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Abstract

For three-dimensional axisymmetric problems, the six compatibility equations for infinitesimal strains reduce to four, but these can be further reduced to only three equations. This is illustrated for both the Saint-Venant and the Beltrami–Michell compatibility equations. As a consequence, there is only one nontrivial differential relationship among the three compatibility equations for three-dimensional axisymmetric problems.

Keywords

axisymmetric problems Beltrami–Michell equations Bianchi identities cylindrical coordinates elasticity Love’s potential Saint-Venant’s compatibility equations

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A note on the compatibility equations for three-dimensional axisymmetric problems

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