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HANGING.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME HANGING
* Problem :
* *********
* A catenary problem in 3 dimensions. A rectangular grid is hung from its
* 4 corners under gravity. The problem is to determine the resulting shape.
* Source:
* an example in a talk by Nesterova and Vial, LLN, 1994.
* SIF input: Ph. Toint, November 1994.
* classification LQR2-AY-V-V
* dimension of the grid
*IE NX 3 $-PARAMETER n = 27
*IE NY 3 $-PARAMETER
*IE NX 5 $-PARAMETER n = 90
*IE NY 6 $-PARAMETER
*IE NX 10 $-PARAMETER n = 300 original value
*IE NY 10 $-PARAMETER
*IE NX 20 $-PARAMETER n = 1800
*IE NY 30 $-PARAMETER
IE NX 40 $-PARAMETER n = 3600
IE NY 30 $-PARAMETER
* maximal X and Y distances
RE LX 1.8
RE LY 1.8
* useful constants
IE 1 1
IA NX-1 NX -1
IA NY-1 NY -1
R* LX2 LX LX
R* LY2 LY LY
RI RNX NX
RI RNY NY
VARIABLES
DO I 1 NX
DO J 1 NY
X X(I,J)
X Y(I,J)
X Z(I,J)
ND
GROUPS
DO I 1 NX
DO J 1 NY
XN OBJ Z(I,J) 1.0
ND
DO I 1 NX
DO J 1 NY-1
XL RC(I,J)
ND
DO I 1 NX-1
DO J 1 NY
XL DC(I,J)
ND
CONSTANTS
DO I 1 NX
DO J 1 NY-1
Z HANGING RC(I,J) LX2
ND
DO I 1 NX-1
DO J 1 NY
Z HANGING DC(I,J) LY2
ND
BOUNDS
FR HANGING 'DEFAULT'
XX HANGING X(1,1) 0.0
XX HANGING Y(1,1) 0.0
XX HANGING Z(1,1) 0.0
ZX HANGING X(NX,1) RNX
XX HANGING Y(NX,1) 0.0
XX HANGING Z(NX,1) 0.0
XX HANGING X(1,NY) 0.0
ZX HANGING Y(1,NY) RNY
XX HANGING Z(1,NY) 0.0
ZX HANGING X(NX,NY) RNX
ZX HANGING Y(NX,NY) RNY
XX HANGING Z(NX,NY) 0.0
START POINT
DO I 1 NX
IA I-1 I -1
RI RI-1 I-1
DO J 1 NY
IA J-1 J -1
RI RJ-1 J-1
ZV HANGING X(I,J) RI-1
ZV HANGING Y(I,J) RJ-1
ND
ELEMENT TYPE
EV ISQ XX YY
IV ISQ D
ELEMENT USES
XT 'DEFAULT' ISQ
DO J 1 NY-1
IA J+1 J 1
DO I 1 NX
ZV RX(I,J) XX X(I,J)
ZV RX(I,J) YY X(I,J+1)
ZV RY(I,J) XX Y(I,J)
ZV RY(I,J) YY Y(I,J+1)
ZV RZ(I,J) XX Z(I,J)
ZV RZ(I,J) YY Z(I,J+1)
ND
DO I 1 NX-1
IA I+1 I 1
DO J 1 NY
ZV DX(I,J) XX X(I,J)
ZV DX(I,J) YY X(I+1,J)
ZV DY(I,J) XX Y(I,J)
ZV DY(I,J) YY Y(I+1,J)
ZV DZ(I,J) XX Z(I,J)
ZV DZ(I,J) YY Z(I+1,J)
ND
GROUP USES
DO I 1 NX
DO J 1 NY-1
XE RC(I,J) RX(I,J) RY(I,J)
XE RC(I,J) RZ(I,J)
ND
DO I 1 NX-1
DO J 1 NY
XE DC(I,J) DX(I,J) DY(I,J)
XE DC(I,J) DZ(I,J)
ND
OBJECT BOUND
* Solution
*LO SOLTN(3,3) -6.1184107487
*LO SOLTN(5,6) -77.260229515
*LO SOLTN(10,10) -620.17603242
*LO SOLTN(20,30) -1025.4292887
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS HANGING
INDIVIDUALS
T ISQ
R D XX 1.0 YY -1.0
F D * D
G D D + D
H D D 2.0
ENDATA