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Homogeneization and periodic structures /
This book gives new insight on plate models in the linear elasticity framework tacking into account heterogeneities and thickness effects. It is targeted to graduate students how want to discover plate models but deals also with latest developments on higher order models. Plates models are both an a...
| Clasificación: | Libro Electrónico |
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| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
Wiley-ISTE,
2015.
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| Edición: | 1st |
| Colección: | Iste.
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| Temas: | |
| Acceso en línea: | Texto completo |
| Sumario: | This book gives new insight on plate models in the linear elasticity framework tacking into account heterogeneities and thickness effects. It is targeted to graduate students how want to discover plate models but deals also with latest developments on higher order models. Plates models are both an ancient matter and a still active field of research. First attempts date back to the beginning of the 19th century with Sophie Germain. Very efficient models have been suggested for homogeneous and isotropic plates by Love (1888) for thin plates and Reissner (1945) for thick plates. However, the extension of such models to more general situations --such as laminated plates with highly anisotropic layers-- and periodic plates --such as honeycomb sandwich panels-- raised a number of difficulties. An extremely wide literature is accessible on these questions, from very simplistic approaches, which are very limited, to extremely elaborated mathematical theories, which might refrain the beginner. Starting from continuum mechanics concepts, this book introduces plate models of progressive complexity and tackles rigorously the influence of the thickness of the plate and of the heterogeneity. It provides also latest research results. The major part of the book deals with a new theory which is the extension to general situations of the well established Reissner-Mindlin theory. These results are completely new and give a new insight to some aspects of plate theories which were controversial till recently. |
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| Notas: | Empirical error estimates and convergence rate 160 7.4.4. Influence of the bending direction 161 7.5. Conclusion 163 Part 3 Periodic Plates 167 Chapter 8. Thin Periodic Plates 169 8.1. The 3D problem 169 8.2. The homogenized plate problem 173 8.3. Determination of the homogenized plate elastic stiffness tensors 174 8.4. A first justification: the asymptotic effective elastic properties of periodic plates 181 8.5. Effect of symmetries 184 8.5.1. Symmetric periodic plate 185 8.5.2. Material symmetry of the homogenized plate 186 8.5.3. Important special cases 187 8.5.4. Rectangular parallelepipedic unit cell 189 8.6. Second justification: the asymptotic expansion method 194 Chapter 9. Thick Periodic Plates 205 9.1. The 3D problem 206 9.2. The asymptotic solution 208 9.3. The Bending-Gradient homogenization scheme 209 9.3.1. Motivation and description of the approach 210 9.3.2. Introduction of corrective terms to the asymptotic solution 210 9.3.3. Identification of the localization tensors 212 9.3.4. Identification of the Bending-Gradient compliance tensor 214 Chapter 10. Application to Cellular Sandwich Panels 219 10.1. Introduction 219 10.2. Questions raised by sandwich panel shear force stiffness 220 10.2.1. The case of homogeneous cores 221 10.2.2. The case of cellular cores 223 10.3. The membrane and bending behavior of sandwich panels 225 10.3.1. The case of homogeneous cores 225 10.3.2. The case of cellular cores 226 10.4. The transverse shear behavior of sandwich panels 229 10.4.1. The case of homogeneous cores 229 10.4.2. A direct homogenization scheme for cellular sandwich panel shear force stiffness 230 10.4.3. Discussion 232 10.5. Application to a sandwich panel including Miura-ori 235 10.5.1. Folded cores 236 10.5.2. Description of the sandwich panel including the folded core 237 10.5.3. Symmetries of Miura-ori 238 10.5.4. Implementation 239 10. |
| Descripción Física: | 1 online resource |
| ISBN: | 9781119008163 1119008166 9781119008156 1119008158 |