New methods in mathematical shell theory

  • I. N. Vekua
Conference paper


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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Мусхелишвили, H. И.: Некоторые основные задачи математической теории упругости, Москва 1954. Английский перевод: Some basic problems of the mathematical theory of elasticity, Groningen: P. Noordhofst 1953.Google Scholar
  2. [2]
    Векуа, И. H.: Обобщенные аналитические функции, Москва: физматгиз 1959. Английский перевод: Generalized analytic functions, Pergamon Press 1962.Google Scholar
  3. [3]
    Vekua, I. N.: Verallgemeinerte analytische Funktionen, Berlin: Akademie-Verlag 1963.MATHGoogle Scholar
  4. [4]
    Vekua, I. N.: A projective property of force and deflection fields. Problems of Continuum Mechanics, Philadelphia 1961.Google Scholar
  5. [5]
    Векуа, И. H.: Системы дифференциальных уравнений первого порядка эллиптического типа и граничные задачи с применинием к теории оболочек. Матем. сб. 31 (73), 2 (1952) 217-314. Немецкий перевод: Systeme von Differentialgleichungen erster Ordnung vom elliptischen Typus und Randwertaufgaben, Berlin: VEB Deutscher Verlag der Wissenschaften 1956.Google Scholar
  6. [6]
    Векуа, И. H.: Об условиях безмоментности напряженного состояния равновесия выпуклой оболочки. Труды всесоюзного совещания по дифференциальным уравнениям, Ереван 1960, ctp. 32-44.Google Scholar
  7. [7]
    Векуа, И. H.: Об одном методе расчета призматических оболочек. Труды Тбилисского математического института 21 (1955) 191-295.Google Scholar
  8. [8]
    Векуа, И. H., и H. И. Мусхелишвили: Методы теории аналитических функций в теории упругости. Труды всесоюзного съезда по теоретической и прикладной механике, Москва 1962, ctp. 310-338.Google Scholar
  9. [9]
    Векуа, И. H.: Новые методы решения эллиптических уравнений, Москва: Гостехиздат 1948.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1966

Authors and Affiliations

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

Personalised recommendations