Homogenization of Heterogeneous Thin and Thick Plates
Homogenization of Heterogeneous Thin and Thick Plates
复制标题
异质薄板和厚板的均匀化
DOI：
--
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
A. Lebée
中科院分区：
文献类型：
--
作者：
K. Sab;A. Lebée
这本书给出了新的见解板模型在考虑到非均匀性和厚度效应的线性弹性框架。它的目标是研究生如何想要发现板模型，但也涉及高阶模型的最新发展。板块模型既是一个古老的问题，也是一个仍然活跃的研究领域。第一次尝试可以追溯到世纪初与索菲热尔曼。Love（1888）对薄板和Reissner（1945）对厚板提出了非常有效的均质和各向同性板模型。然而，将这种模型推广到更一般的情况-如具有高度各向异性层的层压板-和周期性板-如蜂窝夹层板-引起了一些困难。在这些问题上，有非常广泛的文献，从非常简单的方法，这是非常有限的，到非常详细的数学理论，这可能会阻止初学者。从连续介质力学的概念出发，这本书介绍了逐步复杂的板块模型，并严格处理了板块厚度和异质性的影响。它还提供了最新的研究成果。书的主要部分涉及一个新的理论，这是扩展到一般情况下的完善Reissner-Mindlin理论。这些结果是全新的，并提供了一个新的见解，一些方面的板块理论，直到最近有争议的。
This book gives new insight on plate models in the linear elasticity framework taking 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.