Ebook: A Primer in Elasticity

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. © 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 .

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This book presents the foundational issues of linear elasticity in a compact, unabridged manner; it is directed to mathematicians and physical scientists who care for approaching this classical subject with rigor and depth.
There are four chapters: the first two illustrate, respectively, the concepts of deformation and strain and of force and stress; the third is devoted to a study of constitutive relations; the last discusses the posing of equilibrium problems. The emphasis is in the description of elasticity as a model whose construction calls for a delicate interplay between physics and mathematics. The conceptual links with general continuum mechanics are carefully indicated. It would not be easy to find in one other book a treatment of such issues as exact and linearized equilibria, the constitutive problems of classification and representation, internal constraints and material symmetries, elastic equilibrium with the Cauchy relations, and elastic equilibrium in the presence of internal constraints.
The book can be be used to teach one-semester advanced undergraduate and graduate courses in elasticity theory to students in applied mathematics and engineering; for this purpose, it contains one hundred exercises of variable difficulty.

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This book presents the foundational issues of linear elasticity in a compact, unabridged manner; it is directed to mathematicians and physical scientists who care for approaching this classical subject with rigor and depth.
There are four chapters: the first two illustrate, respectively, the concepts of deformation and strain and of force and stress; the third is devoted to a study of constitutive relations; the last discusses the posing of equilibrium problems. The emphasis is in the description of elasticity as a model whose construction calls for a delicate interplay between physics and mathematics. The conceptual links with general continuum mechanics are carefully indicated. It would not be easy to find in one other book a treatment of such issues as exact and linearized equilibria, the constitutive problems of classification and representation, internal constraints and material symmetries, elastic equilibrium with the Cauchy relations, and elastic equilibrium in the presence of internal constraints.
The book can be be used to teach one-semester advanced undergraduate and graduate courses in elasticity theory to students in applied mathematics and engineering; for this purpose, it contains one hundred exercises of variable difficulty.
Content:
Front Matter....Pages i-x
Strain....Pages 1-23
Stress....Pages 25-46
Constitutive Assumptions....Pages 47-73
Equilibrium....Pages 75-102
Back Matter....Pages 103-108

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This book presents the foundational issues of linear elasticity in a compact, unabridged manner; it is directed to mathematicians and physical scientists who care for approaching this classical subject with rigor and depth.
There are four chapters: the first two illustrate, respectively, the concepts of deformation and strain and of force and stress; the third is devoted to a study of constitutive relations; the last discusses the posing of equilibrium problems. The emphasis is in the description of elasticity as a model whose construction calls for a delicate interplay between physics and mathematics. The conceptual links with general continuum mechanics are carefully indicated. It would not be easy to find in one other book a treatment of such issues as exact and linearized equilibria, the constitutive problems of classification and representation, internal constraints and material symmetries, elastic equilibrium with the Cauchy relations, and elastic equilibrium in the presence of internal constraints.
The book can be be used to teach one-semester advanced undergraduate and graduate courses in elasticity theory to students in applied mathematics and engineering; for this purpose, it contains one hundred exercises of variable difficulty.
Content:
Front Matter....Pages i-x
Strain....Pages 1-23
Stress....Pages 25-46
Constitutive Assumptions....Pages 47-73
Equilibrium....Pages 75-102
Back Matter....Pages 103-108
....