New methods in mathematical shell theory

  • I. N. Vekua
Conference paper

Abstract

This outline consists of two chapters. The first considers problems of the membrane theory of the convex shells and the second chapter gives some approaches to the construction of the general moment theory of the elastic shells. Both chapters are closely connected with the application of the methods of the theory of analytic functions. These methods which began to penetrate into the shell theory in the beginning of the forties mainly under the influence of the works of N. I. Muskhelishwili [1], came to be very fruitful especially for analysis of the membrane equilibrium of convex shells. The latter problem and the close by connected geometrical problem of bending of surfaces demanded the further perfection of the classical theory of analytic functions. It also greatly contributed to the development of the new branch of analysis — the theory of generalized analytic functions [2, 3, 5]. The shell theory, which is still in the process of stabilization, is a source for the setting of many interesting problems of analysis. It generates a wide class of boundary value problems for partial differential equations. Here we meet equations and systems of equations of the elliptic type as well as equations of the mixed type, which in order to be solved, require methods of contemporary analysis and the further development of its new branches. But this in no way means that the results of the mathematical shell theory are only of purely theoretical importance.

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References

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Copyright information

© Springer-Verlag Berlin Heidelberg 1966

Authors and Affiliations

  • I. N. Vekua
    • 1
  1. 1.University of NovosibirskRussia

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