Lanterna Rally

Author: T Lewinski

Publisher: World Scientific

Published: 2000-03-23

Total Pages: 768

ISBN-13: 9814497177

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. Contents:Mathematical Preliminaries:Function Spaces, Convex Analysis, Variational ConvergenceElastic Plates:Three-Dimensional Analysis and Effective Models of Composite PlatesThin Plates in Bending and StretchingNonlinear Behavior of PlatesModerately Thick Transversely Symmetric PlatesSandwich Plates with Soft CoreElastic Plates with Cracks:Unilateral Cracks in Thin PlatesUnilateral Cracks in Plates with Transverse Shear DeformationPart-Through the Thickness CracksStiffness Loss of Cracked LaminatesComments and Bibliographical NotesElastic–Perfectly Plastic Plates:Mathematical Complements, Homogenization of Functionals with Linear GrowthHomogenization of Plates Loaded by Forces and MomentsComments and Bibliographical NotesElastic and Plastic Shells:Linear and Nonlinear Models of Elastic ShellsHomogenization and Stiffnesses of Thin Periodic Elastic Shells. Linear ApproachHomogenized Properties of Thin Periodic Elastic Shells Undergoing Moderately Large Rotations Around TangentsPerfectly Plastic ShellsApplication of Homogenization Methods in Optimum Design of Plates and Shells:Mathematical ComplementsTwo-Phase Plate in Bending. Hashin-Shtrikman BoundsTwo-Phase Plate. Hashin-Shtrikman Bounds for the In-Plane ProblemExplicit Formulae for Effective Bending Stiffnesses and Compliances of Ribbed PlatesExplicit Formulae for Effective Membrane Stiffnesses and Compliances of Ribbed PlatesThin Bending Two-Phase Plates of Minimum ComplianceMinimum Compliance Problem for Thin Plates of Varying Thickness: Application of Young MeasuresThin Shells of Minimum ComplianceTruss-Like Michell ContinuaComments and Bibliographical Notes Readership: Applied mathematicians and specialists in plate, shell theory and optimization of structures. keywords:Linear and Nonlinear Plates and Shells;Cracked Plates and Laminates;Perfectly Plastic Plates and Shells;Asymptotic Analysis;Homogenization;Topology Optimization “… the level of mathematical accuracy is very high. The authors present a representative selection of known results, including some of their extensive research, and experts in the field will find a lot of information … the methods used here are of broader significance and thus may provide inspiration for readers interested in quite distant fields of applied mathematics.” European Mathematical Society