Plates, Laminates And Shells: Asymptotic Analysis And Homogenization

by Tomasz Lewinski, Jozef Joachim Telega

Overview

This book gives a systematic and comprehensive presentation of the results concerning effective behavior of elastic and plastic plates with periodic or quasiperiodic structure. One of the chapters covers the hitherto available results concerning the averaging problems in the linear and nonlinear shell models.A unified approach to the problems studied is based on modern variational and asymptotic methods, including the methods of variational inequalities as well as homogenization techniques. Duality arguments are also exploited. A significant part of the book deals with problems important for engineering practice, such as: statical analysis of highly nonhomogeneous plates and shells for which common discretization techniques fail to be efficient, assessing stiffness reduction of cracked [00n/900m]s laminates, and assessing ultimate loads for perfectly plastic plates and shells composed of repeated segments. When possible, the homogenization formulas are cast in closed form expressions. The formulas presented in this manner are then used in constructing regularized formulations of the fundamental optimization problems for plates and shells, since the regularization concepts are based on introducing the composite regions for which microstructural properties play the role of new design variables.

Product Details

ISBN-13:	9789810232061
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	03/27/2000
Series:	Series On Advances In Mathematics For Applied Sciences , #52
Pages:	768
Product dimensions:	6.20(w) x 8.60(h) x 1.80(d)

Editorial Reviews

Lewinski (Warsaw U. of Technology) and Telega (Polish Academic of Sciences) synthesize the applications of the homogenization methods of analyzing the structure of the three shapes of composite materials at both the product and material scales. Their perspective is broad, encompassing various averaging methods, whether starting from three- dimensional or two-dimensional mathematical models. Their analysis is confined to carefully selected structural models that are both important practically and are variationally consistent, and for most of which the dual formulations are given more or less explicitly. They point out that he homogenization results turn out to be realistic only when used at an appropriate scaling. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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