MT-1620 al.2002 Step 2: Use these in the plane stress compatibility equation E6) dX we get quite a mess! After some rearranging and manipulation this results in 02(△T)02(△T) Eat ax temperature term we a= coefficient of thermal expansion haven't yet considered AT= temperature differential This is the basic equation for isotropic plane stress in stress function form Reca:φ is a scalar Paul A Lagace @2001 Unit 8-p. 8MIT - 16.20 Fall, 2002 Step 2: Use these in the plane stress compatibility equation: ∂2εxx ∂2εyy ∂2εxy + = ∂y x y 2 ∂x2 ∂ ∂ (E6) ⇒ we get quite a mess! After some rearranging and manipulation, this results in: V V ∂ ∂ + ∂ ∂ ∂ + ∂ ∂ = − ∂ ( ) ∂ + ∂ ( ) ∂   − ( ) ∂∂ + ∂∂   4 4 4 2 2 4 2 2 2 2 2 2 2 2 1 φ φ α x y y E T x T y y 2 ∆ − 2 φ ν x x ∆ (*) temperature term we haven’t yet considered α = coefficient of thermal expansion ∆T = temperature differential This is the basic equation for isotropic plane stress in Stress Function form Recall: φ is a scalar Paul A. Lagace © 2001 Unit 8 - p. 8