By Ivan Hlavacek, Jan Chleboun

ISBN-10: 044451435X

ISBN-13: 9780444514356

This ebook bargains with the impression of uncertainty in enter information at the outputs of mathematical types. doubtful inputs as scalars, tensors, features, or area barriers are thought of. In sensible phrases, fabric parameters or constitutive legislation, for example, are doubtful, and amounts as neighborhood temperature, neighborhood mechanical rigidity, or neighborhood displacement are monitored. The objective of the worst situation procedure is to extremize the amount over the set of doubtful enter information. A basic mathematical scheme of the worst situation technique, together with approximation by means of finite point tools, is gifted, after which utilized to numerous country difficulties modeled by way of differential equations or variational inequalities: nonlinear warmth circulation, Timoshenko beam vibration and buckling, plate buckling, touch difficulties in elasticity and thermoelasticity with and with no friction, and numerous types of plastic deformation, to checklist a few of the themes. Dozens of examples, figures, and tables are integrated. even if the e-book concentrates at the mathematical elements of the topic, a considerable half is written in an available variety and is dedicated to numerous elements of uncertainty in modeling and to the state-of-the-art ideas proposed to accommodate doubtful enter facts. A bankruptcy on sensitivity research and on useful and convex research is integrated for the reader's comfort. Г‚В·

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**Extra info for Uncertain Input Data Problems and the Worst Scenario Method**

**Sample text**

One should balance all errors arising in the course of modeling. If the mathematical model is only a rough approximation of a physical event, then there is no need to spend time and money to get a very accurate numerical solution (StrakoS and Liesen, 2004). Also, if we analyze a particular feature that is not particularly sensitive to the quality of the approximate solutions, then a rough numerical solution can be acceptable. , 2001), (Oberkampf and Trucano, 2002a) and references therein to list just a few sources; they contain detailed verification and validation methodology analyses as well as various techniques, practical examples, and references.

If verification was not performed, such a conclusion could be totally wrong because the agreement could be just coincidence resulting from chance. If confidence in the numerical method and its implementation is backed by verification, then confidence in the mathematical model is going t o be the issue; then comparisons between numerical results and test results or observations become relevant. , 200l), (Oberkampf and Trucano, 2002a). Another possibility is to use a rejection criterion to reject the tested mathematical model or the assumed set of input data.

6 . The last column refers to probability and will be discussed later. 3) through 7 . 1,.. , 6 , 29 2. 41 17. 13). 13) directly give an approximation to the membership function py;7:Eyl of the single element set { + ( T O ) } , namely p ~ " $ ~ ~= ~ 0( xexcept ) for 3: = + ( T O ) + ) , where the value is = 1 , . , ,5. 2 Worst Scenario and Evidence Theory Let us now combine the evidence theory and the worst scenario method. We need a basic probability assignment m to be able to infer the belief and plausibility mappings.

### Uncertain Input Data Problems and the Worst Scenario Method by Ivan Hlavacek, Jan Chleboun

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