Users:General FEM Analysis/Analyses Reference/Geodesic Lines

Contents 1 General Description 2 Input Parameters 2.1 Parameter Description 2.2 Example of a Complete Input Block 3 Example 4 References

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

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

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References

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

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