This is an advanced mechanics of materials textbook dedicated to upper level undergraduate or postgraduate students in mechanical, civil and aeronautical engineering departments. The text covers subject matter generally referred to as advanced mechanics of materials or advanced strength of materials. Unique features include introduction to modern topics such as fracture mechanics and viscoelasticity. Unlike the competition, the text introduces more applications to contemporary practice, as well as modern computer tools (MATLAB).

Table of Contents:
Each chapter starts with a Summary and ends with References and Problems. Preface 1. Introduction Reference 2. Stress and Equilibrium Equations 2.1: Concept of Stress 2.2: Stress Components and Equilibrium Equations 2.2.1: Stress Components in Cartesian Coordinates--Matrix Representation 2.2.2: Symmetry of Shear Stresses 2.2.3: Stresses Acting on an Inclined Plane 2.2.4: Normal and Tangential Stresses--Stress Boundary Conditions 2.2.5: Transformation of Stress Components--Stress as a Tensor 2.2.7: Equilibrium Equations in Cartesian Coordinates 2.2.8: Equilibrium Equations in Polar Coordinates 2.2.9: Applicability of Equilibrium Equations 2.3: Principal Stresses and Invariants 2.3.1: Characteristic Equation 2.3.2: Principal Stresses and Principal Directions 2.3.3: Plane Stress--Principal Stresses and Principal Directions 2.3.4: Plane Stress--Mohr's Circle 2.3.5: Octahedral Stresses 2.3.6: Mean and Deviatoric Stresses 2.4: Three-dimensional Mohr's Circles 2.5: Stress Analysis and Symbolic Manipulation 3. Displacement and Strain 3.1: Introduction 3.2: Strain-Displacement Equations 3.3: Compatibility 3.4: Specification of the State of Strain at a Point 3.4.1: Strain Gages 3.5: Rotation 3.6: Principal Strains 3.7: Strain Invariants 3.8: Volume Changes and Dilatation 3.9: Strain Deviator 3.10: Strain-Displacement Equations in Polar Coordinates 4. Relationships Between Stress and Strain 4.1: Introduction 4.2: Isotropic Materials--A Physical Approach 4.2.1: Coincidence of Principal Stress and Principal Strain Axes 4.2.2: Relationship between G and E 4.2.3: Bulk Modulus 4.3: Two Dimensional Stress-Strain Laws--Plane Stress and Plane Strain 4.3.1: Plane Stress 4.3.2: Plane Strain 4.4: Restrictions on Elastic Constants for Isotropic Materials 4.5: Anisotropic Materials 4.6: Material Symmetries 4.7: Materials with a Single Plane of Elastic Symmetry 4.8: Orthotropic Materials 4.8.1: Engineering Material Constants for Orthotropic Materials 4.8.2: Orthotropic Materials under Conditions of Plane Stress 4.8.3: Stress-Strain Relations in Coordinates Other than the Principal Material Coordinates 4.9: Transversely Isotropic Materials 4.10: Isotropic Materials--A Mathematical Approach 4.11: Stress-Strain Relations for Viscoelastic Materials 4.12: Material Behavior beyond the Elastic Limit 4.12.1: Additional Experimental Observations 4.13: Criteria for Yielding 4.13.1: Maximum Shear Theory 4.13.2: Distortion Energy Theory 4.13.3: Comparison of the Two Theories 4.14: Stress-Strain Relations for Elastic-Perfectly Plastic Materials 4.15: Stress-Strain Relations when the Temperature Field is Nonuniform 4.16: Stress-Strain Relations for Piezoelectric Materials 5. Energy Concepts 5.1: Fundamental Concepts and Definitions 5.2: Work 5.2.1: Work Done by Stresses Acting on an Infinitesimal Element 5.3: First Law of Thermodynamics 5.4: Second Law of Thermodynamics 5.5: Some Simple Applications Involving the First Law 5.5.1: Maxwell's Reciprocity Theorem 5.6: Strain Energy 5.6.1: Complementary Strain Energy 5.6.2: Strain Energy in Beams 5.7: Castigliano's Theorem 5.8: Principle of Virtual Work 5.8.1: Principle of Virtual Work for Particles and Rigid Bodies 5.8.2: Principle of Virtual Work for Deformable Bodies 5.9: Theorem of Minimum Total Potential Energy 5.10: Applications of the Theorem of Minimum Total Potential Energy 5.11: Rayleigh-Ritz Method 5.12: Principle of Minimum Complementary Energy 5.13: Betti-Rayleigh Reciprocal Theorem 5.14: General Stress-Strain Relationships for Elastic Materials 6. Numerical Methods I 6.1: Method of Finite Differences 6.1.1: Application to Ordinary Differential Equations 6.1.2: Application to Partial Differential Equations 6.2.: Method of Iteration 6.3.: Method of Collocation 7. Numerical Methods II: Finite Elements 7.1: Introduction 7.2: Two-Dimensional Frames 7.3: Overall Approach 7.4: Member Force-Displacement Relationships 7.5: Assembling the Pieces 7.6: Solving the Problem 7.7: An Example 7.8: Notes Concerning the Structure Stiffness Matrix 7.10: Finite Element Analysis 7.11: Constant Strain Triangle 7.12: Element Assembly 7.13: Notes on Using Finite Element Programs 7.13.1: Interelement Compatibility 7.13.2: Inherent Overstiffness in a Finite Element 7.13.3: Bending and the Constant Strain Triangle 7.14: Closure 8. Beams 8.1: Bending of Continuous Beams 8.1.1: Introduction 8.1.2: Method of Initial Parameters 8.1.3: Application of Castigliano's Theorem 8.2: Unsymmetric Bending of Straight Beams 8.3: Curved Beams 8.3.1: Out-of-Plane Loaded Beams and Rings 8.3.2: A Transversely Loaded Circular Ring Supported by Three or More Supports (Biezeno's Theorem) 8.3.3: In-Plane Loaded Curved Beams (Arches) and Rings 8.3.4: Bending, Stretching, and Twisting of Springs 8.4: Beams on Elastic Foundations 8.4.1: Equilibrium Equation for a Straight Beam 8.4.2: Infinite Beams 8.4.3: Finite Beams 8.4.4: Stresses in Storage Tanks 8.5: Influence Functions (Green's Functions) for Beams 8.5.1: Straight Beams 8.5.2: Straight Beams on Elastic Foundations 8.6: Thermal Effects 8.7: Composite Beams 8.7.1: Stresses, Bending Moments, and Bending Stiffness of a Laminated Beam 8.7.2: Differential Equation for Deflection of a Laminated Beam 8.8: Limit Analysis 8.9: Fourier Series and Applications 8.10: Approximate Methods in the Analysis of Beams 8.10.1: Finite Differences--Examples 8.10.2: Rayleigh-Ritz Method--Examples 8.11: Piezoelectric Beams 8.11.1: Piezoelectric Bimorph 8.11.2: Piezoelectric Multimorph 8.11.3: Castigliano's Theorem for Piezoelectric Beams 8.11.4: Thin Curved Piezoelectric Beams 8.11.5: Castigliano's Theorem for Thin Curved Piezoelectric Beams 9. Elementary Problems in Two- and Three-Dimensional Solid Mechanics 9.1: Problem Formulation--Boundary Conditions 9.2: Compatibility of Elastic Stress Components 9.3: Thick-Walled Cylinders and Circular Disks 9.3.1: Equilibrium Equation and Strains 9.3.2: Elastic, Homogeneous Disks and Cylinders 9.3.3: Thermal Effects 9.3.4: Plastic Cylinder 9.3.5: Composite Disks and Cylinders 9.3.6: Rotating Disks of Variable Thickness 9.4: Airy's Stress Function 9.5: Torsion 9.5.1: Circular Cross Section 9.5.2: Noncircular Prisms--Saint-Venant's Theory 9.5.3: Membrane Analogy 9.5.4: Rectangular and Related Cross Sections 9.5.5: Torsion of Hollow, Single-Cell and Multiple-Cell Members 9.5.6: Pure Plastic Torsion 9.6: Application of Numerical Methods to Solution of Two-Dimensional Elastic Problems Elastic Problems 10. Plates 10.1: Introduction 10.2: Axisymmetric Bending of Circular Plates 10.2.1: General Expressions 10.2.2: Particular Solutions for Selected Types of Axisymmetric Loads 10.2.3: Solid Plate: Boundary Conditions, Examples 10.2.4: Solid Plate: Influence Functions (Green's Functions) 10.2.5: Solid Plate with Additional Support 10.2.6.: Annular Plate: Boundary Conditions and Examples 10.2.7: Annular Plate: Influence Functions (Green's Functions) 10.3: Bending of Rectangular Plates 10.3.1: Boundary Conditions 10.3.2: Bending of a Simply Supported Rectangular Plate 10.4: Plates on Elastic Foundation 10.5: Strain Energy of an Elastic Plate 10.6: Membranes 10.7: Composite Plates 10.7.1: Laminated Plates with Isotropic Layers 10.7.2: Laminated Plates with Orthotropic Layers 10.8: Approximate Methods in the Analysis of Plates and Membranes 10.8.1: Application of Finite Differences 10.8.2: Examples of Application of the Rayleigh-Ritz Method 11. Buckling and Vibration 11.1: Buckling and Vibration of Beams and Columns 1.1: Equation of Motion and Its Solution 11.1.2: Frequencies and Critical Loads for Various Boundary Conditions 11.1.3: Applications of Rayleigh-Ritz Method 11.2: Buckling and Vibration of Rings, Arches, and Thin-Walled Tubes 11.2.1: Equations of Motion and Their Solution 11.3: Buckling and Vibration of Thin Rectangular Plates 12. Introduction to Fracture Mechanics 12.1: Introductory Concepts 12.2: Linear Cracks in Two-Dimensional Elastic Solids--Williams' Solution, Stress Singularity 12.3: Stress Intensity Factor 12.4: Crack Driving Force as an Energy Rate 12.5: Relation Between G and the Stress Intensity Factors 12.6: Some Simple Cases of Calculation of Stress Intensity Factors 12.7: The J-Integral Appendix A. Matrices Appendix B. Coordinate Transformations