The use of Airy Stress Functions is a powerful technique for solving 2-D equilibrium elasticity problems. The component equations of equilibrium for 2-D problems without body forces are
∂ σ x x ∂ x + ∂ τ x y ∂ y = 0 and ∂ σ y y ∂ y + ∂ τ x y ∂ x = 0
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Westergaard's Solution for Crackscts. This page will present a very high level summary of each. The following webpages go into more detail: (i) Airy stress functions, and (ii) calculus of complex numbers. Airy Stress Functions <span>The use of Airy Stress Functions is a powerful technique for solving 2-D equilibrium elasticity problems. The component equations of equilibrium for 2-D problems without body forces are ∂σxx∂x+∂τxy∂y=0and∂σyy∂y+∂τxy∂x=0 ∂ σ x x ∂ x + ∂ τ x y ∂ y = 0 and ∂ σ y y ∂ y + ∂ τ x y ∂ x = 0 The Airy stress function, ϕ ϕ , is related to the 2-D stress components by the following cleverly chosen relationships. σ Summary
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