Nonlinear Problems of Elasticity (3rd Ed., 3rd ed. 2024)
I: Strings, Cables, Rods, and Shells
Applied Mathematical Sciences Series, Vol. 216

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Language: English

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382 p. · 15.5x23.5 cm · Hardback

Enlarged, updated, and extensively revised, this second edition illuminates specific problems of nonlinear elasticity, emphasizing the role of nonlinear material response. Opening chapters discuss strings, rods, and shells, and applications of bifurcation theory and the calculus of variations to problems for these bodies. Subsequent chapters cover tensors, three-dimensional continuum mechanics, three-dimensional elasticity , general theories of rods and shells, and dynamical problems. Each chapter includes interesting, challenging, and tractable exercises.

Preface* Chapter 1. Background* Chapter 2. The Equations of Motion for Extensible Strings* Chapter 3. Elementary Problems for Elastic Strings* Chapter 4. Planar Steady-State Problems for Elastic Rods* Chapter 5. Introduction to Bifurcation Theory and it's Applications to Elasticity* Chapter 6. Global Bifurcation Problems for Strings and Rods* Chapter 7. Variational Methods* Chapter 8. Theory of Rods Deforming in Space* Chapter 9. Spatial Problems for Rods* Chapter 10. Axisymmetric Equilibria of Shells* Chapter 11. Tensors* Chapter 12. 3-Dimensional Continuum* Chapter 13. 3-Dimensional Theory of Nonlinear Elasticity* Chapter 14. Problems in Nonlinear Elasticity* Chapter 15. Large-Strain Plasticity* Chapter 16. General Theories of Rods* Chapter 17. General Theories of Shells* Chapter 18. Dynamical Problems* Chapter 19. Appendix: Topics in Linear Analysis* Chapter 20. Appendix: Local Nonlinear Analysis* Chapter 21. Appendix: Degree Theory and it's Applications* References* Index

Highlights the mathematical tools of nonlinear analysis through self-contained presentations

Suitable for mathematicians and industry professionals studying nonlinear elasticity

Contains chapter-level exercises & supplementary material