Geometric Method for Stability of Non-Linear Elastic Thin Shells

PREFACE This book deals with the new developments and applications of the geometric method to the nonlinear stability problem for thin non-elastic shells. There are no other published books on this subject except the basic ones of A. V. Pogorelov (1966,1967,1986), where variational principles define...

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Bibliographic Details
Main Authors: Ivanova, Jordanka, Pastrone, Franco (Author)
Format: eBook
Published: New York, NY Springer US 2002, 2002
Edition:1st ed. 2002
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 1. Postcritical Deformations of Thin Anisotropic Shells
  • 1.1. Geometric Method in the Nonlinear Theory of Thin Shells
  • 1.2. Asymptotic Form of the Poscritical Deformation Energy of Elastic Anisotropic Shells
  • 1.3. Postcritical Deformations of Shallow Strongly Convex Orthotropic Shells
  • 1.4. Cylindrical Orthotropic Shells under Axial Compression
  • 1.5. Mechanical Interpretation of the Berger’s Hypothesis for the Global Stability of Statically Loaded Anisotropic Shells
  • 2. Postcritical Deformations of Thin Elastic Anisotropic Shells with Linear Memory
  • 2.1. Introduction
  • 2.2. Variational Principle A for Thin Elastic Anisotropic Shells with Linear Memory
  • 2.3. Postcritical Deformations of Thin Elastic Orthotropic Cylindrical Shells with Linear Memory under Uniform External Pressure
  • 2.4. Postcritical Deformations of Thin Orthotropic Cylindrical Shells with Linear Memory. Nonlinear Effect of a Kernel Parameter ?
  • 3. Variational Principle for Global Stability of Elasto-Plastic Thin Shells
  • 3.1 Introduction
  • 3.2 Asymptotic Expression for the Energy of Postcritical Deformations of Elasto-Plastic Shells
  • 3.3. Postcritical Behavior of Thin Cylindrical Elasto- Plastic Shells under Axial Compression
  • 4. Instability of Thin Elastic and Elasto-Plastic Orthotropic Shells under Combined Static and Dynamic Loading
  • 4.1 Introduction
  • 4.2 Asymptotic Analysis of Nonlinear Partial Differential Dynamic Equations for Thin Elastic Anisotropic Shells
  • 4.3 Cylindrical Orthotropic Shells under Combined Axial Compression Loading
  • 4.4. Cylindrical Orthotropic Shells under Combined Uniform External Pressure Loading
  • 4.5. Cylindrical Orthotropic Shells under Static Axial Compression and Short-Duration
  • Dynamic Impulse of External Pressure
  • 4.6. Strictly Convex OrthotropicShells under Combined Dynamic Loading. Expression for the Postcritical Deformation Energy
  • 4.7. Dynamic Instability of Strictly Convex Elastic Orthotropic Shells under Combined External Pressure Loading. Critical Parameters of the Process
  • 4.8. Appendix to Section 4.4
  • 4.9. Dynamic Instability of Cylindrical Elasto-Plastic Shells Subjected to Combined Axial Compression Loading
  • 5. Crushing of Plastic Cylindrical Shells Sensitive to the Strain Rate under Axial Impact
  • 5.1. Introduction
  • 5.2. Mathematical Modelling of the Crushing Process
  • 5.3. Axisymmetric (Concertina) Crushing Mode
  • 5.4. Theoretical Method
  • 5.5. Characteristics Independent of the Crushing Mode
  • 5.6. Comparison between Theoretical and Experimental Data
  • 6. Appendices
  • 6.1. Introduction
  • 6.2. Special Isometric Transformations of Cylindrical Surfaces
  • 6.3. Some Information from the Theory of Surfaces
  • References