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* fichier :  rupt1.dgibi
************************************************************************
************************************************************************
*           Test Rupt1.dgibi: Jeux de données         *
*           ---------------------------------         *
*                                                     *
OPTION echo 1;
GRAPH = 'N';
SAUT PAGE;
*******************************************************
*
*              QUALIFICATION DU CALCUL DE K EN
*          ELASTICITE LINEAIRE SUR UN CYLINDRE AVEC
*          UNE FISSURE DEBOUCHANTE CIRCONFERENTIELLE
*       
* Le calcul est compare a celui obtenu par A ZAHOOR
*******************************************************
* R = rayon interne de la tuyauterie (M)
* B = épaisseur de la tuyauterie (M)
* L = longueur de la tuyauterie (M)
* A = longueur de la fissure (M)
* MYOU = module d'Young (Pa)
* TA = chargement appliqué (N) 
***
TA = 1.E6;
R = 1.;
B = 0.1;
A = B / 2.;
L = R * 4.;
MYOU = 2.0E11;
***
*** Maillage
***
OPTION DIME 2 ELEM QUA8 MODE AXIS;
t = a / 100.; densite t ; pf = (a 0.);
c1 = (c ( pf moin (t 0.)) pf ( pf plus (0. t)))
      c pf ( pf plus (t 0.));
sf = cout pf c1;
r1 = t ; rr1 = t;
repeter bhomo 7;
   ri = r1 + ( 0.3 * r1 );
   rri = rr1 + ri; dens ri;
   ci = (c (pf moin (rri 0.)) pf ( pf plus (0. rri)))  
         c pf (pf plus (rri 0.));
   sf = sf et (cout c1 ci);
   c1 = ci ; r1 = ri ; rr1 = rri;
fin bhomo;
dens (a / 3.);
p0  = (0. 0.) ; p1 = (b 0.);
p2  = p0 plus (0. a) ; p3 = p1 plus (0. a);
pi1 = ci poin 1 ; l1 = pi1 d p0 ; n = (nbel l1) * -1;
pi2 = ci poin 4 ; l2 = pi2 d n p2;
pi3 = ci poin 10 ; l3 = pi3 d n p3;
pi4 = ci poin 13 ; l4 = pi4 d p1;
ci  = inve ci ; ligh = p2 d p3;
sc1 = dall l1 (p0 d p2) (inve l2) (ci ELEM comp pi2 pi1);
sc2 = dall l2 ligh (inve l3) (ci ELEM comp pi3 pi2);
sc3 = dall l3 (p3 d p1) (inve l4) (ci ELEM comp pi4 pi3);
sc  = sc1 et sc2 et sc3;
dens (a / 2.);
mrest1 = ligh tran (0. (2.*a)) dini (40*t) dfin (50*t);
l1 = mrest1 cote 3;
YY1 = coor 2 (point l1 init);
l2 = D 3 (B (YY1 + (0.7*a))) (0. (yy1 + (0.7*a)));
S1 = COUT L1 L2; 
YY1 = COOR 2 (l2 point init);
mrest2 = l2 tran (0. (L - YY1)) dini (80*t) 
                                dfin (150*t); 
sut = sf et sc et mrest1 et S1 et mrest2;
ELIM 1.E-8 SUT;
DEPL PLUS SUT (R 0.);
L1 = (CONT SUT) ELEM APPU (SUT POIN
     DROI (R 0.) ((B + R) 0.) 1.E-8);
L2 = (CONT SUT) ELEM APPU (SUT POIN
     DROI ((B + R) 0.) ((B + R) L) 1.E-8);
L3 = (CONT SUT) ELEM APPU (SUT POIN
     DROI ((B + R) L) (R L) 1.E-8);
L4 = (CONT SUT) ELEM APPU (SUT POIN
     DROI (R L) (R 0.) 1.E-8);
L5 = (CONT SUT) ELEM COMP P1 PF;
SI ( NEG GRAPH 'N' );
   TITR 'MAILLAGE DU CYLINDRE';
   TRAC sut;
FINSI;
******
****** RESOLUTION EN ELASTICITE LINEAIRE
******
MO1 = MODELE SUT MECANIQUE ELASTIQUE ;
MA1 = MATER MO1 YOUNG MYOU NU 0.3 ;
RI = (BLOQ UZ L5) ET (RIGI MA1 MO1);
AIR1 = PI*(((R + B)**2.) - (R*R));
FOR1 = PRES 'MASS' MO1 (0. - (TA/AIR1)) L3;
DEP1 = RESO FOR1 RI;
SIG1 = SIGMA MO1 MA1 DEP1;
SI ( NEG GRAPH 'N' );
 TITR 'DEFORMATION DU CYLINDRE SOUS TRACTION UNIFORME';
 TRAC (DEFO SUT DEP1);
FINSI;
***
*** Solution COD (MM) et K (MPA M^0.5) de castem
***
COD_CAL = (EXTR DEP1 'UZ' P1)*2000.;            
SUPTAB = TABLE ;
SUPTAB.'OBJECTIF' = MOT 'J';
SUPTAB.'LEVRE_SUPERIEURE' = l1 diff l5;;
SUPTAB.'FRONT_FISSURE' = PF ; 
SUPTAB.'MODELE' = MO1;
SUPTAB.'CARACTERISTIQUES' = ma1;
SUPTAB.'SOLUTION_RESO' = dep1;
SUPTAB.'CHARGEMENTS_MECANIQUES' = for1;
SUPTAB.'COUCHE' = 5;
G_THETA SUPTAB;                                   
K_CAL = (MYOU*(SUPTAB.'RESULTATS')/(1 - (0.3**2)))**0.5;
K_CAL = K_CAL*1.E-6; 
***
*** Solution Analytique Zahoor
***
RAP1 = R / B; 
SI (RAP1 < 10.); GRANDA = ((0.125*RAP1) - 0.25)**0.25; 
FINSI;
SI (RAP1 >EG 10.); GRANDA = ((0.4*RAP1) - 3.00)**0.25; 
FINSI;
F = (1.9480*((A/B)**1.5)) + (0.3342*((A/B)**4.2));
F = 1.1 + (GRANDA*F);
SIGT = TA / AIR1;
K_ZAH = SIGT*((PI*A)**0.5)*F;
K_ZAH = K_ZAH*1.E-6; 
ERR1 = abs ((K_CAL - K_ZAH)/K_ZAH);
MESS '  Facteur K CASTEM =' K_CAL '(Mpa.M^0.5)';
MESS '  Facteur K ZAHOOR =' K_ZAH '(Mpa.M^0.5)';
MESS '  Erreur relative =' ERR1; 
SI (ERR1 <  1.E-2);
    ERRE 0;
SINO;
    ERRE 5;
FINSI;
FIN;