Lubarda, M. V.; Lubarda, V. A. A note on the compatibility equations for three-dimensional axisymmetric problems. (English) Zbl 1446.74070 Math. Mech. Solids 25, No. 2, 160-165 (2020). Summary: 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. Cited in 1 Document MSC: 74A05 Kinematics of deformation 74A10 Stress Keywords:axisymmetric problems; Beltrami-Michell equations; Bianchi identities; cylindrical coordinates; elasticity; Love’s potential; Saint-Venant’s compatibility equations PDFBibTeX XMLCite \textit{M. V. Lubarda} and \textit{V. A. Lubarda}, Math. Mech. Solids 25, No. 2, 160--165 (2020; Zbl 1446.74070) Full Text: DOI References: [1] Lurie, AI. Three-Dimensional Problems of the Theory of Elasticity (translated from Russian edition by McVean, DB ). New York: Interscience Publishers, 1964. [2] Saada, AS. Elasticity: Theory and Applications. New York: Pergamon Press, 1974. · Zbl 0315.73011 [3] Malvern, LE. Introduction to the Mechanics of a Continuous Medium. Upper Saddle River, NJ: Prentice-Hall, 1969. [4] Wang, C-T. Applied Elasticity. New York: McGraw-Hill, 1953. [5] Barber, JR. Intermediate Mechanics of Materials. New York: McGraw-Hill, 2001. · Zbl 1203.74001 [6] Sneddon, IN. Fourier Transforms. New York: McGraw-Hill, 1951. [7] Timoshenko, SP, Goodier, JN. Theory of Elasticity. New York: McGraw-Hill, 1970. [8] Love, AEH. A Treatise on the Mathematical Theory of Elasticity. New York: Dover, 1944. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.