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Uncertain Input Data Problems and the Worst Scenario Method, Volume 46 (Hardcover, New)
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Uncertain Input Data Problems and the Worst Scenario Method, Volume 46 (Hardcover, New)
Series: North-Holland Series in Applied Mathematics & Mechanics
Expected to ship within 10 - 15 working days
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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.
-Rigorous theory is established for the treatment of uncertainty in
modeling
- Uncertainty is considered in complex models based on partial
differential equations or variational inequalities
- Applications to nonlinear and linear problems with uncertain data
are presented in detail: quasilinear steady heat flow, buckling of
beams and plates, vibration of beams, frictional contact of bodies,
several models of plastic deformation, and more
-Although emphasis is put on theoretical analysis and approximation
techniques, numerical examples are also present
-Main ideas and approaches used today to handle uncertainties in
modeling are described in an accessible form
-Fairly self-contained book
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