Users:General FEM Analysis/Analyses Reference/Cutting Pattern

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== General Description ==
 
== General Description ==
  
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Cutting pattern generation determines a plane and (optimally) stress-free geometry which can be reassembled to build a membrane with a certain prestress and shape (as it was determined in Formfinding).
+
Cutting pattern generation determines a plane and (optimally) stress-free geometry which can be reassembled to build a membrane with a certain prestress and shape (as it was determined in Formfinding).<ref name="Dieringer"> Dieringer, F.: Numerical Methods for the Design and Analysis of Tensile Structures, Dissertation Lehrstuhl für Statik, 2014 </ref>
  
 +
Prerequisites: [[Users:Form_Finding|Formfinding]] and [[Users:General_FEM_Analysis/Analyses_Reference/Geodesic_Lines|Geodesic Line Search]]
 +
 +
'''Note''' that an instruction is included in the "Membran-Workshop" documents.
  
 
=== Structure of Equation System ===
 
=== 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.   
 
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.   
  
−
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'''.  
+
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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|-
 
|-
 
!PC-ANALYSIS
 
!PC-ANALYSIS
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|''int'' : STA_GEO_NONLIN
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|''int'' : CUTTING_PATTERN
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|Keyword of nonlinear analysis with analysis ID
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|Keyword of analysis with analysis ID
−
|-
+
−
!PATHCONTROL
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−
|FORCE or ARCLENGTH or DISPLACEMENT
+
−
|Definition of path control method. (DISPLACEMENT is actually not available.)
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|-
 
|-
 
!SOLVER
 
!SOLVER
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|EL-DOMAIN ''int''
 
|EL-DOMAIN ''int''
 
|Linking to the domain the analysis should work on
 
|Linking to the domain the analysis should work on
−
|-
 
−
!NUM_STEP
 
−
|''int''
 
−
|Number of time steps that have to be calculated
 
 
|-
 
|-
 
!MAX_ITER_EQUILIBRIUM
 
!MAX_ITER_EQUILIBRIUM
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|Equilibrium accuracy that has to be reached for convergence. The convergence is checked with the L2 norm of the incremental displacements.
 
|Equilibrium accuracy that has to be reached for convergence. The convergence is checked with the L2 norm of the incremental displacements.
 
|-
 
|-
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!CURVE
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!PATTERN
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|LD-CURVE ''int''
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|PART ''int''
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|Linking to the load curve.
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|The parts which should be included in the analysis, separation with comma.
 
|-
 
|-
−
|colspan="3" style="background:#efefef;"| Optional Parameters
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!BC_CONFIGURATION
 +
|TYPE ''int''
 +
|The type of boundary condition configuration, for each part one type must be given. 1... first and last node, 2... last two nodes in the list, 3... first two nodes in the list, 4... largest distance between nodes.
 
|-
 
|-
−
!TRACED_NODE
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!RELAXATION_METHOD
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|''int''
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|STATIC or NONE or GALERKIN or COMBINED
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|Node ID of traced node. Used for screen and log file output.
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|Definition of relaxation method.
 
|-
 
|-
−
!TRACED_NODAL_DOF
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!FLATTENING_AREA
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|''dof type''
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|0 or 1 or 2
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|DOF type of node TRACED_NODE that has to be traced (DISP_X, DISP_Y, DISP_Z, ...).
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|0... prestress area. 1... mean surface normal. 2... cylinder with RADIUS and RO_X,RO_Y,RO_Z.
 
|-
 
|-
−
!STEP_LENGTH_CONTROL
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!PATTERNING_METHOD
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|FIXED or CRISFIELD_RAMM
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|GALERKIN or LS_NR or LS_CG or NONE
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|Type of step length control algorithm (for ARCLENGTH method). FIXED specifies a constant step size where the desired step size is defined by the parameter STEP_LENGTH_CONTROL_REALS. CRISFIELD_RAMM specifies an adaptive method according to Crisfield and Ramm, c.f. <ref name="Rei94" />. In this case the parameter  STEP_LENGTH_CONTROL_INTS = ''int'' specifies the number of restarts that are allowed. The other necessary parameters are specified by STEP_LENGTH_CONTROL_REALS. See the example below.
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|Definition of the patterning method. GALERKIN... principle of virtual work. LS_NR and LS_CG... optimization problem solved with Newton-Raphson or Conjugate Gradient approach.
 
|-
 
|-
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!STEP_LENGTH_CONTROL_REALS
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|colspan="3" style="background:#efefef;"| Optional parameters for the consideration of seam lines
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|''float'', ''float'', ...
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−
|respective number of floats for step length control algorithm
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|-
 
|-
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!STEP_LENGTH_CONTROL_INTS
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!EQUAL_SEAM_LINES
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|''int'', ''int'', ...
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|TRUE or FALSE
−
|respective number of integers for step length control algorithm
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|Includes the seam lengths into the cutting pattern analysis and minimizes the length difference of common edges.
 
|-
 
|-
−
!SIMULTANEOUS_EIGENVALUE_ANALYSIS
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!PENALTY_FAC
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|1 or 0
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|''int''
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|flag to specify if a simultaneous eigenvalue analysis should be performed, 0 - no eigenvalue analysis, 1 - perform eigenvalue analysis. This flag requires definition of parameter EIGEN_SOLVER.  
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|Definition of a penalty factor for the seam line length optimization.
 
|-
 
|-
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!EIGEN_SOLVER
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!SEAM_LINES
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|PC-SOLVER ''int''
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|TRUE or FALSE
−
|Linking to an eigenvalue solver
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|Includes the increased stiffness along the seam lines into the analysis.
 
|-
 
|-
−
!IMPERFECTION_MODES
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!SEAM_AREA
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|''int'', ''int'', ''int'', ...
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|''float''
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|specifies which eigen modes should be summarized to the imperfection mode. Computation of imperfect design requires definition of parameter EIGEN_SOLVER.
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|Definition of the seam area for an analysis which includes the seam lines.
 
|-
 
|-
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!IMPERFECTION_SIZE
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!SEAM_MATERIAL
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|''int''
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|Definition of the seam line material for an analysis which includes the seam lines.
 +
|-
 +
|-
 +
|colspan="3" style="background:#efefef;"| Optional parameters for a cylinder projection before flattening the stripes
 +
|-
 +
!RADIUS
 
|''float''
 
|''float''
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|specifies the size of the imperfection mode.
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|If a cylinder is defined for the projection area (FLATTENING_AREA=2) Definition of the cylinder radius.
 +
|-
 +
!RO_X; RO_Y; RO_Z
 +
|''float''
 +
|Definition of the root point for the cylinder as a projection area.
 +
|-
 +
|-
 +
|colspan="3" style="background:#efefef;"| Optional parameters for a possible restart analysis after the cutting-pattern generation
 +
|-
 +
!MOUNTING_ANALYSIS
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|''int''
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|Starts the mounting analysis after the cutting pattern generation.
 +
|-
 +
!MOUNTING_ANALYSIS_TYPE
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|FULL or RESTART or INCREMENTAL
 +
|Definition of the mounting analysis type.
 
|}
 
|}
  
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<pre>
 
<pre>
−
PC-ANALYSIS 1: STA_GEO_NONLIN
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PC-ANALYSIS 1: CUTTING_PATTERN
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  PATHCONTROL = ARCLENGTH ! or DISPLACEMENT or ARCLENGTH
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−
  SOLVER = PC-SOLVER 1
+
−
  OUTPUT = PC-OUT 1
+
−
  COMPCASE = LD-COM 1
+
 
   DOMAIN = EL-DOMAIN 1
 
   DOMAIN = EL-DOMAIN 1
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  NUM_STEP = 30
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   MAX_ITER_EQUILIBRIUM = 20
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   MAX_ITER_EQUILIBRIUM = 100
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   EQUILIBRIUM_ACCURACY = 1e-06
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   EQUILIBRIUM_ACCURACY = 1e-10
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   COMPCASE = LD-COM 1
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   CURVE=LD-CURVE 1
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   OUTPUT   = PC-OUT 1
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   TRACED_NODE=2
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   PATTERN = PART 1,3
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   TRACED_NODAL_DOF=DISP_Y
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   BC_CONFIGURATION = TYPE 4,4
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   ! Example: fixed step length of 0.05
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   SOLVER = PC-SOLVER 1
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    STEP_LENGTH_CONTROL = FIXED
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   RELAXATION_METHOD=STATIC    !NONE, STATIC, GALERKIN, COMBINED
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    STEP_LENGTH_CONTROL_REALS = 0.05        ! constant step length of 0.05
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  FLATTENING_AREA=1           !0 ...Prestress area, 1  ...Mean surface normal
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  ! Example adaptive step length according to Crisfield and Ramm
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  PATTERNING_METHOD=GALERKIN  !LS_NR, GALERKIN, LS_CG, NONE
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    STEP_LENGTH_CONTROL = CRISFIELD_RAMM
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−
    STEP_LENGTH_CONTROL_REALS = 0.1, 1.0    ! initial step length = 0.1, exponent p = 1.0
+
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    STEP_LENGTH_CONTROL_INTS = 5            ! 5 equilibrium iterations per step are desired
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−
   ! Example: no simultaneous eigenvalue analysis
+
−
    SIMULTANEOUS_EIGENVALUE_ANALYSIS = 0
+
−
   ! Example: simultaneous eigenvalue analysis
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−
    SIMULTANEOUS_EIGENVALUE_ANALYSIS = 1
+
−
    EIGEN_SOLVER = PC-SOLVER 2
+
−
   ! Example: use imperfect design with modes 1, 2, 4, and 6
+
−
    IMPERFECTION_MODES = 1, 2, 4, 6
+
−
    IMPERFECTION_SIZE = 0.015                ! maximum size of imperfection mode equals 0.015
+
−
    EIGEN_SOLVER = PC-SOLVER 2
+
 
</pre>
 
</pre>
  
 
== Example ==
 
== Example ==
  
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The following simple example shows a geometrically nonlinear analysis of a 2bar truss system using the arclength method. It uses a fixed step size for computation.
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The following simple example shows the cutting pattern analysis of two parts from a four-point sail. It uses a static relaxation method, the flattening area is the mean surface normal and a Galerkin approach is used for the patterning method.
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The respective input file can be found in the SVN repository under
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−
<pre>
+
−
carat20/examples/benchmark_examples/analyses/stanln_2bartruss_arclength_l/2bartruss_arclength_fixed.txt
+
−
</pre>
+
−
The problem computes a snap through problem. The [[Users:General FEM Analysis/BCs Reference|boundary conditions]] are visualized by the figure below.
+
 
{|
 
{|
−
|[[File:2bar_truss_org.png‎|frame|up|Simple 2bar truss structure discretized with [[Users:General FEM Analysis/Elements Reference/Truss1|truss elements]]]]  
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|[[File:Benchmark_cutpat_4point.png]]
 
|}
 
|}
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The load f is increased by the arclength method such that the displacements depicted in the figure below occur.
+
The cutting pattern of the two stripes is shown in the picture below.
 
{|
 
{|
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|[[File:2bar_truss_defo.gif|frame|up|Truss snap through]]
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|[[File:Benchmark_cutpat_4point_relaxed.png]]  
−
|}
+
−
The figure below shows the load displacement path of the y-displacement of the center node. The well known snap through behavior is clearly visible. For a load factor of approx. 0.14 the structure shows instability. In the following the arclength control reduces the load factor until -0.14 to compute equilibrium states. Obviously these states can be only be computed by arclength or displacement control. After a complete snap through the load can be increased further. Now the complete structure works in tension which does not yield to further instability points.
+
−
{|
+
−
|[[File:2bar_truss_load_disp_curve.png|frame|up|Load displacement path of 2bar truss]]  
+
 
|}
 
|}
 +
 +
=== Benchmark examples ===
 +
* four point sail with coarse discretization: ..\examples\benchmark_examples\analyses\cutPat_Membrane1\cbm_CutPat.dat
 +
* four point sail with coarse discretization and automatic mounting analysis after restart: ..\examples\benchmark_examples\analyses\cutPatWithMounting_Membrane1\cbm_CutPatWithMounting.dat
 +
* four point sail with linear elastic material and membrane 1 elements (not included in regular benchmarks due to amount of time for running, but working!) ..\examples\benchmark_examples\analyses\cutting_patterning_membrane1_I\x_cbm_4_point_patterning.txt
  
 
== References ==
 
== References ==
  
 
<references/>
 
<references/>

Latest revision as of 08:16, 27 April 2020


Contents

General Description

Cutting pattern generation determines a plane and (optimally) stress-free geometry which can be reassembled to build a membrane with a certain prestress and shape (as it was determined in Formfinding).[1]

Prerequisites: Formfinding and Geodesic Line Search

Note that an instruction is included in the "Membran-Workshop" documents.

Structure of Equation System

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.

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.

Input Parameters

Parameter Description

Compulsory Parameters
Parameter Values, Default(*) Description
PC-ANALYSIS int : CUTTING_PATTERN 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.
PATTERN PART int The parts which should be included in the analysis, separation with comma.
BC_CONFIGURATION TYPE int The type of boundary condition configuration, for each part one type must be given. 1... first and last node, 2... last two nodes in the list, 3... first two nodes in the list, 4... largest distance between nodes.
RELAXATION_METHOD STATIC or NONE or GALERKIN or COMBINED Definition of relaxation method.
FLATTENING_AREA 0 or 1 or 2 0... prestress area. 1... mean surface normal. 2... cylinder with RADIUS and RO_X,RO_Y,RO_Z.
PATTERNING_METHOD GALERKIN or LS_NR or LS_CG or NONE Definition of the patterning method. GALERKIN... principle of virtual work. LS_NR and LS_CG... optimization problem solved with Newton-Raphson or Conjugate Gradient approach.
Optional parameters for the consideration of seam lines
EQUAL_SEAM_LINES TRUE or FALSE Includes the seam lengths into the cutting pattern analysis and minimizes the length difference of common edges.
PENALTY_FAC int Definition of a penalty factor for the seam line length optimization.
SEAM_LINES TRUE or FALSE Includes the increased stiffness along the seam lines into the analysis.
SEAM_AREA float Definition of the seam area for an analysis which includes the seam lines.
SEAM_MATERIAL int Definition of the seam line material for an analysis which includes the seam lines.
Optional parameters for a cylinder projection before flattening the stripes
RADIUS float If a cylinder is defined for the projection area (FLATTENING_AREA=2) Definition of the cylinder radius.
RO_X; RO_Y; RO_Z float Definition of the root point for the cylinder as a projection area.
Optional parameters for a possible restart analysis after the cutting-pattern generation
MOUNTING_ANALYSIS int Starts the mounting analysis after the cutting pattern generation.
MOUNTING_ANALYSIS_TYPE FULL or RESTART or INCREMENTAL Definition of the mounting analysis type.

Example of a Complete Input Block 

PC-ANALYSIS 1: CUTTING_PATTERN
  DOMAIN = EL-DOMAIN 1
  MAX_ITER_EQUILIBRIUM = 20
  EQUILIBRIUM_ACCURACY = 1e-06
  COMPCASE = LD-COM 1
  OUTPUT   = PC-OUT 1
  PATTERN = PART 1,3
  BC_CONFIGURATION = TYPE 4,4
  SOLVER = PC-SOLVER 1
  RELAXATION_METHOD=STATIC    !NONE, STATIC, GALERKIN, COMBINED
  FLATTENING_AREA=1           !0 ...Prestress area, 1  ...Mean surface normal				
  PATTERNING_METHOD=GALERKIN  !LS_NR, GALERKIN, LS_CG, NONE

Example

The following simple example shows the cutting pattern analysis of two parts from a four-point sail. It uses a static relaxation method, the flattening area is the mean surface normal and a Galerkin approach is used for the patterning method.

Benchmark cutpat 4point.png

The cutting pattern of the two stripes is shown in the picture below.

Benchmark cutpat 4point relaxed.png

Benchmark examples

  • four point sail with coarse discretization: ..\examples\benchmark_examples\analyses\cutPat_Membrane1\cbm_CutPat.dat
  • four point sail with coarse discretization and automatic mounting analysis after restart: ..\examples\benchmark_examples\analyses\cutPatWithMounting_Membrane1\cbm_CutPatWithMounting.dat
  • four point sail with linear elastic material and membrane 1 elements (not included in regular benchmarks due to amount of time for running, but working!) ..\examples\benchmark_examples\analyses\cutting_patterning_membrane1_I\x_cbm_4_point_patterning.txt

References

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




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