© 2014

Nonlinear Mechanics of Thin-Walled Structures

Asymptotics, Direct Approach and Numerical Analysis


  • Hybrid approach is for the first time applied to thin-walled rods of open profile

  • Simulations in Wolfram Mathematica environment on the basis of high level theoretical investigations will make the book attractive

  • A combination of modern analytical methods leads to trustworthy and transparent results even for electromechanically coupled problems


Part of the Foundations of Engineering Mechanics book series (FOUNDATIONS)

Table of contents

  1. Front Matter
    Pages I-X
  2. Yury Vetyukov
    Pages 1-35
  3. Yury Vetyukov
    Pages 37-70
  4. Yury Vetyukov
    Pages 71-112
  5. Yury Vetyukov
    Pages 113-194
  6. Yury Vetyukov
    Pages 195-236
  7. Yury Vetyukov
    Pages 237-257
  8. Back Matter
    Pages 259-272

About this book


This book presents a hybrid approach to the mechanics of thin bodies. Classical theories of rods, plates and shells with constrained shear are based on asymptotic splitting of the equations and boundary conditions of three-dimensional elasticity. The asymptotic solutions become accurate as the thickness decreases, and the three-dimensional fields of stresses and displacements can be determined. The analysis includes practically important effects of electromechanical coupling and material inhomogeneity. The extension to the geometrically nonlinear range uses the direct approach based on the principle of virtual work. Vibrations and buckling of pre-stressed structures are studied with the help of linearized incremental formulations, and direct tensor calculus rounds out the list of analytical techniques used throughout the book.

A novel theory of thin-walled rods of open profile is subsequently developed from the models of rods and shells, and traditionally applied equations are proven to be asymptotically exact. The influence of pre-stresses on the torsional stiffness is shown to be crucial for buckling analysis. Novel finite element schemes for classical rod and shell structures are presented with a comprehensive discussion regarding the theoretical basis, computational aspects and implementation details. Analytical conclusions and closed-form solutions of particular problems are validated against numerical results. The majority of the simulations were performed in the Wolfram Mathematica environment, and the compact source code is provided as a substantial and integral part of the book.


Asymptotic Splitting Classical Rod Theory Classical Shell Theory Finite Element Method

Authors and affiliations

  1. 1.Institute of Technical MechanicsJohannes Kepler UniversityLinzAustria

Bibliographic information

  • Book Title Nonlinear Mechanics of Thin-Walled Structures
  • Book Subtitle Asymptotics, Direct Approach and Numerical Analysis
  • Authors Yury Vetyukov
  • Series Title Foundations of Engineering Mechanics
  • Series Abbreviated Title Foundations Engineering Mechanics
  • DOI
  • Copyright Information Springer-Verlag Wien 2014
  • Publisher Name Springer, Vienna
  • eBook Packages Engineering Engineering (R0)
  • Hardcover ISBN 978-3-7091-1776-7
  • Softcover ISBN 978-3-7091-1976-1
  • eBook ISBN 978-3-7091-1777-4
  • Series ISSN 1612-1384
  • Series E-ISSN 1860-6237
  • Edition Number 1
  • Number of Pages X, 272
  • Number of Illustrations 457 b/w illustrations, 17 illustrations in colour
  • Topics Solid Mechanics
    Solid Mechanics
  • Buy this book on publisher's site
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