Test name
rupt5
Calculation type
MECHANICS ELASTIC
Finite element type
QUA8 PLANE STRAIN MODE
Topic
THE USE OF J-INTEGRAL FOR A SIMPLE AXISYMETRICAL
TUBE WITH A CENTRAL CRACK STRIP SUBJECTED TO
UNIFORM INTERNAL PRESSURE
The structure is a solid cylinder tub containing a central crack . This structure is subject to an internal pressure.
Due to symmetry only 1/4 of the structure is analysed. The CASTEM solution for the stress intensity factors K is given
by the relationship (axisymetrical model) :
Finally this CASTEM K value for the stres intensity factor is compared with the result obtained from the
analytical formula defined by the relationship :
Reference CASTEM
Test NAFEMS : D.P.Rooke and D. J. Cartwright in Copendium of Intensity Factors HMSO (1976) :
rupt5 Modélisation des structures élastiques dans CASTEM 2000.
Version
97' customer version
Model description
Test rupt5 Results
RESULTS
CASTEM FIGURES
* Test Rupt5.dgibi: Jeux de données *
* --------------------------------- *
* *
OPTION ECHO 0 ;
GRAPH = 'N' ;
SAUT PAGE ;
* ;
******************************************************;
* ;
* ;
* QUALIFICATION DU CALCUL DE G ;
* EN ELASTICITE LINEAIRE SUR ;
* UN TUBE A FISSURE INTERNE ;
* SOUMISE A UNE PRESSION LINEAIRE ;
* ;
* ;
* le calcul est compare a celui obtenu par ;
* ROOKE et CARTWRIGHT ;
* dans Compendium of Stress Intensity Factors ;
* ;
******************************************************;
* ;
OPTION DIME 2 ELEM QUA8 MODE AXIS ;
* ;
*-------------- DEFINITION DU MAILLAGE ---------------;
* ;
a = 100. ; b = 200. ; h = 500. ;
m = 1000 ; 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 comp pi2 pi1) ;
sc2 = dall l2 ligh (inve l3) (ci comp pi3 pi2) ;
sc3 = dall l3 (p3 d p1) (inve l4) (ci comp pi4 pi3) ;
sc = sc1 et sc2 et sc3 ;
dens (a / 2.) ;
ligh1 = p1 d p3 ;
mrest1 = ligh1 tran ((m-b) 0.) dini (a/2.) ;
ala = mrest1 cote 3 ;
al = mrest1 cote 2 ;
mrest = ligh tran (0. (h - a)) dini (a / 2.) ;
mrest2 = al tran (0. (h - a)) dini (a / 2.) ;
lihaut1= mrest cote 3 ;
lihaut = mrest cote 3 ;
lihaut2= mrest2 cote 3 ;
lihaut = lihaut1 et lihaut2 ;
ccp = sf et sc et mrest et mrest1 et mrest2 ;
elim ccp 0.001 ;
cccp = cont ccp ;
pj = ala poin fina ;
lifis = cccp comp pf p0 ;
libas = cccp comp pj pf ;
SI ( NEG GRAPH 'N' ) ;
TRAC CCP ;
FINSI ;
* ;
*--------------- CREATION DU MODELE ------------------;
* ;
objaf = modl ccp mecanique elastique isotrope ;
* ;
*--------- DEFINITION DES CARACTERISTIQUES -----------;
*------------- MATERIELLES ET GEOMETRIQUES -------;
* ;
mat = matr objaf YOUN 2.e4 NU 0.3 ;
* ;
*--------- CALCUL DES RIGIDITES ELEMENTAIRES ---------;
*------ - ET DEFINITION DES BLOCAGES ----------;
* ;
rig = rigi objaf mat ;
cdl1 = bloq Uz libas ;
cdl2 = bloq Uz lihaut ;
* ;
*-------------- DEFINITION DU CHARGEMENT -------------;
* ;
pchx = coor 1 lifis ;
pcha = manu chpo lifis 1 scal a ;
pchx = nomc 'P' (pcha - pchx) ;
pcht = pchx * (1/a) ;
pch0 = pcht *0. ;
Fp = pres mass objaf pcht ;
* ;
*------- RESOLUTION ET CALCUL DES CONTRAINTES --------;
* ;
U = reso (rig et cdl1 et cdl2 ) Fp ;
SIG = sigm mat objaf U ;
* ;
*----- INITIALISATION DE LA TABLE EN ENTREE ----------;
*------ DE LA PROCEDURE G_THETA --------;
* ;
SUPTAB = TABLE ;
SUPTAB.'OBJECTIF' = MOT 'J';
SUPTAB.'LEVRE_SUPERIEURE' = lifis;
SUPTAB.'FRONT_FISSURE' = PF ;
SUPTAB.'MODELE' = objaf;
SUPTAB.'CARACTERISTIQUES' = mat;
SUPTAB.'SOLUTION_RESO' = u;
SUPTAB.'CHARGEMENTS_MECANIQUES' = Fp;
SUPTAB.'COUCHE' = 4;
* ;
*----------- APPEL A LA PROCEDURE G_THETA ------------;
* ;
SAUT PAGE ;
G_THETA suptab ;
* ;
*------ RECUPERATION DU RESULTAT ET COMPARAISONS -----;
* ;
G = suptab.'RESULTATS' ;
Kth = 2.4215 ;
K = (20000. * G / (1 - (0.3**2)))**0.5 ;
mess ' ' ;
mess ' ' ;
mess 'taux de restitution energetique G :' G ;
mess 'solution calculee Kcal :' K ;
mess 'solution analytique Kthe :' Kth ;
* CODE FONCTIONNEMENT ;
RESI = abs (( k - Kth ) / Kth ) ;
SI (RESI < 5E-2) ;
ERRE 0 ;
SINO ;
ERRE 5 ;
FINSI ;
fin;