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Introduction

  • Yury Vetyukov
Chapter
Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)

Abstract

We begin with a brief discussion of mathematical methods, which to a large extent determine the success of the analysis of thin-walled structures: a compact and consistent notation for the invariant tensor calculus in the three-dimensional Euclidean space; the procedure of asymptotic splitting, which is proven to be efficient for the dimensional reduction in the theories of thin bodies; the principle of virtual work in application to continuum mechanics; variational methods as a basis for numerical applications. The state of the art in the mechanics of thin-walled structures is discussed on the example plane stress problem of bending of a straight strip. In the literature review, the past research in the field is classified into the method of hypotheses, variational approaches, direct approaches and asymptotic methods. The introduction is concluded with a discussion of a hybrid asymptotic–direct approach, which is applied throughout the book to various kinds of thin-walled structures.

Keywords

Internal Force Virtual Work Reference Configuration Invariant Vector Rank Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Supplementary material

310026_1_En_1_MOESM1_ESM.nb (363 kb)
(NB 363 kB)

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Copyright information

© Springer-Verlag Wien 2014

Authors and Affiliations

  • Yury Vetyukov
    • 1
  1. 1.Institute of Technical MechanicsJohannes Kepler UniversityLinzAustria

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