Jan Lovisek's Books

Solution of Variational Inequalities in Mechanics

By: Ivan Hlavacek,Jaroslav Haslinger,Jindrich Necas,Jan Lovisek

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Solution of Variational Inequalities in Mechanics

By: Ivan Hlavacek,Jaroslav Haslinger,Jindrich Necas,Jan Lovisek

The idea for this book was developed in the seminar on problems of con tinuum mechanics, which has been active for more than twelve years at the Faculty of Mathematics and Physics, Charles University, Prague. This seminar has been pursuing recent directions in the development of mathe matical applications in physics; especially in continuum mechanics, and in technology. It has regularly been attended by upper division and graduate students, faculty, and scientists and researchers from various institutions from Prague and elsewhere. These seminar participants decided to publish in a self-contained monograph the results of their individual and collective efforts in developing applications for the theory of variational inequalities, which is currently a rapidly growing branch of modern analysis. The theory of variational inequalities is a relatively young mathematical discipline. Apparently, one of the main bases for its development was the paper by G. Fichera (1964) on the solution of the Signorini problem in the theory of elasticity. Later, J. L. Lions and G. Stampacchia (1967) laid the foundations of the theory itself. Time-dependent inequalities have primarily been treated in works of J. L. Lions and H. Bnlzis. The diverse applications of the variational in equalities theory are the topics of the well-known monograph by G. Du vaut and J. L. Lions, Les iniquations en micanique et en physique (1972).

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285

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461210488

ISBN 13

9781461210481

Introduction to Shape Optimization

Shape Sensitivity Analysis

By: Jan Sokolowski,Jean-Paul Zolesio

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Introduction to Shape Optimization

Shape Sensitivity Analysis

By: Jan Sokolowski,Jean-Paul Zolesio

This book is motivated largely by a desire to solve shape optimization prob lems that arise in applications, particularly in structural mechanics and in the optimal control of distributed parameter systems. Many such problems can be formulated as the minimization of functionals defined over a class of admissible domains. Shape optimization is quite indispensable in the design and construction of industrial structures. For example, aircraft and spacecraft have to satisfy, at the same time, very strict criteria on mechanical performance while weighing as little as possible. The shape optimization problem for such a structure consists in finding a geometry of the structure which minimizes a given functional (e. g. such as the weight of the structure) and yet simultaneously satisfies specific constraints (like thickness, strain energy, or displacement bounds). The geometry of the structure can be considered as a given domain in the three-dimensional Euclidean space. The domain is an open, bounded set whose topology is given, e. g. it may be simply or doubly connected. The boundary is smooth or piecewise smooth, so boundary value problems that are defined in the domain and associated with the classical partial differential equations of mathematical physics are well posed. In general the cost functional takes the form of an integral over the domain or its boundary where the integrand depends smoothly on the solution of a boundary value problem.

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Page Count

254

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642581064

ISBN 13

9783642581069

Uncertain Input Data Problems and the Worst Scenario Method

By: Ivan Hlavacek,Jan Chleboun,Ivo Babuska

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Uncertain Input Data Problems and the Worst Scenario Method

By: Ivan Hlavacek,Jan Chleboun,Ivo Babuska

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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485

Publisher

Elsevier

Published Date

ISBN 10

0080543375

ISBN 13

9780080543376

Averaging Methods in Nonlinear Dynamical Systems

By: Jan A. Sanders,Ferdinand Verhulst,James Murdock

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Averaging Methods in Nonlinear Dynamical Systems

By: Jan A. Sanders,Ferdinand Verhulst,James Murdock

Perturbation theory and in particular normal form theory has shown strong growth in recent decades. This book is a drastic revision of the first edition of the averaging book. The updated chapters represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are survey appendices on invariant manifolds. One of the most striking features of the book is the collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with illuminating diagrams.

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Page Count

447

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387489185

ISBN 13

9780387489186

Solution of Variational Inequalities in Mechanics

By: Ivan Hlavacek,Jaroslav Haslinger,Jindrich Necas,Jan Lovisek

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Solution of Variational Inequalities in Mechanics

By: Ivan Hlavacek,Jaroslav Haslinger,Jindrich Necas,Jan Lovisek

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

285

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1461210488

ISBN 13

9781461210481

Book's by Jan Lovisek

Solution of Variational Inequalities in Mechanics

Solution of Variational Inequalities in Mechanics

Introduction to Shape Optimization

Introduction to Shape Optimization

Uncertain Input Data Problems and the Worst Scenario Method

Uncertain Input Data Problems and the Worst Scenario Method

Averaging Methods in Nonlinear Dynamical Systems

Averaging Methods in Nonlinear Dynamical Systems

Solution of Variational Inequalities in Mechanics

Solution of Variational Inequalities in Mechanics

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