- 480 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
About this book
Stability of NonLinear Shells is a compilation of the author's work on analyzing the behaviour of spherical caps and related shell structures under various (axisymmetric) load systems. Differing from other texts on shells of revolution, it is one of the first attempts to deal with effects of multi-parameter load systems. This extension leads to the discovery of some new, hitherto unknown phenomena exhibited by these structures. In addition, the book presents a novel way to characterize properties of solutions of the governing equations for spherical caps - a classification anchored in a theory called reciprocal systems. The author has introduced a deformation map, a projection of multi-dimensional solutions to two-dimensional graphs, to enable analysts to gain insight into the physical meaning of the results obtained. Numerous examples illustrate the concepts introduced. This book also comes to grips with many misconceptions existing in engineering literature about the question of the stability of solutions.
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Subtopic
Mathématiques appliquéesChapter 1
Basic Equations for Geometrically Nonlinear Shells
Dov Shilkrut
1.1 Axisymmetric thermo-elastic deformation of shells of revolution
In this first section, we will consider the thermo-elastic axisymmetric deformation of geometrically nonlinear, rotationally orthotropic shells of revolution. The basic equations given below are based on E. Reissner’s well-known theory of non-shallow shells of revolution [see, e.g., Reissner, 1950]. The main assumptions of this theory are:
• The shell is thin (h/R < < 1; h and R are the shell’s thickness and its smallest radius of curvature, respectively).
• The thickness (divided everywhere in two by the middle-surface of the shell) is measured along the normal to the midsurface.
• The strains are very small as compared to unity.
• The displacements and angles of rotations of the normals to the midsurface are finite without any restrictions regarding th...
Table of contents
- Cover image
- Title page
- Table of Contents
- Copyright page
- Series Editor
- In memoriam Dov Shilkrut, 1925-1998 loving husband, father, and grandfather
- A Personal Note
- Preface
- Introduction
- Chapter 1: Basic Equations for Geometrically Nonlinear Shells
- Chapter 2: Qualitative Investigations of Geometrically Nonlinear Shells
- Chapter 3: Numerical Investigations of Axisymmetrically Loaded Geometrically Nonlinear Shallow Spherical Caps and Circular Plates (A Survey)
- Chapter 4: Spherical Caps Subjected to Multi-Parameter Loading. The Deformation Map. Influence of the Loading Path on the Cap’s Behavior. Thermo-Elastic Deformations.
- Chapter 5: Some Special Problems and the Behavior of Deep Caps
- Chapter 6: The Stability of Equilibrium States of Geometrically Nonlinear Shells
- Figures
- References
- Index
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Yes, you can access Stability of Nonlinear Shells by D. Shilkrut,E. Riks in PDF and/or ePUB format, as well as other popular books in Technologie et ingénierie & Mathématiques appliquées. We have over 1.5 million books available in our catalogue for you to explore.