Karam Sab, Arthur Lebée

Homogenization of Heterogeneous Thin and Thick Plates

• Gebundenes Buch

Produktbeschreibung

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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Produktdetails

• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 294
• Erscheinungstermin: 9. November 2015
• Englisch
• Abmessung: 240mm x 161mm x 22mm
• Gewicht: 648g
• ISBN-13: 9781848216525
• ISBN-10: 1848216521
• Artikelnr.: 40054886

Autorenporträt

Karam Sab is a Professor and head of Laboratoire Navier, which is a joint research unit between Ecole des Ponts ParisTech, IFSTTAR and CNRS. The research concerns the mechanics and physics of materials and structures, in geotechnics, and their applications to in particular civil engineering and petroleum geophysics. His main research topics concern the homogenization of heterogeneous materials and plates: Random materials, Representative Volume Element (RVE), Simulation, Higher order models (Cosserat), Multi-layered plates, Periodic plates, Random plates, Shear effects. The applications concern solid foams, aggregate composites, bituminous materials, cementitious materials, masonry walls, reinforced structures, functionally graded materials, sandwich plates, and space frames. Arthur Lebee is Researcher at Laboratoire Navier, which is a joint research unit between Ecole des Ponts ParisTech, IFSTTAR and CNRS. The research concerns the mechanics and physics of materials and structures, in geotechnics, and their applications to in particular civil engineering and petroleum geophysics.

Inhaltsangabe

FIRST PART: INTRODUCTION
Chapter 1. Why plate models?
Chapter 2. Linear elasticity
Chapter 3. A static approach for deriving a plate model
SECOND PART: LAMINATED PLATES
Chapter 4. Plate models for laminated plates, a review
Chapter 5. The asymptotic expansions for laminated plates
Chapter 6. Plate theories for laminates
Chapter 7. Application of the Bending-Gradient theory
THIRD PART: THIN PERIODIC PLATES
Chapter 8. Introduction to homogenization of thin periodic plates
Chapter 9. Illustrations of homogenization of thin periodic plates
Chapter 10. Green's operator for thin periodic plates
Chapter 11. asymptotic expansion for periodic plates
FOURTH PART: THICK PERIODIC PLATES
Chapter 12. Homogenization scheme for the Bending-Gradient model
Chapter 13. Application to Cellular Sandwich panels
Chapter 14. Application to space frames