Uncertain Input Data Problems and the Worst Scenario Method

by Ivan Hlavacek, Jan Chleboun, Ivo Babuska, Jan Achenbach

Overview

This book deals with the impact of uncertainty in input data on the outputs of mathematical models. Uncertain inputs as scalars, tensors, functions, or domain boundaries are considered. In practical terms, material parameters or constitutive laws, for instance, are uncertain, and quantities as local temperature, local mechanical stress, or local displacement are monitored. The goal of the worst scenario method is to extremize the quantity over the set of uncertain input data.A general mathematical scheme of the worst scenario method, including approximation by finite element methods, is presented, and then applied to various state problems modeled by differential equations or variational inequalities: nonlinear heat flow, Timoshenko beam vibration and buckling, plate buckling, contact problems in elasticity and thermoelasticity with and without friction, and various models of plastic deformation, to list some of the topics. Dozens of examples, figures, and tables are included.Although the book concentrates on the mathematical aspects of the subject, a substantial part is written in an accessible style and is devoted to various facets of uncertainty in modeling and to the state of the art techniques proposed to deal with uncertain input data.A chapter on sensitivity analysis and on functional and convex analysis is included for the reader's convenience.

Product Details

ISBN-13:	9780444514356
Publisher:	Elsevier Science
Publication date:	12/30/2004
Series:	North-Holland Series in Applied Mathematics and Mechanics , #46
Pages:	484
Product dimensions:	8.70(w) x 11.25(h) x (d)

Table of Contents

Preface List of FiguresList of Tables Introduction Acknowledgments I Reality, Mathematics, and ComputationII General Abstract Scheme and the Analysis of the Worst Scenario MethodIII Quasilinear Elliptic Boundary Value ProblemsIV Parabolic Problems V Elastic and Thermoelastic Beams VI Elastic Plates and Pseudoplates VII Contact Problems in Elasticity and Thermoelasticity VIII Hencky's and Deformation Theories of Plasticity IX Flow Theories of Plasticity X Domains With Uncertain Boundary XI Essentials of Sensitivity and Functional Analysis Appendix Bibliography Subject Index List of Symbols