Given a three dimensional solid element in a state of plane stress or plane strain with conservative body forces, the stress components are equal to the appropriate second order partial derivatives of a bi-harmonic function, ϕ , called an Airy Stress Function. It follows that the stress components automatically satisfy the equilibrium conditions.
The function ϕ depends on both the geometry of the body and the loading, which leaves infinite possible stress functions to be developed. As thesis work, I have researched and collected currently existing Airy Stress Functions, made plots of thier stress fields in order to gain a better understanding of how they are developed, and attempted to take the Finite Element Analysis of a real world example support structure for a door under the loading of a gas shock and compare to results obtained from the use of Airy Stress Functions.
Library of Congress Subject Headings
Strains and stresses--Mathematical models
Mechanical Engineering (MS)
Department, Program, or Center
Mechanical Engineering (KGCOE)
Roman, Matthew David, "Plane Elasticity Using Airy Stress Functions" (2006). Thesis. Rochester Institute of Technology. Accessed from
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