* fichier : elas13.dgibi
* Test Elas13.dgibi: Jeux de données *
* --------------------------------- *
* *
*******************************************************
* CAS TEST DU 91/06/13 PROVENANCE : TEST
SAUT PAGE;
*
*******************************************************
* *
* TEST ELAS13 *
* *
* POUTRE SUR SOL ELASTIQUE, EXTREMITES ARTICULEES *
* *
* Test V.P.C.S. numero SSLL16/89 *
* *
* Reference : M. Courtand et P. Lebelle, Formulaire *
* du beton arme, T. 2, Paris, Eyrolles, 1976 *
* *
* La structure est constituee d'une poutre articulee*
* aux extremites et reposant sur un sol elastique. *
* *
* On se propose de calculer la rotation et la *
* reaction a une extremite, ainsi que la fleche et *
* le moment de flexion au centre de la poutre. *
* *
* Les valeurs trouvees sont ensuites comparees *
* aux valeurs de reference obtenues par solution *
* analytique. *
* *
*******************************************************
*
OPTI ECHO 0;
*
OPTI DIME 3;
OPTI ELEM SEG2;
*
GRAPH = 'N';
*
*+++++++++++++++++++++++++++++++++++++++++++++++++++++*
* maillage - geometrie *
*+++++++++++++++++++++++++++++++++++++++++++++++++++++*
*
L = PI * (10 ** .5) / 2.;
*
PA = (-.5 * L) 0. 0.;
PB = (0.5 * L) 0. 0.;
*
SUR1 = PA DROI 8 PB;
PD = SUR1 POIN PROC (0. 0. 0.);
*
SI (NEG GRAPH 'N');
TITR 'ELAS13 : MAILLAGE';
TRAC (0. 0. 1000.) QUAL SUR1;
FINSI;
*
*+++++++++++++++++++++++++++++++++++++++++++++++++++++*
* calcul de la rigidite *
*+++++++++++++++++++++++++++++++++++++++++++++++++++++*
*
MODL1 = MODL SUR1 MECANIQUE ELASTIQUE ISOTROPE POUT;
MATR1 = MATR MODL1 YOUN 2.E11 NU 0.3 TORS 1000.
SECT 1000 INRY 1.E-4 INRZ 1.E-4;
RIGI1 = RIGI MODL1 MATR1;
*
*+++++++++++++++++++++++++++++++++++++++++++++++++++++*
* conditions aux limites *
*+++++++++++++++++++++++++++++++++++++++++++++++++++++*
*
* - Rotule en A et B,
* - Appui continu elastique : sol de raideur lineique
* constante : K = 840 000 N/m2 ,
* - Conditions d'un probleme plan.
*
CL1 = BLOQ UX (PA ET PB);
CL2 = BLOQ UY (PA ET PB);
*
CL3 = BLOQ UZ SUR1;
CL4 = BLOQ RX SUR1;
*
NEL1 = NBEL SUR1;
K = 840000;
KNOEUD = K * L / (2. * NEL1);
I = 0;
CL5 = APPUI DEPL 0. SUR1;
REPETER BLOC2 NEL1;
I = I + 1;
POI1 = SUR1 POIN I;
POI2 = SUR1 POIN (I + 1);
APP1 = APPUI DEPL KNOEUD POI1;
APP2 = APPUI DEPL KNOEUD POI2;
CL5 = CL5 ET APP1 ET APP2;
FIN BLOC2;
*
RIGI1 = RIGI1 ET CL1 ET CL2 ET CL3 ET CL4 ET CL5;
*
*+++++++++++++++++++++++++++++++++++++++++++++++++++++*
* chargement *
*+++++++++++++++++++++++++++++++++++++++++++++++++++++*
*
* - Force ponctuelle verticale de -10000 N au point D,
* - Force lineique repartie verticale de -5000 N/m,
* - Moments opposes aux extremites de 15000 N.m .
*
CHA1 = FORC (0. -10000. 0.) PD;
*
FTOTAL = -5000. * L;
FPOINT = FTOTAL / (2. * NEL1);
CHA2 = FORC FY 0. PA;
I = 0;
REPETER BLOC1 NEL1;
I = I + 1;
POI1 = SUR1 POIN I;
POI2 = SUR1 POIN (I + 1);
FOR1 = FORC FY FPOINT POI1;
FOR2 = FORC FY FPOINT POI2;
CHA2 = CHA2 ET FOR1 ET FOR2;
FIN BLOC1;
*
CHA3 = (MOMENT MZ -15000 PA) ET (MOMENT MZ 15000 PB);
*
CHAR1 = CHA1 ET CHA2 ET CHA3;
*
*+++++++++++++++++++++++++++++++++++++++++++++++++++++*
* resolution : champs de deplacements *
* champ de contraintes *
*+++++++++++++++++++++++++++++++++++++++++++++++++++++*
*
DEPL1 = RESO RIGI1 CHAR1;
*
* Trace facultatif de la deformee
*
REAC1 = REAC RIGI1 DEPL1;
SI (NEG GRAPH 'N');
TITR 'ELAS13 : DEFORMEE, CHARGEMENT, REACTIONS';
VECT1 = VECT CHAR1 3.E-4 FX FY FZ ROUGE;
VECT2 = VECT REAC1 3.E-4 FX FY FZ BLEU;
DEF0 = DEFO SUR1 DEPL1 0.;
DEF1 = DEFO SUR1 DEPL1 100. (VECT1 ET VECT2) VERT;
TRAC (0. 0. 1000.) SUR1 (DEF0 ET DEF1);
FINSI;
*
SIGM1 = SIGM MODL1 MATR1 DEPL1;
SIGM2 = CHAN NOEUD MODL1 SIGM1;
SIGM3 = CHAN CHPO MODL1 SIGM2;
*
*+++++++++++++++++++++++++++++++++++++++++++++++++++++*
* extraction des resultats *
*+++++++++++++++++++++++++++++++++++++++++++++++++++++*
*
* Rotation du point A :
RZA1 = EXTR DEPL1 RZ PA;
RZA2 = -3.045E-3;
ERG1 = 100 * (ABS ((RZA2 - RZA1) / RZA2));
*
* Reaction au point A :
VA1 = EXTR REAC1 FY PA;
VA2 = 1.1674E4;
ERG2 = 100 * (ABS ((VA2 - VA1) / VA2));
*
* Fleche au point D :
UYD1 = EXTR DEPL1 UY PD;
UYD2 = -4.23326E-3;
ERG3 = 100 * (ABS ((UYD2 - UYD1) / UYD2));
*
* Moment de flexion au point D :
MD1 = EXTR SIGM3 MOMZ PD;
MD2 = 3.3840E4;
ERG4 = 100 * (ABS ((MD1 - MD2) / MD2));
*
*+++++++++++++++++++++++++++++++++++++++++++++++++++++*
* affichage des resultats *
*+++++++++++++++++++++++++++++++++++++++++++++++++++++*
*
MESS 'RESULTATS : TEST ELAS13';
MESS '-----------------------';
SAUT LIGN;
*
MESS ' Rotation du point A ';
MESS ' ------------------- ';
MESS ' Valeur theorique :' RZA2 'rad';
MESS ' Valeur calculee :' RZA1 'rad';
MESS ' Ecart :' ERG1 '%';
SAUT LIGN;
*
MESS ' Reaction au point A ';
MESS ' ------------------- ';
MESS ' Valeur theorique :' VA2 'N';
MESS ' Valeur calculee :' VA1 'N';
MESS ' Ecart :' ERG2 '%';
SAUT LIGN;
*
MESS ' Fleche au point D ';
MESS ' ----------------- ';
MESS ' Valeur theorique :' UYD2 'm';
MESS ' Valeur calculee :' UYD1 'm';
MESS ' Ecart :' ERG3 '%';
SAUT LIGN;
*
MESS ' Moment de flexion au point D ';
MESS ' ---------------------------- ';
MESS ' Valeur theorique :' MD2 'N.m';
MESS ' Valeur calculee :' MD1 'N.m';
MESS ' Ecart :' ERG4 '%';
SAUT LIGN;
*
*+++++++++++++++++++++++++++++++++++++++++++++++++++++*
* code fonctionnement *
*+++++++++++++++++++++++++++++++++++++++++++++++++++++*
*
ERGMAX = MAXI (PROG ERG1 ERG2 ERG3 ERG4);
SI (ERGMAX <EG 5.);
ERRE 0;
SINON;
ERRE 5;
FINSI;
*
SAUT 1 LIGN ;
*
TEMPS;
*
FIN;
*
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