Chapitre 3
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Calcul de , ( )-On a :
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Calcul de , ( )-
Chapitre 3
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Calcul de , ( )-
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{
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Chapitre 3
[B3 ( k)]
f f 0
Calcul de [B4(k)]
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aN4 {f33
aZ
[B4 ( k)]
f
23 f130
La matrice [ B] se présente comme suit :
[ B( k)] = [[ B1( k)] [B2(k)] [
B3 ( k)] [ B4 ( k)]]
Avec :
74 /176
Chapitre 3
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3.3.4. Construction de la matrice de rigidité
élémentaire
La matrice de rigidité élémentaire se
calcule grâce à la formule suivante :
, - ? , ( )- , -, ( )-
En ramenant l'intégral sur l'espace des
éléments de référence, on a :
, - ? e ( ) , ( )- , -, ( )- e ( )
Chapitre 3
,
- ?, ( )- , -, ( )-
e ( ) Comme la matrice des
fonctions de déformation, dans le cas
l'élément
finis tétraédrique à 4 noeuds,
est indépendante des coordonnées , on peut écrire
:
, - e ( ) ,
, - ,
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, - , ( )- , -, ( )-
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Termes de la matrice de
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84 /176
Tableau 3.1 : Tableau des valeurs de la matrice de
rigidité élémentaire de l'élément
tétraédrique à 4 noeuds (douze
degrés de
liberté).
85 /176
| 
