كتاب Principles of Solid Mechanics

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Principles of Solid Mechanics
Rowland Richards, Jr.

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Introduction
Types of Linearity
Linear Shapes—The “Elastic Line”
Linear Displacement (Plane Sections)
Linear Stress Strain Behavior (Hooke’s Law)
Geometric Linearity
Linear Tangent Transformation
Displacements—Vectors and Tensors
Finite Linear Transformation
Symmetric and Asymmetric Components
Asymmetric Transformation
Symmetric Transformation
Principal or Eigenvalue Representation
Field Theory
Problems and Questions
Strain and Stress
Deformation (Relative Displacement)
The Strain Tensor
The Stress Tensor
Components at an Arbitrary Orientation
(Tensor Transformation)
Invariants and Principal Orientation
Isotropic and Deviatoric Components
Principal Space and the Octahedral Representation
Two-Dimensional Stress or Strain
Mohr’s Circle for a Plane Tensor
Mohr’s Circle in Three Dimensions
Equilibrium of a Differential Element
Other Orthogonal Coordinate Systems
Cylindrical Coordinates (
Spherical Coordinates (
Plane Polar Coordinates (
Summary
Problems and Questions
Stress–Strain Relationships (Rheology)
Linear Elastic Behavior
Linear Viscous Behavior
Simple Viscoelastic Behavior
Fitting Laboratory Data with Viscoelastic Models
Elastic–Viscoelastic Analogy
Elasticity and Plasticity
Yield of Ductile Materials
Yield (Slip) of Brittle Materials
Problems and Questions
Strategies for Elastic Analysis and Design
Rational Mechanics
Boundary Conditions
Tactics for Analysis
Direct Determination of Displacements
Direct Determination of Stresses
St Venant’s Principle
Two- Dimensional Stress Formulation
Types of Partial Differential Field Equations
Properties of Elliptic Equations
The Conjugate Relationship Between Mean
Stress and Rotation
The Deviatoric Field and Photoelasticity
Solutions by Potentials
Problems and Questions
Linear Free Fields
Isotropic Stress
Uniform Stress
Geostatic Fields
Uniform Acceleration of the Half-space
Pure Bending of Prismatic Bars
Pure Bending of Plates
Problems and Questions
Two-Dimensional Solutions for Straight
and Circular Beams
The Classic Stress-Function Approach
Airy’s Stress Function in Cartesian Coordinates
Polynomial Solutions and Straight Beams
Polar Coordinates and Airy’s Stress Function
Simplified Analysis of Curved Beams
Pure bending of a Beam of Circular Arc
Circular Beams with End Loads
Concluding Remarks
Problems and Questions
Ring, Holes, and Inverse Problems
Lamés Solution for Rings under Pressure
Small Circular Holes in Plates, Tunnels, and Inclusions
Isotropic Field
Deviatoric Field
General Biaxial Field
Harmonic Holes and the Inverse Problem
Design Condition
Harmonic Holes for Free Fields
Harmonic Holes for Biaxial Fields
Harmonic Holes for Gradient Fields
Neutral Holes
Solution Tactics for Neutral Holes—Examples
Isotropic Field
Deviatoric Field
General Biaxial Field
Gradient Fields with an Isotropic Component
Summary
Rotating Disks and Rings
Disk of Constant Thickness
Variable Thickness and the Inverse Problem
Problems and Questions
Wedges and the Half-Space
Concentrated Loadings at the Apex
Uniform Loading Cases
Uniform Loading over a Finite Width
Nonuniform Loadings on the Half-Space
Line Loads within the Half-Space
Diametric Loading of a Circular Disk
Wedges with Constant Body Forces
Corner Effects—Eigenfunction Strategy
Problems and Questions
Torsion
Elementary (Linear) Solution
St Venant’s Formulation (Noncircular Cross-Sections)
Solutions by St Venant
Prandtl’s Stress Function
Membrane Analogy
Thin-Walled Tubes of Arbitrary Shape
Hydrodynamic Analogy and Stress Concentration
Problems and Questions
Concepts of Plasticity
Plastic Material Behavior
Plastic Structural Behavior
Plasticity Field Equations
Example—Thick Ring
Limit Load by a “Work” Calculation
Theorems of Limit Analysis
The Lower-Bound Theorem
The Upper-Bound Theorem
Example—the Bearing Capacity (Indentation) Problem
Circular Mechanisms
Sliding Block Mechanisms
Problems and Questions
One-Dimensional Plasticity for Design
Plastic Bending
Plastic “Hinges”
Limit Load (Collapse) of Beams
Limit Analysis of Frames and Arches
Limit Analysis of Plates
Plastic Torsion
Sand-Hill and Roof Analogies
Sections with Holes and Keyways
Combined Torsion with Tension and/or Bending
Problems and Questions
Slip-Line Analysis
Mohr-Coulomb Criterion (Revisited)
Lateral “Pressures” and the Retaining Wall Problem
Graphic Analysis and Minimization
Slip-Line Theory
Purely Cohesive Materials
Weightless Material
Retaining Wall Solution for
(EPS Material)
Comparison to the Coulomb Solution
Other Special Cases: Slopes and Footings
Solutions for Weightless Mohr-Coulomb Materials
The General Case
An Approximate “Coulomb Mechanism”
Problems and Questions
Index

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