leccion 3 - ejercicio 1 (14.1) v.2005 - solution to go ... · leccion 3 - ejercicio 1 (14.1) v.2005...
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LECCION 3 - EJERCICIO 1 (14.1) v.2005 - SOLUTION TO GO FROM PLANE STRAIN
TO PLANE STRESS
Off@General::"spell1"DOff@General::"spell"D
ClearAll@Em, Ν, Emstar, ΝstarD;
Efac = Em*H1 - ΝL�HH1 + ΝL*H1 - 2 ΝLL;
Emat = Efac*881, Ν�H1 - ΝL, 0<, 8Ν�H1 - ΝL, 1, 0<, 80, 0, H1 - 2 ΝL�H2 H1 - ΝLL<<;
MatrixForm@Emat�EfacD
1Ν
1-Ν0
Ν
1-Ν1 0
0 01-2 Ν
2 H1-ΝL
Print@"PLANE STRAIN E MATRIX:", Emat �� MatrixFormD
PLANE STRAIN E MATRIX:
Em H1-ΝLH1-2 ΝL H1+ΝL
Em Ν
H1-2 ΝL H1+ΝL0
Em Ν
H1-2 ΝL H1+ΝLEm H1-ΝL
H1-2 ΝL H1+ΝL0
0 0Em
2 H1+ΝL
EEmat = Simplify@Emat �. 8Em ® Emstar, Ν ® Νstar<D;
EEmat �� MatrixForm
Emstar H-1+ΝstarL-1+Νstar+2 Νstar
2-
Emstar Νstar
-1+Νstar+2 Νstar2
0
-Emstar Νstar
-1+Νstar+2 Νstar2
Emstar H-1+ΝstarL-1+Νstar+2 Νstar
20
0 0Emstar
2+2 Νstar
EEmat@@1, 1DD
Emstar H-1 + ΝstarL
-1 + Νstar + 2 Νstar2
eq1 = EEmat@@1, 1DD � Em� I1 - Ν2M
Emstar H-1 + ΝstarL
-1 + Νstar + 2 Νstar2
�
Em
1 - Ν2
eq2 = EEmat@@1, 2DD � HEm*ΝL� I1 - Ν2M
-
Emstar Νstar
-1 + Νstar + 2 Νstar2
�
Em Ν
1 - Ν2
sol = Solve@8eq1, eq2<, 8Emstar, Νstar<D
::Emstar ®
Em H1 + 2 ΝL
H1 + ΝL2
, Νstar ®
Ν
1 + Ν
>>
sol = Simplify@solD
::Emstar ®
Em H1 + 2 ΝL
H1 + ΝL2
, Νstar ®
Ν
1 + Ν
>>
� COMPROBACION
Simplify@EEmat �. sol@@1DD �� MatrixFormD
Em
1-Ν2
Em Ν
1-Ν2
0
Em Ν
1-Ν2
Em
1-Ν2
0
0 0Em
2+2 Ν
2 m6-04-Ch14-Ex-1-v2015-c.nb