Introduction to Linear Elasticity
Phillip L. Gould(Author)
Springer (Publisher)
2nd Edition
Published on 31. July 2012
Book
Paperback/Softback
256 pages
978-1-4612-8728-5 (ISBN)
Article exhausted; check different version
Description
This applications-oriented introduction fills an important gap in the field of solid mechanics. Offering a thorough grounding in the tensor-based theory of elasticity for courses in mechanical, civil, materials or aeronautical engineering, it allows students to apply the basic notions of mechanics to such important topics as stress analysis. Further, they will also acquire the necessary background for more advanced work in elasticity, plasticity, shell theory, composite materials and finite element mechanics. This second edition features new chapters on the bending of thin plates, time-dependent effects, and strength and failure criteria.
More details
Edition
2nd ed. 1994
Language
English
Place of publication
NY
United States
Target group
Professional and scholarly
Edition type
Revised edition
Product notice
Paperback (trade)
Illustrations
2
2 s/w Tabellen
black & white illustrations
Dimensions
Height: 23.5 cm
Width: 15.5 cm
Thickness: 13 mm
Weight
393 gr
ISBN-13
978-1-4612-8728-5 (9781461287285)
DOI
10.1007/978-1-4612-4296-3
Schweitzer Classification
Other editions
Additional editions
Phillip L. Gould
Introduction to Linear Elasticity
Book
12/1993
2nd Edition
Springer
€101.60
Article exhausted; check for reprint
Content
1. Introduction and Mathematical Preliminaries.- 1.1 Scope.- 1.2 Vector Algebra.- 1.3 Scalar and Vector Fields.- 1.3.1 Definitions.- 1.3.2 Gradient.- 1.3.3 Operators.- 1.3.4 Divergence.- 1.3.5 Curl.- 1.3.6 Integral Theorems.- 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.- 2.2.1 Traction and Couple-Stress Vectors.- 2.2.2 Components of Stress.- 2.2.3 Stress at a Point.- 2.2.4 Stress on a Normal Plane.- 2.2.5 Dyadic Representation of Stress.- 2.2.6 Computational Example.- 2.3 Equilibrium.- 2.3.1 Physical and Mathematical Principles.- 2.3.2 Linear Momentum.- 2.3.3 Angular Momentum.- 2.3.4 Computational Example.- 2.4 Principal Stress.- 2.4.1 Definition and Derivation.- 2.4.2 Computational Format, Stress Invariants and Principal Coordinates.- 2.4.3 Computational Example.- 2.5 Stresses in Principal Coordinates.- 2.5.1 Stresses on an Oblique Plane.- 2.5.2 Stresses on Octahedral Planes.- 2.5.3 Absolute Maximum Shearing Stress.- 2.5.4 Computational Example.- 2.6 Properties and Special States of Stress.- 2.6.1 Projection Theorem.- 2.6.2 Plane Stress.- 2.6.3 Linear Stress.- 2.6.4 Pure Shear.- 2.6.5 Hydrostatic 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.- 6.3.1 Elementary Beam Theory.- 6.3.2 Elasticity Theory.- 6.4 Torsion.- 6.4.1 Torsion of Circular Shaft.- 6.4.2 Torsion of Solid Prismatic Shafts.- 6.4.3 Torsion of Elliptical Shaft.- 6.4.4 Membrane Analogy.- Exercises.- References.- 7. Two-Dimensional Elasticity.- 7.1 Introduction.- 7.2 Plane Stress Equations.- 7.3 Plane Strain Equations.- 7.4 Cylindrical Coordinates.- 7.4.1 Geometric Relations.- 7.4.2 Transformation of Stress Tensor and Compatibility Equation.- 7.4.3 Axisymmetric Stresses and Displacements.- 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.- 8.3.1 Geometric Relationships.- 8.3.2 Strains and Stresses.- 8.3.3 Plate Equation.- 8.3.4 Polar Coordinates.- 8.4 Solutions.- 8.4.1 Rectangular Plate.- 8.4.2 Circular Plate.- 8.5 Commentary.- Exercises.- References.- 9. Time-Dependent Effects.- 9.1 Introduction.- 9.2 Vibrations in an Infinite Elastic Medium.- 9.2.1 Equilibrium Equations.- 9.2.2 Longitudinal Vibrations.- 9.2.3 Transverse Vibrations.- 9.2.4 Harmonic Vibrations.- 9.3 Free Vibration.- 9.3.1 Equations of Motion.- 9.3.2 Orthogonality Conditions.- 9.3.3 Rayleigh's Quotient.- 9.3.4 Axial Vibration of a Bar.- 9.4 Uniform Rotation of a Beam.- 9.4.1 Equilibrium Equations.- 9.4.2 Boundary Conditions.- 9.4.3 Semi-Inverse Solution.- 9.4.4 Two-Dimensional Problem.- 9.4.5 Circular Cross Section.- Exercises.- References.- 10. Energy Principles.- 10.1 Introduction.- 10.2 Conservation of Energy.- 10.3 Strain Energy.- 10.3.1 Strain Energy Density.- 10.3.2 Strain Energy Density of Distortion.- 10.4 Work of External Loading.- 10.5 Principle of Virtual Work.- 10.5.1 Definitions.- 10.5.2 Principle of Virtual Displacements.- 10.5.3 Principle of Virtual Forces.- 10.5.4 Reciprocal Theorems.- 10.6 Variational Principles.- 10.6.1 Definitions.- 10.6.2 Principle of Minimum Total Potential Energy.- 10.6.3 Principle of Minimum Complementary Energy.- 10.7 Direction Variational Methods.- 10.7.1 Motivation.- 10.7.2 Rayleigh-Ritz Method.- 10.7.3 Torsion of Rectangular Cross Section.- 10.7.4 Commentary.- Exercises.- References.- 11. Strength and Failure Criteria.- 11.1 Introduction.- 11.2 Isotropic Materials.- 11.2.1 Classical Tests.- 11.2.2 Failure Theories.- 11.2.3 Invariants.- 11.3 Yield Surfaces.- 11.3.1 General.- 11.3.2 Tresca Yield Condition.- 11.3.3 von Mises Yield Condition.- 11.3.4 General Criterion for Isotropic Media.- 11.4 Anisotropic Materials.- 11.4.1 Objectives.- 11.4.2 Failure Surface.- 11.4.3 Specializations.- 11.4.4 Evaluation of Components.- 11.5 Failure of Structures.- Exercises.- References.- 12. Something New.