup>-6</sup>. Distortion control is enabled and used for elements releated to the elemnt properties with ID 1. The maximum allowed element distortion is 1.1 and relaxation of the element distortion control is set to 0.  
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The input block shown below defines a formfinding analysis with the IDs 1,2 and 8. The analysis performs 10 formfinding steps and stops the computation after 100 equilibrium iteration steps within each formfinding step if no convergence is achieved. The equilibrium accuracy of the analysis is defined as 10<sup>-6</sup>.
  
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The (optional) distortion control is enabled and used for elements releated to the elemnt properties with ID 1. The maximum allowed element distortion is 1.1 and the relaxation of the element distortion control is set to 0.
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For a detailed discussion of the element distortion control see e.g. to <ref name=Lin2009">Linhard, J.: Numerisch-mechanische Betrachtung des Entwurfsprozesses von Membrantragwerken, Lehrstuhl für Statik, Technische Universität München, 2009</ref>
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and <ref name="Die14">Dieringer, F.: Numerical Methods for the Design and Analysis of Tensile Structures, Lehrstuhl für Statik, Technische Universität München, 2014</ref>.
  
 
<pre>
 
<pre>
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   SOLVER = PC-SOLVER 1
 
   SOLVER = PC-SOLVER 1
 
   COMPCASE = LD-COM 1
 
   COMPCASE = LD-COM 1
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   FORMFINDING_STEP = 20
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   FORMFINDING_STEP = 10
 
   MAX_ITER_EQUILIBRIUM = 100
 
   MAX_ITER_EQUILIBRIUM = 100
 
   EQUILIBRIUM_ACCURACY = 1e-06
 
   EQUILIBRIUM_ACCURACY = 1e-06
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  FORMFINDING_ELEMENTS = PROP_ID 1,2,8
 
   STRESS_ADAPTION = PROP_ID 1
 
   STRESS_ADAPTION = PROP_ID 1
 
   LAMBDA_MAX=1.1
 
   LAMBDA_MAX=1.1
 
   MUE_RELAX=0.0
 
   MUE_RELAX=0.0
 
</pre>
 
</pre>
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=== Benchmark examples ===
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* form-finding of a four-point sail: ..\examples\benchmark_examples\analyses\formfinding_membrane1_I\cbm_4_point_Fofi.txt
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* form-finding of a catenoid with xURS: ..\examples\benchmark_examples\analyses\cbm_formfinding_xURS_Membrane1\cbm_formfinding_xURS_Membrane1.dat
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== References ==
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 +
<references/>

Latest revision as of 11:19, 8 June 2017

The following table shows the important commands to define a form finding analysis in CARAT++ and gives an explanation for each parameter.

Compulsory Parameters
Parameter Values Description
PC-ANALYSIS int Analysis with the number int the number have to be followed by : FORMFINDING
DOMAIN EL-DOMAIN int Domain which should be calculated. The parameter EL-DOMAIN should be defined in the Element Block of the Inputfile
OUTPUT PC-OUT int Definition of the Output object. The Parameter PC-OUT should be defined in the PC-Problem Block of the Inputfile
SOLVER PC-SOLVER int Definition of the Solver object. The Parameter PC-SOLVER should be defined in the PC-Problem Block of the Inputfile
COMPCASE LD-COM int Definition of the Computation Case. The Parameter LD-COM should defined in the Load-Block of the Inputfile
FORMFINDING_STEP int Definition of the number of form finding steps
MAX_ITER_EQUILIBRIUM int Maximum of number of equilibrium iterations before CARAT++ stops the calculation
EQUILIBRIUM_ACCURACY real Equilibrium accuracy
FORMFINDING_ELEMENTS PROP_ID ints elements that have to be formfound (i.e. that have no material contribution, but only geometrical stiffness), identified through their property ID
Optional parameters for full URS
HOMOTOPY_CURVE LD-CURVE int Defines the homotopy factor (has to be between 0 and 1) for the different form-finding steps in a separate curve. If not used, the homotopy factor is set to 0, i.e. the reference problem is solved.
Optional parameters for stress adaption / distortion control
STRESS_ADAPTION PROP_ID ints Defines for which elements the distortion control is active through their property ID
LAMBDA_MAX real Maximum allowable element distortion in case of stress adaption
MUE_RELAX real Relaxation of the element distortion (Values between 0 and 1 are valid)
Optional parameters for restart file
ELASTIC_RESTART_METHOD string Defines the update of elastic members for the restart file (NONE = everything is updated and results set to 0, FORCE = geometry is updated, results set to 0 and inital stresses added, DISPLACEMENT = geometry of elastic members is not updated, initial displacement is added and nodes with different neighbouring elements are doubled)
Optional parameters for eXtended URS
X_URS bool Defines whether or not the xURS shall be applied to the computation resp. to the Membrane1 properties; Default is FALSE, leading to normal URS
X_URS_STEP int Defines the form-finding step from which on xURS is applied

For the better understanding of the syntax of this kind of analysis in the following an example of an input block for a form finding will be shown.

Example of an Input Block

The input block shown below defines a formfinding analysis with the IDs 1,2 and 8. The analysis performs 10 formfinding steps and stops the computation after 100 equilibrium iteration steps within each formfinding step if no convergence is achieved. The equilibrium accuracy of the analysis is defined as 10-6.

The (optional) distortion control is enabled and used for elements releated to the elemnt properties with ID 1. The maximum allowed element distortion is 1.1 and the relaxation of the element distortion control is set to 0. For a detailed discussion of the element distortion control see e.g. to [1] and [2]. 

PC-ANALYSIS 1: FORMFINDING
  DOMAIN = EL-DOMAIN 1
  OUTPUT = PC-OUT 1
  SOLVER = PC-SOLVER 1
  COMPCASE = LD-COM 1
  FORMFINDING_STEP = 10
  MAX_ITER_EQUILIBRIUM = 100
  EQUILIBRIUM_ACCURACY = 1e-06
  FORMFINDING_ELEMENTS = PROP_ID 1,2,8
  STRESS_ADAPTION = PROP_ID 1
  LAMBDA_MAX=1.1
  MUE_RELAX=0.0

Benchmark examples

  • form-finding of a four-point sail: ..\examples\benchmark_examples\analyses\formfinding_membrane1_I\cbm_4_point_Fofi.txt
  • form-finding of a catenoid with xURS: ..\examples\benchmark_examples\analyses\cbm_formfinding_xURS_Membrane1\cbm_formfinding_xURS_Membrane1.dat

References

  1. ↑ Linhard, J.: Numerisch-mechanische Betrachtung des Entwurfsprozesses von Membrantragwerken, Lehrstuhl für Statik, Technische Universität München, 2009
  2. ↑ Dieringer, F.: Numerical Methods for the Design and Analysis of Tensile Structures, Lehrstuhl für Statik, Technische Universität München, 2014




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