Homogenization of Heterogeneous Thin and Thick Plates

Homogenization of Heterogeneous Thin and Thick Plates

Karam Sab and Arthur Lebée, Laboratoire Navier, France

ISBN : 9781848216525

Publication Date : October 2015

Hardcover 318 pp

145.00 USD



This book gives new insight on plate models in the linear elasticity framework taking into account heterogeneities and thickness effects. It is targeted at graduate students who want to discover plate models, but also deals with the latest developments in higher order models.

Plate 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 available on these questions, from very simplistic approaches, which are very limited, to extremely elaborate mathematical theories.

Starting from continuum mechanics concepts, this book introduces plate models of progressive complexity and rigorously tackles the influence of the thickness of the plate and of the heterogeneity. It also provides the latest research results on that matter. The authors give a comprehensive view of rigorously established models accessible to both students and researchers. The majority 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 fresh insight into some aspects of plate theories which have, until recently, been controversial.


1. Linear Elasticity.
2. A Static Approach for Deriving the Kirchhoff–Love Model for Thin Homogeneous Plates.
3. The Kirchhoff–Love Model for Thin Laminated Plates.
4. Thick Homogeneous Plate Subjected to Out-of-Plane Loading.
5. Thick Symmetric Laminated Plate Subjected to Out-of-Plane Loading.
6. The Bending-Gradient Theory.
7. Application to Laminates.
8. Thin Periodic Plates.
9. Thick Periodic Plates.
10. Application to Cellular Sandwich Panels.
11. Application to Space Frames.

About the authors/editors

Karam Sab is a Professor and head of Laboratoire Navier, in France, a joint research unit between Ecole des Ponts ParisTech, IFSTTAR and CNRS. His main research topics concern the homogenization of heterogeneous materials and plates: random materials, Representative Volume Element (RVE), simulation, higher order models (Cosserat), laminated plates, periodic plates, random plates and shear effects.

Arthur Lebée is a researcher at Laboratoire Navier, in France. His main topics concerns homogenization of structures, generalized continua and also origami. He is interested in applications in civil engineering.