Overview
- 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
- Includes supplementary material: sn.pub/extras
Part of the book series: Foundations of Engineering Mechanics (FOUNDATIONS)
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Table of contents (6 chapters)
Keywords
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.
Authors and Affiliations
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
DOI: https://doi.org/10.1007/978-3-7091-1777-4
Publisher: Springer Vienna
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag Wien 2014
Hardcover ISBN: 978-3-7091-1776-7Published: 05 February 2014
Softcover ISBN: 978-3-7091-1976-1Published: 17 September 2016
eBook ISBN: 978-3-7091-1777-4Published: 23 January 2014
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, Mechatronics