Introduction to Linear Elasticity
2nd Edition
Published on 6. December 2012
256 pages
978-1-4612-4296-3 (ISBN)
Description
"Elasticity is one of the crowning achievements of Western culture!" ex claimed my usually reserved colleague Professor George Zahalak during a meeting to discuss the graduate program in Solid Mechanics. Although my thoughts on the theory of elasticity had not been expressed in such noble terms, it was the same admiration for the creative efforts of the premier physicists, mathematicians and mechanicians of the 19th and 20th centuries that led me to attempt to popularize the basis of solid mechanics in this introductory form. The book is intended to provide a thorough grounding in tensor-based theory of elasticity, which is rigorous in treatment but limited in scope. It is directed to advanced undergraduate and graduate students in civil, mechani calor aeronautical engineering who may ultimately pursue more applied studies. It is also hoped that a few may be inspired to delve deeper into the vast literature on the subject. A one-term course based on this material may replace traditional Advanced Strength of Materials in the curriculum, since many of the fundamental topics grouped under that title are treated here, while those computational techniques that have become obsolete due to the availability of superior, computer-based numerical methods are omitted. Little, if any, originality is claimed for this work other than the selection, organization and presentation of the material. The principal historical con tributors are noted in the text and several modern references are liberally cited.
More details
Series
Edition
Second Edition 1994
Language
English
Place of publication
New York
United States
Publishing group
Springer US
Target group
Primary & secondary/elementary & high school
Illustrations
256 p.
ISBN-13
978-1-4612-4296-3 (9781461242963)
DOI
10.1007/978-1-4612-4296-3
Schweitzer Classification
Other editions
New editions
Phillip L. Gould
Introduction to Linear Elasticity
E-Book
03/2013
3rd Edition
Springer
€80.24
Available for download
Additional editions
Phillip L. Gould
Introduction to Linear Elasticity
Book
12/1993
2nd Edition
Springer
€101.60
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Content
1. Introduction and Mathematical Preliminaries.- 1.1 Scope.- 1.2 Vector Algebra.- 1.3 Scalar and Vector Fields.- 1.4 Indicial Notation.- 1.5 Coordinate Rotation.- 1.6 Cartesian Tensors.- 1.7 Algebra of Cartesian Tensors.- 1.8 Operational Tensors.- 1.9 Computational Examples.- Exercises.- References.- 2. Traction, Stress and Equilibrium.- 2.1 Introduction.- 2.2 State of Stress.- 2.3 Equilibrium.- 2.4 Principal Stress.- 2.5 Stresses in Principal Coordinates.- 2.6 Properties and Special States of Stress.- Exercises.- References.- 3. Deformations.- 3.1 Introduction.- 3.2 Strain.- 3.3 Physical Interpretation of Strain Tensor.- 3.4 Principal Strains.- 3.5 Volume and Shape Changes.- 3.6 Compatibility.- 3.7 Computational Example.- Exercises.- References.- 4. Material Behavior.- 4.1 Introduction.- 4.2 Uniaxial Behavior.- 4.3 Generalized Hooke's Law.- 4.4 Thermal Strains.- 4.5 Physical Data.- Exercises.- References.- 5. Formulation, Uniqueness and Solution Strategies.- 5.1 Introduction.- 5.2 Displacement Formulation.- 5.3 Force Formulation.- 5.4 Other Formulations.- 5.5 Uniqueness.- 5.6 Membrane Equation.- 5.7 Solution Strategies.- Exercises.- References.- 6. Extension, Bending and Torsion.- 6.1 Introduction.- 6.2 Prismatic Bar under Axial Loading.- 6.3 Cantilever Beam under End Loading.- 6.4 Torsion.- Exercises.- References.- 7. Two-Dimensional Elasticity.- 7.1 Introduction.- 7.2 Plane Stress Equations.- 7.3 Plane Strain Equations.- 7.4 Cylindrical Coordinates.- 7.5 Thick-Walled Cylinder or Disk.- 7.6 Sheet with Small Circular Hole.- 7.7 Curved Beam.- 7.8 Rotational Dislocation.- 7.9 Narrow, Simply Supported Beam.- 7.10 Semi-Infinite Plate with a Concentrated Load.- Exercises.- References.- 8. Bending of Thin Plates.- 8.1 Introduction.- 8.2 Assumptions.- 8.3 Formulation.- 8.4Solutions.- 8.5 Commentary.- Exercises.- References.- 9. Time-Dependent Effects.- 9.1 Introduction.- 9.2 Vibrations in an Infinite Elastic Medium.- 9.3 Free Vibration.- 9.4 Uniform Rotation of a Beam.- Exercises.- References.- 10. Energy Principles.- 10.1 Introduction.- 10.2 Conservation of Energy.- 10.3 Strain Energy.- 10.4 Work of External Loading.- 10.5 Principle of Virtual Work.- 10.6 Variational Principles.- 10.7 Direction Variational Methods.- Exercises.- References.- 11. Strength and Failure Criteria.- 11.1 Introduction.- 11.2 Isotropic Materials.- 11.3 Yield Surfaces.- 11.4 Anisotropic Materials.- 11.5 Failure of Structures.- Exercises.- References.- 12. Something New.
