Summary
The Airy stress function, coupled with the theory of functions of a complex variable, is used to investigate the bending of plates in plane strain. In the limiting case of a thin plate, the theory reproduces the well-known result of elasticity theory known as Love's Equation [1] and systematic corrections in powers of the plate thickness are easily derived.
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References
A.E.H. Love, A treatise on the mathematical theory of elasticity, Cambridge University Press (1959) 455.
N.I. Muskhelishvili, Singular integral equations: boundary problems of function theory and their application to mathematical physics, 2nd Edition, Moscow (1946).
D.E. Jesson and J.P. Sargent, The deformation of the adherends in an adhesive joint undergoing water uptake, J. Adhesion 14 (1982) 119–128.
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Jesson, D.E., Cottingham, W.N. An investigation of beam theory using the Airy stress function coupled with analytic function theory. J Eng Math 20, 73–79 (1986). https://doi.org/10.1007/BF00039324
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DOI: https://doi.org/10.1007/BF00039324