* fichier : rupt1.dgibi ************************************************************************ * Section : Mecanique Endommagement ************************************************************************ * 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;