Nonlinear Problems of Elasticity
Springer International Publishing (Verlag)
978-3-031-31329-5 (ISBN)
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This monograph, the second of the two volumes forming the third edition, is an enlarged, completely updated, and extensively revised version of the corresponding material from the authoritative second edition. It is completely self-contained.
This volume contains chapters on tensors, three-dimensional continuum mechanics, constitutive equations and their physically natural restrictions for three-dimensional elasticity and strain-rate viscoelasticity, steady-state and dynamical problems for these theories, general geometrically and mechanically exact theories of rods and shells, methods for treating dynamical problems of strain-rate viscoelasticity, and the role of material response for quasilinear hyperbolic systems of elasticity.
Each chapter contains a wealth of interesting, challenging, and tractable exercises.
From the reviews of the second edition:
"The second extended edition of the reviewed monograph gives a fundamental presentation of problems of nonlinear elasticity. Every chapter is equipped by instructive exercises, unsolved problems and exhaustive historical comments. The book could be very useful to applied mathematicians and engineers using in their works the elasticity theory and ... to specialists dealing with applications of differential equations and bifurcation theory." (Boris V. Loginov, Zentralblatt MATH, Vol. 1098 (24), 2006)
"Antman's impressive work is ... a comprehensivetreatise on nonlinear elasticity and a quintessential example of applied nonlinear analysis. ... The text has been revised and updated, Several new sections have been added ... This book is a 'must' for researchers and graduate students interested in nonlinear continuum mechanics and applied analysis. The work is scholarly and well written. ... 'This book is directed toward scientists, engineers, and mathematicians who wish to see careful treatments of uncompromised problems.'" (Timothy J. Healey, SIAM Review, Vol. 49 (2), 2007)
Background.- The Equations of Motion for Extensible Strings.- Elementary Problems for Elastic Strings.- Planar Steady-State Problems for Elastic Rods.- to Bifurcation Theory and its Applications to Elasticity.- Global Bifurcation Problems for Strings and Rods.- Variational Methods.- Theory of Rods Deforming in Space.- Spatial Problems for Rods.- Axisymmetric Equilibria of Shells.- Tensors.- 3-Dimensional Continuum Mechanics.- 3-Dimensional Theory of Nonlinear Elasticity.- Problems in Nonlinear Elasticity.- Large-Strain Plasticity.- General Theories of Rods.- General Theories of Shells.- Dynamical Problems.- Appendix. Topics in Linear Analysis.- Appendix. Local Nonlinear Analysis.- Appendix. Degree Theory.
| Erscheint lt. Verlag | 14.3.2025 |
|---|---|
| Reihe/Serie | Applied Mathematical Sciences |
| Zusatzinfo | X, 376 p. 25 illus., 1 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Informatik ► Theorie / Studium ► Künstliche Intelligenz / Robotik |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Schlagworte | Applied mathematics • Calculus • Continuum Mechanics • differential equation • Elasticity • Mathematics • Mechanics • Model • Plasticity |
| ISBN-10 | 3-031-31329-1 / 3031313291 |
| ISBN-13 | 978-3-031-31329-5 / 9783031313295 |
| Zustand | Neuware |
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