Principles of Solid Mechanics
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Book Description
Evolving from more than 30 years of research and teaching experience, Principles of Solid Mechanics offers an in-depth treatment of the application of the full-range theory of deformable solids for analysis and design. Unlike other texts, it is not either a civil or mechanical engineering text, but both. It treats not only analysis but incorporates design along with experimental observation. Principles of Solid Mechanics serves as a core course textbook for advanced seniors and first-year graduate students.
The author focuses on basic concepts and applications, simple yet unsolved problems, inverse strategies for optimum design, unanswered questions, and unresolved paradoxes to intrigue students and encourage further study. He includes plastic as well as elastic behavior in terms of a unified field theory and discusses the properties of field equations and requirements on boundary conditions crucial for understanding the limits of numerical modeling.
Designed to help guide students with little experimental experience and no exposure to drawing and graphic analysis, the text presents carefully selected worked examples. The author makes liberal use of footnotes and includes over 150 figures and 200 problems. This, along with his approach, allows students to see the full range, non-linear response of structures.
Table of Contents
PREFACE
INTRODUCTION
Types of Linearity
Displacements-Vectors and Tensors
Finite Linear Transformation
Symmetric and Asymmetric Components
Principal or Eigenvalue Representation
Field Theory
STRAIN AND STRESS
Deformation (Relative Displacement)
The Strain Tensor
The Stress Tensor
Components at an Arbitrary Orientation (Tensor Transformation)
Isotropic and Deviatoric Components
Principal Space and 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
Summary
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
STRATEGIES FOR ELASTIC ANALYSIS AND DESIGN
Rational Mechanics
Boundary Conditions
Tactics for Analysis
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
LINEAR FREE FIELDS
Isotropic Stress
Uniform Stress
Geostatic Fields
Uniform Acceleration of the Half-Space
Pure Bending of Prismatic Bars
Pure Bending of Plates
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
Circular Beams with End Loads
Concluding Remarks
RING, HOLES AND INVERSE PROBLEMS
Lames Solution for Rings under Pressure
Small Circular Holes in Plates, Tunnels, and Inclusions
Harmonic Holes and the Inverse Problem
Harmonic Holes for Free Fields
Neutral Holes
Solution Tactics for Neutral Holes-Examples
Rotating Disks and Rings
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 Loadings of a Circular Disk
Wedges with Constant Body Forces
Corner Effects-Eigenfunction Strategy
TORSION
Elementary (Linear) Solution
St. Venant's Formulation (Noncircular Cross-Sections)
Prandtl's Stress Function
Membrane Analogy
Thin-Walled Tubes of Arbitrary Shape
Hydrodynamic Analogy and Stress Concentration
CONCEPTS OF PLASTICITY
Plastic Material Behavior
Plastic Structural Behavior
Plastic 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
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
Combined Torsion with Tension and/or Bending
SLIP-LINE ANALYSIS
Mohr-Coulomb Criterion (Revisited)
Lateral "Pressures" and the Retaining Wall Problem
Graphic Analysis and Minimization
Slip-Line Theory
Purely Cohesive Materials (f = 0)
Weightless Materials (g = 0)
Retaining Wall Solution for f = 0 (EPS Material)
Comparison to the Coulomb Solution (f = 0)
Other Special Cases: Slopes and Footings (f = 0)
Solutions for Weightless Mohr-Coulomb Materials
The General Case
An Approximate "Coulomb Mechanism"
Note: Each chapter also contains a section of Problems and Questions