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CATENA.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME CATENA
* Problem:
* ********
* The classical problem of the hanging catenary. Here the catenary consists
* of N+1 beams of length BL, with the first beam fixed at the origin and
* the final bean fixed at a fraction FRACT of the total length of all
* beams.
* This is the correct version of problem CATENARY.
* The problem is non-convex.
* Source:
* K. Veselic,
* "De forma catenarum in campo gravitatis pendentium",
* Klasicna Gimnazija u Zagrebu, Zagreb, 1987.
* SIF input: Ph. L. Toint, May 1993.
* correction by F. Ruediger, Mar 1997.
* classification LQR2-AY-V-V
* Number of beams = N+1 ; the number of variables is 3*(N+2)
*IE N+1 4 $-PARAMETER n = 15
*IE N+1 10 $-PARAMETER n = 33
*IE N+1 32 $-PARAMETER n = 99
*IE N+1 166 $-PARAMETER n = 501 original value
IE N+1 1000 $-PARAMETER n = 3003
RE GAMMA 9.81 $ gravity
RE TMASS 500.0 $ total mass of the N+1 beams
RE BL 1.0 $ beam length
RE FRACT 0.6 $ shortening factor
IE 0 0
IE 1 1
IA N N+1 -1
RI RN+1 N+1
R* TMP BL RN+1
R* LENGTH TMP FRACT
R/ MASS TMASS RN+1
R* MG MASS GAMMA
RM MG/2 MG 0.5
R* BLSQ BL BL
VARIABLES
* Positions of the beam joints
DO I 0 N+1
X X(I)
X Y(I)
Z Z(I)
OD I
GROUPS
ZN OBJ Y(0) MG/2
DO I 1 N
ZN OBJ Y(I) MG
OD I
ZN OBJ Y(N+1) MG/2
* Constraints on beam lengths
DO I 1 N+1
XE C(I)
OD I
CONSTANTS
DO I 1 N+1
Z CATENA C(I) BLSQ
OD I
BOUNDS
XR CATENA 'DEFAULT'
* Fix initial joint at the origin
XX CATENA X0 0.0
XX CATENA Y0 0.0
XX CATENA Z0 0.0
* Fix position of final joint
ZX CATENA X(N+1) LENGTH
START POINT
R/ TMP LENGTH RN+1
DO I 1 N+1
RI RI I
R* VAL TMP RI
RM -VAL VAL -1.0
ZV CATENA X(I) VAL
ZV CATENA Y(I) -VAL
OD I
ELEMENT TYPE
EV ISQ V W
IV ISQ U
ELEMENT USES
DO I 1 N+1
IA I-1 I -1
XT EX(I) ISQ
ZV EX(I) V X(I)
ZV EX(I) W X(I-1)
XT EY(I) ISQ
ZV EY(I) V Y(I)
ZV EY(I) W Y(I-1)
XT EZ(I) ISQ
ZV EZ(I) V Z(I)
ZV EZ(I) W Z(I-1)
OD I
GROUP USES
DO I 1 N+1
XE C(I) EX(I) EY(I)
XE C(I) EZ(I)
OD I
OBJECT BOUND
*LO SOL(15) -8349.79513564
*LO SOL(33) -20976.3971877
*LO SOL(99) -67180.5782438
*LO SOL(501) -348529.577196
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS CATENA
INDIVIDUALS
* The square element type
T ISQ
R U V 1.0 W -1.0
F U*U
G U U+U
H U U 2.0
ENDATA