A Primer in Elasticity

ISBN-13: 9789048155927 / Angielski / Miękka / 2010 / 108 str.

P. Podio-Guidugli

Opis

I want to thank R. L. Fosdick, M. E. Gurtin and W. O. Williams for their detailed criticism of the manuscript. I also thank F. Davi, M. Lembo, P. Nardinocchi and M. Vianello for valuable remarks prompted by their reading of one or another of the many previous drafts, from 1988 to date. Since it has taken me so long to bring this writing to its present form, many other colleagues and students have episodically offered useful comments and caught mistakes: a list would risk to be incomplete, but I am heartily grateful to them all. Finally, I thank V. Nicotra for skillfully transforming my hand sketches into book-quality figures. P. PODIO-GUIDUGLI Roma, April 2000 Journal of Elasticity 58: 1-104,2000. 1 P. Podio-Guidugli, A Primer in Elasticity. (c) 2000 Kluwer Academic Publishers. CHAPTER I Strain 1. Deformation. Displacement Let 8 be a 3-dimensional Euclidean space, and let V be the vector space associated with 8. We distinguish a point p E 8 both from its position vector p(p): = (p-o) E V with respect to a chosen origin 0 E 8 and from any triplet ( 1, 2, 3) E R3 of coordinates that we may use to label p. Moreover, we endow V with the usual inner product structure, and orient it in one of the two possible manners. It then makes sense to consider the inner product a

Spis treści

Preface. I: Strain. 1. Deformation Displacement. 2. Rigid Deformations. Pure Strains. 3. Strain Measures. 4. Small Strain. 5. Simple Deformations. 6. Divergence Identities. II: Stress. 7. Forces. Balances. 8. Stress. Dynamical Processes. 9. Simple Equilibrium Solutions. Normal and Shear Forces. 10. Alternative Forms of the Basic Balance Laws. 11. Power. Stress Power. 12. Exact and Linearized Equilibrium Theories. III: Constitutive Assumptions. 13. Linearly Elastic Materials. 14. Material Symmetry. 15. Fourth-Order Tensors. 16. Problems of Classification and Representation. 17. Internal Constraints. 18. Constraints and Material Symmetries. 19. Interpretation of Material Moduli. IV: Equilibrium. 20. Classical, Strong, and Weak Formulations. 21. Variational Formulation. The Principle of Minimum Potential Energy. 22. Minimum Complementary Energy. Variational Principles. 23. Compatible Field and Boundary Operators. 24. Generalized Boundary Conditions. 25. Elastic Equilibrium with the Cauchy Relations. 26. Elastic Equilibrium in the Presence of Internal Constraints. References. Subject Index.