Users:General FEM Analysis/Analyses Reference/Geodesic Lines

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Contents

General Description

Geodesic line generation determines geodesic lines on a surface between two given nodes/points.


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 : 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

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.

Geodesic lines.png

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

Geodesic lines formfound.png

References





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