MT-1620 al.2002 E1) 0(0p +V|+ dy axd ao dv d'o dv es) 0(0 E2) 0=0? dx dxdy dy( dx dφ0p,dv a_0 (yes =Equilibrium automatically satisfied using Airy stress function Does that mean that any function we pick for o(x, y) will be valid? No, it will satisfy equilibrium, but we still have the strain-displacement and stress-strain equations If we use these we can get to the governing equation Paul A Lagace @2001 Unit 8-p. 6 ∂ ∂ ∂ ∂ MIT - 16.20 Fall, 2002 2 ∂  ∂2φ ( ) E1 :  2 +V  + ∂ − ∂ φ  − ∂V = 0 ? ∂x  ∂y  ∂y  ∂ ∂x y ∂x ∂3φ + ∂V − ∂3φ − ∂ V = 0 ⇒ (yes) ∂ ∂x y x y 2 ∂x ∂ ∂ 2 ∂x 2 ∂ − ∂ φ  ∂  ∂2φ (E2) : ∂x  ∂ ∂y  + ∂y  ∂x 2 + V  − ∂V = 0 ? x ∂y ∂3φ + ∂3φ + ∂ V − ∂ V ⇒ = 0 (yes) 2 2 xy xy ∂y ∂y ⇒Equilibrium automatically satisfied using Airy stress function! Does that mean that any function we pick for φ (x, y) will be valid? No, it will satisfy equilibrium, but we still have the strain-displacement and stress-strain equations. If we use these, we can get to the governing equation: Paul A. Lagace © 2001 Unit 8 - p. 6