MT-1620 al.2002 2(1+ xy E Xy xy 2(1+v) (10-6) E 1/G 2(1+y) XZ XZ (10-7) only Ox, and o stresses exist Look at orthotropic case Xx v12yy13 0 11 230zz V32yy +Oxx, Ow, On=0 still equal zero Paul A. Lagace @2001 Unit 10-p. 11
MIT - 16.20 Fall, 2002 ( ε = 21 + ν) xy σ = 0 ⇒ σ = 0 E xy xy ε = 21 + ν) yz σ ( E yz (10 - 6) 1/ G ( εxz = 21 + ν) σxz (10 - 7) E ⇒ only σxz and σyz stresses exist Look at orthotropic case: 1 εxx = E11 [σxx − ν12 σyy − ν13 σzz ] = 0 1 εyy = E22 [σyy − ν21 σxx − ν23 σzz ] = 0 1 εzz = E33 [σzz − ν31 σxx − ν32 σyy ] = 0 ⇒ σxx, σyy, σzz = 0 still equal zero Paul A. Lagace © 2001 Unit 10 - p. 11
MT-1620 Fall 2002 Z 13 Differences are in E and e here as there are two different shear moduli (G23 and G13) which enter in here for anisotropic material coefficients of mutual influence and chentsoy coefficients foul everything up(no longer"simple" torsion theory). [cant separate torsion from extension Back to general case Look at the equilibrium Equations x2=0 Paul A. Lagace @2001 Unt10-p.12
MIT - 16.20 Fall, 2002 1 εyz = σ G23 yz 1 εxz = σxz G13 Differences are in εyz and εxz here as there are two different shear moduli (G23 and G13) which enter in here. for anisotropic material: coefficients of mutual influence and Chentsov coefficients foul everything up (no longer “simple” torsion theory). [can’t separate torsion from extension] Back to general case… Look at the Equilibrium Equations: ∂σxz ∂z = 0 ⇒ σxz = σxz ( , x y) ∂σyz ∂z = 0 ⇒ σyz = σyz ( , x y) Paul A. Lagace © 2001 Unit 10 - p. 12