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CATENARY.SIF
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***************************
* SET UP THE INITIAL DATA *
***************************
NAME CATENARY
* Problem:
* ********
* An erroneous but interesting version of 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.
* The correct version of the same problem is given by problem CATENA.SIF
* 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.
* 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 CATENARY C(I) BLSQ
OD I
BOUNDS
XR CATENARY 'DEFAULT'
* Fix initial joint at the origin
XX CATENARY X0 0.0
XX CATENARY Y0 0.0
XX CATENARY Z0 0.0
* Fix position of final joint
ZX CATENARY X(N+1) LENGTH
START POINT
R/ TMP LENGTH RN+1
DO I 1 N+1
RI RI I
R* VAL TMP RI
ZV CATENARY X(I) TMP
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 X(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) -8184.81057777
*LO SOL(33) -20837.3763330
*LO SOL(99) -67050.9978802
*LO SOL(501) -348403.164505
ENDATA
***********************
* SET UP THE FUNCTION *
* AND RANGE ROUTINES *
***********************
ELEMENTS CATENARY
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