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Geometric Methods for Stability of Non-Linear Elastic Thin Shells - Jordanka Ivanova

Geometric Methods for Stability of Non-Linear Elastic Thin Shells

Hardcover Published: 31st October 2001
ISBN: 9780792375241
Number Of Pages: 244

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This book deals with the new developments and application of the geometric method to the nonlinear stability problem for thin non-elastic 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 explicityly the asymptotic formulas for the upper and lower critical loads. The geometric method by Pogorelov is one of the most importanty analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the post critical form of a deformed shell surface, successfully applied to a direct variational approach to the nonlinear shell stability problems. Until now, most of 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 researchers in this field to apply the geometric method and the related results to everyday engineering practice. Further developments of the geometric method are carried out in this book and are directed to stability of thin shells in the case of elastic anisotropy, elastic anisotropy with linear memory and elasto-plastic properties of the shell material. This book is intended to serve both as a textbook for post-graduate students in structural engineering and applied mathematics, and as a revference monograph for academic and industrial researchers.

Prefacep. xi
Acknowledgementp. xiii
Postcritical Deformations of Thin Anisotropic Shells
Geometric Method in the Nonlinear Theory of Thin Shellsp. 1
Postcritical Deformations of Convex Shellsp. 10
Stability Loss of Strictly Convex Shellsp. 12
Stability Loss of Convex Developable Shellsp. 13
Asymptotic Form of the Poscritical Deformation Energy of Elastic Anisotropic Shellsp. 16
Postcritical Deformations of Shallow Strongly Convex Orthotropic Shellsp. 25
Lower Critical Load for Spherical Shells (Caps) under External Pressurep. 40
Cylindrical Orthotropic Shells under Axial Compressionp. 42
Mechanical Interpretation of the Berger's Hypothesis for the Global Stability of Statically Loaded Anisotropic Shellsp. 58
Postcritical Deformations of Thin Elastic Anisotropic Shells with Linear Memory
Introductionp. 65
Variational Principle A for Thin Elastic Anisotropic Shells with Linear Memoryp. 66
Postcritical Deformations of Thin Elastic Orthotropic Cylindrical Shells with Linear Memory under Uniform External Pressurep. 71
Linear Effect of the Kernel Parameter [gamma]p. 74
Postcritical Deformations of Thin Orthotropic Cylindrical Shells with Linear Memory. Nonlinear Effect of a Kernel Parameter [gamma]p. 78
Variational Principle for Global Stability of Elasto-Plastic Thin Shells
Introductionp. 87
Asymptotic Expression for the Energy of Postcritical Deformations of Elasto-Plastic Shellsp. 88
Variational Principle A for Elasto-Plastic thin shellsp. 95
Postcritical Behavior of Thin Cylindrical Elasto-Plastic Shells under Axial Compressionp. 101
Instability of Thin Elastic and Elasto-Plastic Orthotropic Shells under Combined Static and Dynamic Loading
Introductionp. 109
Asymptotic Analysis of Nonlinear Partial Differential Dynamic Equations for Thin Elastic Anisotropic Shellsp. 116
Cylindrical Orthotropic Shells under Combined Axial Compression Loadingp. 124
Cylindrical Orthotropic Shells under Combined Uniform External Pressure Loadingp. 132
Cylindrical Orthotropic Shells under Static Axial Compression and Short-Duration Dynamic Impulse of External Pressurep. 139
Strictly Convex Orthotropic Shells under Combined Dynamic Loading. Expression for the Postcritical Deformation Energyp. 144
Dynamic Instability of Strictly Convex Elastic Orthotropic Shells under Combined External Pressure Loading. Critical Parameters of the Processp. 148
Appendix to Section 4.4p. 155
Dynamic Instability of Cylindrical Elasto-Plastic Shells Subjected to Combined Axial Compression Loadingp. 159
Crushing of Plastic Cylindrical Shells Sensitive to the Strain Rate under Axial Impact
Introductionp. 169
Mathematical Modelling of the Crushing Processp. 171
Axisymmetric (Concertina) Crushing Modep. 172
Asymmetric (Diamond) Crushing Modep. 176
Mixed (Transitive) Crushing Modep. 177
Theoretical Method
Axisymmetric (Concertina) Crushing Modep. 178
Asymmetric (Diamond) Crushing Modep. 183
Mixed Crushing Modep. 193
Characteristics Independent of the Crushing Modep. 193
Characteristics of the Asymetric (Diamond) Crushing Modep. 193
Characteristics of the Mixed Crushing Modep. 195
Comparison between Theoretical and Experimental Datap. 196
Appendices
Introductionp. 205
Special Isometric Transformations of Cylindrical Surfacesp. 206
Isometric transformation of Cylindrical Surfaces with Periodic Structurep. 207
Isometric transformation of Cylindrical Surfaces with Helical Symmetryp. 209
Isometric transformation of Cylindrical Surfaces Satisfying Boundary Conditions at the Shell edgep. 211
Extension of the Isometric Transformation of Cylindrical Surfaces with Periodic Structure to the Case of Axial Mass Impactp. 213
Isometric Transformation of Convex Surfacesp. 215
Some Information from the Theory of Surfacesp. 217
Referencesp. 227
Indexp. 239
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780792375241
ISBN-10: 0792375246
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 244
Published: 31st October 2001
Publisher: SPRINGER VERLAG GMBH
Country of Publication: US
Dimensions (cm): 23.39 x 15.6  x 1.6
Weight (kg): 0.56

Earn 496 Qantas Points
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