Abstract
In this paper the representation of displacement fields in linear elasticity in terms of harmonic functions is considered. In the original work of Papkovich and Neuber four harmonic functions were presented with a subsequent reduction to three on the grounds that only three are sufficient for the representation of displacements fields. This reduction is unsubstantiated and several authors have investigated the generality of the Papkovich-Neuber solutions. The paper derives by simple means the conditions under which it is possible to omit one of the four harmonic functions and considers the significance of the subsequent three function form.
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References
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Tran Cong, T., Steven, G.P. On the representation of elastic displacement fields in terms of three harmonic functions. J Elasticity 9, 325–333 (1979). https://doi.org/10.1007/BF00041103
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DOI: https://doi.org/10.1007/BF00041103