a análise de placas laminadas compostas inteligentes
a análise de placas laminadas compostas inteligentes
a análise de placas laminadas compostas inteligentes
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7.5 Solução <strong>de</strong> Navier 150<br />
<br />
B11α 2 m + B66β 2 n<br />
<br />
+<br />
<br />
+<br />
<br />
<br />
+<br />
+ αm<br />
+<br />
<br />
D12 + D66<br />
<br />
<br />
Umn +<br />
αmβnYmn +<br />
<br />
+ Ac55<br />
<br />
npiez <br />
<br />
+ αm e (k) 1<br />
31<br />
2hk<br />
k=1<br />
<br />
<br />
αmβnUmn +<br />
<br />
Ymn +<br />
<br />
+ Ac44<br />
npiez <br />
<br />
+ βn e (k) 1<br />
32<br />
2hk<br />
B12 + B66<br />
<br />
D66α 2 m + D22β 2 n<br />
L11α 2 m + L66β 2 n<br />
F12 + F66<br />
npiez <br />
k=1<br />
e (k)<br />
31<br />
k=1<br />
<br />
Umn +<br />
<br />
<br />
αmβnYmn +<br />
<br />
+ 3Dc55<br />
1<br />
4hk<br />
L12 + L66<br />
<br />
F66α 2 m + F22β 2 n<br />
+ βn<br />
npiez <br />
k=1<br />
e (k)<br />
32<br />
B12 + B66<br />
F11α 2 m + F66β 2 n<br />
Xmn + αmWmn<br />
<br />
<br />
αmβnVmn +<br />
<br />
Xmn +<br />
<br />
+ 3Dc55Xmn<br />
<br />
Φ (k−1)<br />
mn = 0<br />
(z 2 k − z 2 k−1) + e (k)<br />
15<br />
B66α 2 m + B22β 2 n<br />
F12 + F66<br />
Ymn + βnWmn<br />
<br />
(z 2 k − z 2 k−1) + e (k)<br />
24<br />
L12 + L66<br />
H11α 2 m + H66β 2 n<br />
Xmn + αmWmn<br />
(z 4 k − z 4 k−1)Φ (k−1)<br />
mn<br />
<br />
<br />
αmβnUmn +<br />
<br />
Ymn +<br />
<br />
+ 3Dc44<br />
1<br />
4hk<br />
+ αm<br />
hk<br />
2<br />
<br />
Vmn +<br />
hk<br />
2<br />
D11α 2 m + D66β 2 n<br />
F12 + F66<br />
αmβnXmn +<br />
<br />
+ 3Dc44Ymn<br />
<br />
Φ (k−1)<br />
mn = 0<br />
<br />
<br />
αmβnVmn +<br />
<br />
Xmn +<br />
<br />
+ 9F c55Xmn<br />
npiez <br />
k=1<br />
L66α 2 m + L22β 2 n<br />
H12 + H66<br />
<br />
Ymn + βnWmn<br />
(z 4 k − z 4 k−1)Φ (k−1)<br />
mn<br />
+ βn<br />
3e (k)<br />
15<br />
1<br />
hk<br />
<br />
Vmn +<br />
αmβnXmn +<br />
<br />
+ 9F c44Ymn<br />
npiez <br />
k=1<br />
3e (k)<br />
24<br />
1<br />
hk<br />
<br />
<br />
<br />
Xmn<br />
αmβnYmn<br />
D12 + D66<br />
<br />
αmβnXmn<br />
F66α 2 m + F22β 2 <br />
n Ymn<br />
F11α 2 m + F66β 2 n<br />
H12 + H66<br />
<br />
<br />
Xmn<br />
αmβnYmn<br />
4 zk 12 − zkz3 k−1<br />
3 + z4 k−1<br />
4<br />
<br />
F12 + F66<br />
<br />
αmβnXmn<br />
H66α 2 m + H22β 2 <br />
n Ymn<br />
4 zk 12 − zkz3 k−1<br />
3 + z4 k−1<br />
4<br />
(7.112)<br />
(7.113)<br />
<br />
Φ (k−1)<br />
mn = 0<br />
(7.114)<br />
<br />
Φ (k−1)<br />
mn = 0<br />
(7.115)
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