×

zbMATH — the first resource for mathematics

The method of I. N. Vekua for nonshallow cylindrical shells. (English. Russian original) Zbl 1180.35514
J. Math. Sci., New York 157, No. 1, 43-51 (2009); translation from Sovrem. Mat. Prilozh. 51 (2008).
Summary: The refined theory of shells is constructed by reducing three-dimensional problems of the theory of elasticity to two-dimensional problems. I. Vekua obtained the equations of shallow shells. This means that the interior geometry of the shell does not vary in thickness. This method for nonshallow shells in the case of geometrical and physical nonlinear theory was generalized by T. Meunargia.
MSC:
35Q74 PDEs in connection with mechanics of deformable solids
74K25 Shells
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] B. R. Gulua, ”On one boundary-value problem for the nonshallow cylindrical shells,” Repts. Semin. VIAM, 20, No. 2, 36–40 (2005). · Zbl 1187.74134
[2] B. R. Gulua, ”A method of the small parameter for the nonshallow cylindrical shells,” Bull. Georgian Acad. Sci., 173, No. 1, 42–45 (2006).
[3] T. V. Meunargia, ”On one method of construction of geometrically and physically nonlinear theory of nonshallow shells,” Proc. of A. Razmadze Math. Inst., 119 (1999). · Zbl 0984.74048
[4] N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, Holland (1953). · Zbl 0052.41402
[5] I. N. Vekua, ”On a method of computation of prismatic shells,” Tr. Tbilis. Mat. Inst. 21, 191–259 (1955).
[6] I. N. Vekua, Theory on Thin and Shallow Shells with Variable Thickness [in Russian], Metsniereba, Tbilisi (1965). · Zbl 0239.73062
[7] I. N. Vekua, Shell Theory. General Methods of Construction [in Russian], Nauka, Moscow (1982).
[8] I. N. Vekua, ”On the integration of equilibrium equations of a cylindrical shell,” Dokl. Akad. Nauk SSSR, 186, No. 4, 787–790 (1969). · Zbl 0194.57203
[9] I. N. Vekua, ”On the construction of approximate solutions of the equation of the shallow spherical shells,” Int. J. Solids Struct., 10, 991–1003 (1968). · Zbl 0175.22806
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.