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