Modelling and control in solid mechanics [electronic resource] / A.M. Khludnev, J. Sokolowski.
This book covers the boundary value problems for a wide range of mathematical models of the mechanics of deformable bodies, in particular, the boundary value problems concerning plates and shells, crack theory, and elastoplastic bodies. An essential feature of the discussed boundary value problems i...
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| Online Access: |
Full Text (via Springer) |
|---|---|
| Main Author: | |
| Other Authors: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Basel ; Boston :
Birkhäuser,
1997.
|
| Series: | International series of numerical mathematics ;
v. 122. |
| Subjects: |
MARC
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| 100 | 1 | |a Khludnev, A. M. |0 http://id.loc.gov/authorities/names/n92086196 |1 http://isni.org/isni/0000000033544224. | |
| 245 | 1 | 0 | |a Modelling and control in solid mechanics |h [electronic resource] / |c A.M. Khludnev, J. Sokolowski. |
| 260 | |a Basel ; |a Boston : |b Birkhäuser, |c 1997. | ||
| 300 | |a 1 online resource (xiii, 366 pages) | ||
| 336 | |a text |b txt |2 rdacontent. | ||
| 337 | |a computer |b c |2 rdamedia. | ||
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| 347 | |a text file. | ||
| 347 | |b PDF. | ||
| 490 | 1 | |a International series of numerical mathematics ; |v vol. 122. | |
| 504 | |a Includes bibliographical references (pages 353-363) | ||
| 505 | 0 | |a 1 Introduction -- 1 Elements of mathematical analysis and calculus of variations -- 2 Mathematical models of elastic bodies. Contact problems -- 2 Variational Inequalities in Contact Problems of Elasticity -- 1 Contact between an elastic body and a rigid body -- 2 Contact between two elastic bodies -- 3 Contact between a shallow shell and a rigid punch -- 4 Contact between two elastic plates -- 5 Regularity of solutions to variational inequalities of order four -- 6 Boundary value problems for nonlinear shells -- 7 Boundary value problems for linear shells -- 8 Dynamic problems -- 3 Variational Inequalities in Plasticity -- 1 Preliminaries -- 2 The Hencky model -- 3 Dynamic problem for generalized equations of the flow model -- 4 The Kirchhoff-Love shell. Existence of solutions to the dynamic problem -- 5 Existence of solutions to one-dimensional problems -- 6 Existence of solutions for a quasistatic shell -- 7 Contact problem for the Kirchhoff plate -- 8 Contact problem for the Timoshenko beam -- 9 The case of tangential displacements -- 10 Beam under plasticity and creep conditions -- 11 The contact viscoelastoplastic problem for a beam -- 4 Optimal Control Problems -- 1 Optimal distribution of external forces for plates with obstacles -- 2 Optimal shape of obstacles -- 3 Other cost functionals -- 4 Plastic hinge on the boundary -- 5 Optimal control problem for a beam -- 6 Optimal control problem for a fourth-order variational inequality -- 7 The case of two punches -- 8 Optimal control of stretching forces -- 9 Extreme shapes of cracks in a plate -- 10 Extreme shapes of unilateral cracks -- 11 Optimal control in elastoplastic problems -- 12 The case of vertical and horizontal displacements -- 5 Sensitivity Analysis -- 5.1 Properties of metric projection in Hilbert spaces -- 5.2 Shape sensitivity analysis -- 5.3 Unilateral problems in H20 -- 5.4 Unilateral problems in H2? H10 -- 5.5 Systems with unilateral conditions -- 5.6 Shape estimation problems -- 5.7 Domain optimization problem for parabolic equations -- References. | |
| 520 | |a This book covers the boundary value problems for a wide range of mathematical models of the mechanics of deformable bodies, in particular, the boundary value problems concerning plates and shells, crack theory, and elastoplastic bodies. An essential feature of the discussed boundary value problems is the availability of the inequality type constraints imposed on solutions such as the impenetration condition for contact problems, the yield plasticity condition, etc. As a consequence, the presence of free boundaries is typical of the boundary value problems concerned. The objective of the book is to display some new methods of analyzing such problems, as well as to perform research on new models evolved from engineering practice. Readers will find a variety of new mathematical models describing some contact problems for plates and shells, an equilibrium of plates involving cracks, etc. Furthermore, some new mathematical methods are presented which were specially developed by the authors to study the problems concerned. These help to convey a comprehensive picture of the present state of mathematical problems on the free-boundary elasticity and plasticity theory. The book is intended for postgraduates, scientists and engineers.and for Students interested in problems of modelling and optimal control in the mechanics of deformable bodies. | ||
| 546 | |a English. | ||
| 588 | 0 | |a Print version record. | |
| 650 | 0 | |a Contact mechanics |x Mathematical models. | |
| 650 | 0 | |a Control theory. |0 http://id.loc.gov/authorities/subjects/sh85031658. | |
| 650 | 0 | |a Mathematical optimization. |0 http://id.loc.gov/authorities/subjects/sh85082127. | |
| 650 | 7 | |a Contact mechanics |x Mathematical models. |2 fast |0 (OCoLC)fst00876507. | |
| 650 | 7 | |a Control theory. |2 fast |0 (OCoLC)fst00877085. | |
| 650 | 7 | |a Mathematical optimization. |2 fast |0 (OCoLC)fst01012099. | |
| 700 | 1 | |a Sokołowski, Jan, |d 1949- |0 http://id.loc.gov/authorities/names/n92013717 |1 http://isni.org/isni/0000000081608886. | |
| 776 | 0 | 8 | |i Print version: |a Khludnev, A.M. |t Modelling and control in solid mechanics. |d Basel ; Boston : Birkhäuser, 1997 |w (DLC) 96052344 |w (OCoLC)36074547. |
| 830 | 0 | |a International series of numerical mathematics ; |v v. 122. |0 http://id.loc.gov/authorities/names/n42013597. | |
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| 952 | f | f | |p Can circulate |a University of Colorado Boulder |b Online |c Online |d Online |e TA353 .K47 1997 |h Library of Congress classification |i Ebooks, Prospector |n 1 |