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References
H.M. Westergaard, Theory of Elasticity and Plasticity, Dover, New York, (1964), §66.
A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity, 4th.edn., Dover, New York, (1944), §188.
Seefor example, Westergaard, loc. cit. §69 and R.D. Mindlin, Note on the Galerkin and Papcovich stress functions, Bull. Am. Math. Soc., Vol. 42 (1936), 373–376.
For further discussion of the question, see R.A. Eubanks and E. Sternberg, On the completeness of the Boussinesq-Papcovich stress functions, J. Rat. Mech. Anal., Vol. 5 (1956), 735–746., P.M. Naghdi and C.S. Hsu, On a representation of displacements in linear elasticity in terms of three stress functions, J.Math.Mech., Vol. 10 (1961), 233–246, T. Tran Cong and G.P. Steven, On the respresentation of elastic displacement fields in terms of three harmonic functions, J. Elasticity, Vol. 9 (1979), 325–333.
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(2004). Displacement Function Solutions. In: Elasticity. Solid Mechanics and Its Applications, vol 107. Springer, Dordrecht. https://doi.org/10.1007/0-306-48395-5_18
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