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Library | Item Barcode | Call Number | Material Type | Item Category 1 | Status |
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Searching... | 30000010082107 | Q375 H52 2004 | Open Access Book | Book | Searching... |
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Summary
Summary
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.
Table of Contents
Preface |
List of Figures List of Tables |
Introduction |
Acknowledgments |
I Reality, Mathematics, and Computation |
II General Abstract Scheme and the Analysis of the Worst Scenario Method |
III Quasilinear Elliptic Boundary Value Problems |
IV 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 |