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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 defined over isometric surfaces, are postulated, and applied mainly to static and dynamic problems of elastic isotropic thin shells. A. V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicitely the asymptotic formulas for the upper and lower critical loads. In most cases, these formulas were presented in a closed analytical form, and confirmed by experimental data. The geometric method by Pogorelov is one of the most important analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the postcritical form of a deformed shell surface, successfully applied to a direct variational approach to the nonlinear shell stability problems. Until now most Pogorelov's monographs were written in Russian, which limited the diffusion of his ideas among the international scientific community. The present book is intended to assist and encourage the researches in this field to apply the geometric method and the related results to everyday engineering practice.
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.
