MT-1620 al.2002 and forφsml →U=Zφ v(x,y,z)=0 (x,y)≈w(x) (13-2) Now look at the strain-displacement equations du d (13-3) dx dx dv dy Es a=0(no deformation through thickness) 0 du dv dy dx dv dw 0z0 y du dw 00w dz dx dx dx Paul A Lagace @2001 Unit 13-8MIT - 16.20 Fall, 2002 and for φ small: ⇒ u = -z φ v x( , y,) z = 0 w x( , y,) z ≈ w x( ) (13 - 2) Now look at the strain-displacement equations: 2 ∂ u d w ε xx = ∂ x = − z dx2 (13 - 3) ∂ v ε = = 0 yy ∂ y ∂ w ε = = 0 (no deformation through thickness) zz ∂ z ∂ u ∂ v ε = + = 0 xy ∂ y ∂ x ∂ v ∂ w ε = + = 0 yz ∂ z ∂ y ∂ u ∂ w ∂ w ∂ w ε = + = − + = 0 xz ∂ z ∂ x ∂ x ∂ x Paul A. Lagace © 2001 Unit 13 - 8