A course in elasticity

by Fraeijs de Veubeke, B.

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Title Statements

Full title :A course in elasticity / B.M. Fraeijs de Veubeke ; translated by F.A. Ficken ; with the editorial assistance of D.A. Simons.

Summary

This book is based on lecture notes of the late Professor de Veubeke. The subject is presented at a level suitable for graduate students in engineering, physics, or mathematics. Some exposure to linear algebra, complex analysis, variational calculus, or basic continuum mechanics would be helpful. The first third of the book contains the fundamentals of the theory of elasticity. Kinematics of continuous media, the notions of stress and equilibrium, conservation of energy, 'and the elastic constitutive law are each treated first in a nonlinear context, then specialized to the linear case. The remainder of the book is given to three classic applications of the theory, each supplemented by original re sults based on the use of complex variables. Each one of the three topics - Saint-Venant's theory of prismatic beams, plane deformations, and the bending of plates - is first pre sented and analyzed in general, then rounded out with numerous specific and sometimes novel examples. The following notational conventions are generally in force, except where noted to the contrary: lower case boldface letters denote vectors or triples of Cartesian co ordinates, upper case boldface letters denote 3 x 3 matrices, repeated lower case Latin subscripts are summed over (1,2,3), and non-repeated lower case Latin subscripts are assumed to range over (1,2,3).

Edition Statements

Publication Date:©1979.

Publication Statements

Publisher(s):Springer-Verlag
Place of Publication:New York
Language:eng
Publication Date:©1979.

The Physical Object

Description:1 online resource (xi, 330 pages) : : illustrations

Edition Identifiers

oclc:ocn698408403
LC Classification:QA1
Dewey Decimal:510/.8 s

1. Kinematics of Continuous Media -- 1.1. Material and Spatial Coordinates -- 1.2. Neighborhood Transformations -- 1.3 Composition of Changes of Configuration -- 1.4 Measure of the State of Local Deformation. Green's and Jaumann's Strain -- 1.5 Rigid-Body Rotations of a Neighborhood -- 1.6 The Kinematical Decomposition of the Jacobian Matrix -- 1.7 Geometric Interpretation of Infinitesimal Strains -- 1.8 The Eulerian Viewpoint in Kinematics. Almansi's Strain -- 1.9 Eulerian Measures of Rates of Deformation and Rotation -- 1.10 Temporal, Variation of the Polar Decomposition of the Jacobian Matrix -- 2. Statics and Virtual Work -- 2.1. The Concept of Stress. True Stress -- 2.2. The Piola Stresses -- 2.3. Translational Equilibrium Equations -- 2.4. Rotational Equilibrium Equations -- 2.5. Statics and Virtual Work -- 2.6. Commutativity of the Operators? and Di -- 2.7 Virtual Work in a Continuous Medium -- 2.8. Statics and Virtual Power for True Stresses -- 2.9. Statics and Virtual Work in Infinitesimal Changes of Configuration -- 3. Conservation of Energy -- 3.1. Constitutive Equations for Piola's Stresses -- 3.2. The Kirchhoff-Trefftz Stresses -- 3.3 The Constitutive Equations of Geo…

Subjects

Analyse élastique (Ingénierie) Elastic analysis (Engineering) élasticité elasticiteit Elasticity Elastizitätstheorie Engenharia civil (estruturas) Matemática aplicada Mecanica, Elasticidade E Reologia modulus of elasticity