Users:General FEM Analysis/Analyses Reference/Cutting Pattern
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).
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.
|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 two nodes in the list, 2... last two nodes in the list, 3... first and last node, 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
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.
The cutting pattern of the two stripes is shown in the picture below.
- 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
- ↑ Dieringer, F.: Numerical Methods for the Design and Analysis of Tensile Structures, Dissertation Lehrstuhl für Statik, 2014
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