Users:General FEM Analysis/Analyses Reference/Cutting Pattern

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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).


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, 4 means largest distance between the supports. For each part, one type must be given.
RELAXATION_METHOD STATIC or NONE or GALERKIN or COMBINED Definition of relaxation method.
FLATTENING_AREA 0 or 1 0... prestress area. 1... mean surface normal.
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
SEAM_LENGTH
Includes the seam lengths into the cutting pattern analysis.

Example of a Complete Input Block

PC-ANALYSIS 1: STA_GEO_NONLIN
  PATHCONTROL = ARCLENGTH ! or DISPLACEMENT or ARCLENGTH
  SOLVER = PC-SOLVER 1
  OUTPUT = PC-OUT 1
  COMPCASE = LD-COM 1
  DOMAIN = EL-DOMAIN 1
  NUM_STEP = 30
  MAX_ITER_EQUILIBRIUM = 100
  EQUILIBRIUM_ACCURACY = 1e-10
  CURVE=LD-CURVE 1
  TRACED_NODE=2
  TRACED_NODAL_DOF=DISP_Y 
  ! Example: fixed step length of 0.05
    STEP_LENGTH_CONTROL = FIXED
    STEP_LENGTH_CONTROL_REALS = 0.05         ! constant step length of 0.05
  ! Example adaptive step length according to Crisfield and Ramm
    STEP_LENGTH_CONTROL = CRISFIELD_RAMM
    STEP_LENGTH_CONTROL_REALS = 0.1, 1.0     ! initial step length = 0.1, exponent p = 1.0
    STEP_LENGTH_CONTROL_INTS = 5             ! 5 equilibrium iterations per step are desired
  ! Example: no simultaneous eigenvalue analysis
    SIMULTANEOUS_EIGENVALUE_ANALYSIS = 0 
  ! Example: simultaneous eigenvalue analysis
    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

Example

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. The respective input file can be found in the SVN repository under

carat20/examples/benchmark_examples/analyses/stanln_2bartruss_arclength_l/2bartruss_arclength_fixed.txt

The problem computes a snap through problem. The boundary conditions are visualized by the figure below.

Simple 2bar truss structure discretized with truss elements

The load f is increased by the arclength method such that the displacements depicted in the figure below occur.

Truss snap through

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.

Load displacement path of 2bar truss

References





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