# Article

 Title: On integration of differential equations in elastostatics through determination of the mean stress (English) Author: Golecki, Joseph J. Language: English Journal: Aplikace matematiky ISSN: 0373-6725 Volume: 19 Issue: 5 Year: 1974 Pages: 293-306 Summary lang: English Summary lang: Czech . Category: math . Summary: 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. () MSC: 35Q99 MSC: 74B99 idZBL: Zbl 0314.73017 idMR: MR0366160 . Date available: 2008-05-20T17:59:36Z Last updated: 2015-08-05 Stable URL: http://hdl.handle.net/10338.dmlcz/103546 . Reference: [1] Almansi E.: Sull'integrazione dell' equazione differenziale \$\nabla^{2n} =0.Ann. Mat. Рurа Appl. (3), 2, pp. 1-51, 1899. Reference: [2] Biderman V. L.: Design of rubber and rubber-cord elements.(in Russian). Strength Analysis in Machine Design, 2nd ed., S. D. Ponomarev (Ed.), Vol. 2, 7, pp. 487-491. Mashgiz, Moskva, 1958. Reference: [3] Dubnov J. S.: Foundations of vector calculus.Vol. 2 (in Russian), Gos. Izd. Teh.-Teor. Lit., Moskva, 1952. Reference: [4] Dyminkov S. J., Pribylov T. A.: Variational equations of the theory of elasticity for an incompressible medium.(in Russian). Editorial Committee Zh. ,,Mekhanika Polimerov", Riga, 1969. Reference: [5] Föppl A., and Föppl L.: Drang und Zwang, Eine höhere Festigkeitslehre für Ingenieure.2nd Ed. Vol. 1, München und Berlin, 1924 (1st Ed. Oldenbourg, Munich and Berlin 1920). 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K.: A comparison of various elasticity formulations valid for admissible value of Poisson's ratio.Astronautica Acta, 14, pp. 317-326, 1969. .

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