By
Ivan Hlavacek
Jan Achenbach
Jan Chleboun
Ivo Babuska
Description
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.
Included in series
North-Holland Series in Applied Mathematics and Mechanics
Audience:
* Researchers and graduate students working in applied mathematics with emphasize on problems described by differential equations or variational
inequalities.
* Researchers and graduate students working in computational science related to engineering
problems.
* Researchers and graduate students working in the area of numerical methods.
