Geodesic
On integration of differential equations in elastostatics through determination of the mean stress
Applications of Mathematics, Tome 19 (1974) no. 5, pp. 293-306.

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The presented method of integration of differential equations in elastostatics - the so-called menas-stress approach - yields a solution dependent on the elastic parameters and the topology of the body, and accordingly directly affected by Poisson's ratio: for example, the assumption of incompressibility $(v=\frac{1}{2})$ transforms its component Poisson's equation into a harmonic equation. Moreover, the solution for a multiply-connected region has to satisfy additional conditions depending inter alia on the geometry of the latter. These conditions ensure a single-valued mean normal stress.
DOI : 10.21136/AM.1974.103546
Classification : 35Q99, 74B99 
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Golecki, Joseph J. On integration of differential equations in elastostatics through determination of the mean stress. Applications of Mathematics, Tome 19 (1974) no. 5, pp. 293-306. doi : 10.21136/AM.1974.103546. http://geodesic.mathdoc.fr/articles/10.21136/AM.1974.103546/

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