Advanced Mechanics of Materials / Edition 1

by Roman Solecki, R. Jay Conant

Overview

Advanced Mechanics of Materials bridges the gap between elementary mechanics of materials courses and more rigorous graduate courses in mechanics of deformable bodies (i.e., continuum mechanics, elasticity, plasticity) taken by graduate students. Covering both traditional and modern topics, the text is ideal for senior undergraduate and beginning graduate courses in advanced strength of materials, advanced mechanics of materials, or advanced mechanics of solids. Rather than exclusively emphasizing either fundamentals or applications, it provides a balance between the two, teaching fundamentals while using real-world applications to solidify student comprehension.
Advanced Mechanics of Materials features: · applications to contemporary practice · use of modern computer tools, including Mathcad · an introduction to modern topics, such as piezoelectricity, fracture mechanics, and viscoelasticity
Chapters two through five cover theoretical and conceptual development and contain relatively simple examples aimed at enhancing student understanding. The remaining chapters apply the theory to specific classes of problems such as: · beam bending, including the effects of piezoelectricity · plate bending · beam and plate vibration and buckling · introductory concepts of fracture mechanics · finite element analysis
The authors assume that students will have an understanding of elementary (statics, dynamics, strength of materials) and intermediate (aircraft structures, machine design) mechanics.

Product Details

ISBN-13:	9780195143720
Publisher:	Oxford University Press
Publication date:	02/06/2003
Series:	Engineering & Technology
Edition description:	New Edition
Pages:	784
Product dimensions:	9.20(w) x 7.50(h) x 1.40(d)

About the Author

University of Connecticut

Montana State University

Table of Contents

Each chapter starts with a Summary and ends with References and Problems.Preface1. IntroductionReference2. Stress and Equilibrium Equations2.1. Concept of Stress2.2. Stress Components and Equilibrium Equations2.2.1. Stress Components in Cartesian Coordinates—Matrix Representation2.2.2. Symmetry of Shear Stresses2.2.3. Stresses Acting on an Inclined Plane2.2.4. Normal and Tangential Stresses—Stress Boundary Conditions2.2.52.2.6. Transformation of Stress Components—Stress as a TensorStress Components in Polar Coordinates2.2.7. Equilibrium Equations in Cartesian Coordinates2.2.8. Equilibrium Equations in Polar Coordinates2.2.9. Applicability of Equilibrium Equations2.3. Principal Stresses and Invariants2.3.1. Characteristic Equation2.3.2. Principal Stresses and Principal Directions2.3.3. Plane Stress—Principal Stresses and Principal Directions2.3.4. Plane Stress—Mohr's Circle2.3.5. Octahedral Stresses2.3.6. Mean and Deviatoric Stresses2.4. Three-dimensional Mohr's Circles2.5. Stress Analysis and Symbolic Manipulation3. Displacement and Strain3.1. Introduction3.2. Strain-Displacement Equations3.3. Compatibility3.4. Specification of the State of Strain at a Point3.4.1. Strain Gages3.5. Rotation3.6. Principal Strains3.7. Strain Invariants3.8. Volume Changes and Dilatation3.9. Strain Deviator3.10. Strain-Displacement Equations in Polar Coordinates4. Relationships Between Stress and Strain4.1. Introduction4.2. Isotropic Materials—A Physical Approach4.2.1. Coincidence of Principal Stress and Principal Strain Axes4.2.2. Relationship between G and E4.2.3. Bulk Modulus4.3. Two Dimensional Stress-Strain Laws—Plane Stress and Plane Strain4.3.1. Plane Stress4.3.2. Plane Strain4.4. Restrictions on Elastic Constants for Isotropic Materials4.5. Anisotropic Materials4.6. Material Symmetries4.7. Materials with a Single Plane of Elastic Symmetry4.8. Orthotropic Materials4.8.1. Engineering Material Constants for Orthotropic Materials4.8.2. Orthotropic Materials under Conditions of Plane Stress4.8.3. Stress-Strain Relations in Coordinates Other than the Principal Material Coordinates4.9. Transversely Isotropic Materials4.10. Isotropic Materials—A Mathematical Approach4.11. Stress-Strain Relations for Viscoelastic Materials4.12. Material Behavior beyond the Elastic Limit4.12.1. Additional Experimental Observations4.13. Criteria for Yielding4.13.1. Maximum Shear Theory4.13.2. Distortion Energy Theory4.13.3. Comparison of the Two Theories4.14. Stress-Strain Relations for Elastic-Perfectly Plastic Materials4.15. Stress-Strain Relations when the Temperature Field is Nonuniform4.16. Stress-Strain Relations for Piezoelectric Materials5. Energy Concepts5.1. Fundamental Concepts and Definitions5.2. Work5.2.1. Work Done by Stresses Acting on an Infinitesimal Element5.3. First Law of Thermodynamics5.4. Second Law of Thermodynamics5.5. Some Simple Applications Involving the First Law5.5.1. Maxwell's Reciprocity Theorem5.6. Strain Energy5.6.1. Complementary Strain Energy5.6.2. Strain Energy in Beams5.7. Castigliano's Theorem5.8. Principle of Virtual Work5.8.1. Principle of Virtual Work for Particles and Rigid Bodies5.8.2. Principle of Virtual Work for Deformable Bodies5.9. Theorem of Minimum Total Potential Energy5.10. Applications of the Theorem of Minimum Total Potential Energy5.11. Rayleigh-Ritz Method5.12. Principle of Minimum Complementary Energy5.13. Betti-Rayleigh Reciprocal Theorem5.14. General Stress-Strain Relationships for Elastic Materials6. Numerical Methods I6.1. Method of Finite Differences6.1.1. Application to Ordinary Differential Equations6.1.2. Application to Partial Differential Equations6.2.. Method of Iteration6.3.. Method of Collocation7. Numerical Methods II: Finite Elements7.1. Introduction7.2. Two-Dimensional Frames7.3. Overall Approach7.4. Member Force-Displacement Relationships7.5. Assembling the Pieces7.6. Solving the Problem7.7. An Example7.8. Notes Concerning the Structure Stiffness Matrix7.10. Finite Element Analysis7.11. Constant Strain Triangle7.12. Element Assembly7.13. Notes on Using Finite Element Programs7.13.1. Interelement Compatibility7.13.2. Inherent Overstiffness in a Finite Element7.13.3. Bending and the Constant Strain Triangle7.14. Closure8. Beams8.1. Bending of Continuous Beams8.1.1. Introduction8.1.2. Method of Initial Parameters8.1.3. Application of Castigliano's Theorem8.2. Unsymmetric Bending of Straight Beams8.3. Curved Beams8.3.1. Out-of-Plane Loaded Beams and Rings8.3.2. A Transversely Loaded Circular Ring Supported by Three or More Supports (Biezeno's Theorem)8.3.3. In-Plane Loaded Curved Beams (Arches) and Rings8.3.4. Bending, Stretching, and Twisting of Springs8.4. Beams on Elastic Foundations8.4.1. Equilibrium Equation for a Straight Beam8.4.2. Infinite Beams8.4.3. Finite Beams8.4.4. Stresses in Storage Tanks8.5. Influence Functions (Green's Functions) for Beams8.5.1. Straight Beams8.5.2. Straight Beams on Elastic Foundations8.6. Thermal Effects8.7. Composite Beams8.7.1. Stresses, Bending Moments, and Bending Stiffness of a Laminated Beam8.7.2. Differential Equation for Deflection of a Laminated Beam8.8. Limit Analysis8.9. Fourier Series and Applications8.10. Approximate Methods in the Analysis of Beams8.10.1. Finite Differences—Examples8.10.2. Rayleigh-Ritz Method—Examples8.11. Piezoelectric Beams8.11.1. Piezoelectric Bimorph8.11.2. Piezoelectric Multimorph8.11.3. Castigliano's Theorem for Piezoelectric Beams8.11.4. Thin Curved Piezoelectric Beams8.11.5. Castigliano's Theorem for Thin Curved Piezoelectric Beams9. Elementary Problems in Two- and Three-Dimensional Solid Mechanics9.1. Problem Formulation—Boundary Conditions9.2. Compatibility of Elastic Stress Components9.3. Thick-Walled Cylinders and Circular Disks9.3.1. Equilibrium Equation and Strains9.3.2. Elastic, Homogeneous Disks and Cylinders9.3.3. Thermal Effects9.3.4. Plastic Cylinder9.3.5. Composite Disks and Cylinders9.3.6. Rotating Disks of Variable Thickness9.4. Airy's Stress Function9.5. Torsion9.5.1. Circular Cross Section9.5.2. Noncircular Prisms—Saint-Venant's Theory9.5.3. Membrane Analogy9.5.4. Rectangular and Related Cross Sections9.5.5. Torsion of Hollow, Single-Cell and Multiple-Cell Members9.5.6. Pure Plastic Torsion9.6. Application of Numerical Methods to Solution of Two-Dimensional Elastic Problems Elastic Problems10. Plates10.1. Introduction10.2. Axisymmetric Bending of Circular Plates10.2.1. General Expressions10.2.2. Particular Solutions for Selected Types of Axisymmetric Loads10.2.3. Solid Plate: Boundary Conditions, Examples10.2.4. Solid Plate: Influence Functions (Green's Functions)10.2.5. Solid Plate with Additional Support10.2.6.. Annular Plate: Boundary Conditions and Examples10.2.7. Annular Plate: Influence Functions (Green's Functions)10.3. Bending of Rectangular Plates10.3.1. Boundary Conditions10.3.2. Bending of a Simply Supported Rectangular Plate10.4. Plates on Elastic Foundation10.5. Strain Energy of an Elastic Plate10.6. Membranes10.7. Composite Plates10.7.1. Laminated Plates with Isotropic Layers10.7.2. Laminated Plates with Orthotropic Layers10.8. Approximate Methods in the Analysis of Plates and Membranes10.8.1. Application of Finite Differences10.8.2. Examples of Application of the Rayleigh-Ritz Method11. Buckling and Vibration11.1. Buckling and Vibration of Beams and Columns1.1. Equation of Motion and Its Solution11.1.2. Frequencies and Critical Loads for Various Boundary Conditions11.1.3. Applications of Rayleigh-Ritz Method11.2. Buckling and Vibration of Rings, Arches, and Thin-Walled Tubes11.2.1. Equations of Motion and Their Solution11.3. Buckling and Vibration of Thin Rectangular Plates12. Introduction to Fracture Mechanics12.1. Introductory Concepts12.2. Linear Cracks in Two-Dimensional Elastic Solids—Williams' Solution, Stress Singularity12.3. Stress Intensity Factor12.4. Crack Driving Force as an Energy Rate12.5. Relation Between G and the Stress Intensity Factors12.6. Some Simple Cases of Calculation of Stress Intensity Factors12.7. The J-IntegralAppendix A. MatricesAppendix B. Coordinate Transformations