Homogenization of Heterogeneous Thin and Thick Plates

This book gives new insight on plate models in the linearelasticity framework tacking into account heterogeneities andthickness effects. It is targeted to graduate students how want todiscover plate models but deals also with latest developments onhigher order models. Plates models are both an ancient matterand a still active field of research. First attempts date back tothe beginning of the 19th century with Sophie Germain. Veryefficient models have been suggested for homogeneous and isotropicplates by Love (1888) for thin plates and Reissner (1945) for thickplates. However, the extension of such models to more generalsituations --such as laminated plates with highly anisotropiclayers-- and periodic plates --such as honeycomb sandwich panels--raised a number of difficulties. An extremely wide literature isaccessible on these questions, from very simplistic approaches,which are very limited, to extremely elaborated mathematicaltheories, which might refrain the beginner. Starting from continuummechanics concepts, this book introduces plate models ofprogressive complexity and tackles rigorously the influence of thethickness of the plate and of the heterogeneity. It provides alsolatest research results. The major part of the book dealswith a new theory which is the extension to general situations ofthe well established Reissner-Mindlin theory. These results arecompletely new and give a new insight to some aspects of platetheories which were controversial till recently.