Elasticity: Theory, Applications, and Numerics

Description

Elasticity: Theory, Applications, and Numerics, Fourth Edition, continues its market-leading tradition of concisely presenting and developing the linear theory of elasticity, moving from solution methodologies, formulations, and strategies into applications of contemporary interest, such as fracture mechanics, anisotropic and composite materials, micromechanics, nonhomogeneous graded materials, and computational methods. Developed for a one- or two-semester graduate elasticity course, this new edition has been revised with new worked examples and exercises, and new or expanded coverage of areas such as treatment of large deformations, fracture mechanics, strain gradient and surface elasticity theory, and tensor analysis. Using MATLAB software, numerical activities in the text are integrated with analytical problem solutions. Online ancillary support materials for instructors include a solutions manual, image bank, and a set of PowerPoint lecture slides. Provides a thorough yet concise introduction to linear elasticity theory and applicationsOffers detailed solutions to problems of nonhomogeneous/graded materialsFeatures a comparison of elasticity solutions with elementary theory, experimental data, and numerical simulationsIncludes online solutions manual and downloadable MATLAB code Cover Elasticity: Theory, Applications, and Numerics Copyright Preface Contents summary The subject Exercises and web support Feedback Acknowledgments About the Author Part 1: Foundations and elementary applications 1 - Mathematical preliminaries 1.1 Scalar, vector, matrix, and tensor definitions 1.2 Index notation 1.3 Kronecker delta and alternating symbol 1.4 Coordinate transformations 1.5 Cartesian tensors 1.6 Principal values and directions for symmetric second-order tensors 1.7 Vector, matrix, and tensor algebra 1.8 Calculus of Cartesian tensors 1.8.1 Divergence or Gauss theorem 1.8.2 Stokes theorem 1.8.3 Green's theorem in the plane 1.8.4 Zero-value or localization theorem 1.9 Orthogonal curvilinear coordinates References 1 . . Exercises 2 - Deformation: displacements and strains 2.1 General deformations 2.2 Geometric construction of small deformation theory 2.3 Strain transformation 2.4 Principal strains 2.5 Spherical and deviatoric strains 2.6 Strain compatibility 2.7 Curvilinear cylindrical and spherical coordinates References 2 Exercises 3 - Stress and equilibrium 3.1 Body and surface forces 3.2 Traction vector and stress tensor 3.3 Stress transformation 3.4 Principal stresses 3.5 Spherical, deviatoric, octahedral, and von Mises stresses 3.6 Stress distributions and contour lines 3.7 Equilibrium equations 3.8 Relations in curvilinear cylindrical and spherical coordinates References 3 Exercises 4 - Material behavior—linear elastic solids 4.1 Material characterization 4.2 Linear elastic materials—Hooke's law 4.3 Physical meaning of elastic moduli 4.3.1 Simple tension 4.3.2 Pure shear 4.3.3 Hydrostatic compression (or tension) 4.4 Thermoelastic constitutive relations References 4 Exercises 5 - Formulation and solution strategies 5.1 Review of field equations 5.2 Boundary conditions and fundamental problem classifications 5.3 Stress formulation 5.4 Displacement formulation 5.5 Principle of superposition 5.6 Saint–Venant's principle 5.7 General solution strategies 5.7.1 Direct method 5.7.2 Inverse method 5.7.3 Semi-inverse method 5.7.4 Analytical solution procedures Power series method Fourier method Integral transform method Complex variable method 5.7.5 Approximate solution procedures Ritz method 5.7.6 Numerical solution procedures Finite difference method Finite element method Boundary element method 5.8 Singular elasticity solutions References 5 Exercises 6 - Strain energy and related principles 6.1 Strain energy 6.2 Uniqueness of the elasticity boundary-value problem 6.3 Bounds on the elastic constants 6.3.1 Uniaxial tension 6.3.2 Simple shear 6.3.3 Hydrostatic compression 6.4 Related integral theorems 6.4.1 Clapeyron's theorem 6.4.2 Betti/Rayleigh reciprocal theorem 6.4.3 Integral formulation of elasticity—Somigliana's identity 6.5 Principle of virtual work 6.6 Principles of minimum potential and complementary energy 6.7 Rayleigh–Ritz method References 6 Exercises 7 - Two-dimensional formulation 7.1 Plane strain 7.2 Plane stress 7.3 Generalized plane stress 7.4 Antiplane strain 7.5 Airy stress function 7.6 Polar coordinate formulation References 7 Exercises 8 - Two-dimensional problem solution 8.1 Cartesian coordinate solutions using polynomials 8.2 Cartesian coordinate solutions using Fourier methods 8.2.1 Applications involving Fourier series 8.3 General solutions in polar coordinates 8.3.1 General Michell solution 8.3.2 Axisymmetric solution 8.4 Example polar coordinate solutions 8.4.1 Pressurized hole in an infinite medium 8.4.2 Stress-free hole in an infinite medium under equal biaxial loading at infinity 8.4.3 Biaxial and shear loading cases 8.4.4 Quarter-plane example 8.4.5 Half-space examples 8.4.6 Half-space under uniform normal stress over x≤0 8.4.7 Half-space under concentrated surface force system (Flamant problem) 8.4.8 Half-space under a surface concentrated moment 8.4.9 Half-space under uniform normal loading over −a≥x≥a 8.4.10 Notch and crack problems 8.4.11 Pure bending example 8.4.12 Curved cantilever under end loading 8.5 Simple plane contact problems References 8 Exercises 9 - Extension, torsion, and flexure of elastic cylinders 9.1 General formulation 9.2 Extension formulation 9.3 Torsion formulation 9.3.1 Stress–stress function formulation 9.3.2 Displacement formulation 9.3.3 Multiply connected cross-sections 9.3.4 Membrane analogy 9.4 Torsion solutions derived from boundary equation 9.5 Torsion solutions using Fourier methods 9.6 Torsion of cylinders with hollow sections 9.7 Torsion of circular shafts of variable diameter 9.8 Flexure formulation 9.9 Flexure problems without twist References 9 Exercises Part 2: Advanced applications 10 - Complex variable methods 10.1 Review of complex variable theory 10.2 Complex formulation of the plane elasticity problem 10.3 Resultant boundary conditions 10.4 General structure of the complex potentials 10.4.1 Finite simply connected domains 10.4.2 Finite multiply connected domains 10.4.3 Infinite domains 10.5 Circular domain examples 10.6 Plane and half-plane problems 10.7 Applications using the method of conformal mapping 10.8 Applications to fracture mechanics 10.9 Westergaard method for crack analysis References 10 - Exercises 11 - Anisotropic elasticity 11.1 Basic concepts 11.2 Material symmetry 11.2.1 Plane of symmetry (monoclinic material) 11.2.2 Three perpendicular planes of symmetry (orthotropic material) 11.2.3 Axis of symmetry (transversely isotropic material) 11.2.4 Cubic symmetry 11.2.5 Complete symmetry (isotropic material) 11.3 Restrictions on elastic moduli 11.4 Torsion of a solid possessing a plane of material symmetry 11.4.1 Stress formulation 11.4.2 Displacement formulation 11.4.3 General solution to the governing equation 11.5 Plane deformation problems 11.5.1 Uniform pressure loading case 11.6 Applications to fracture mechanics 11.7 Curvilinear anisotropic problems 11.7.1 Two-dimensional polar-orthotropic problem 11.7.2 Three-dimensional spherical-orthotropic problem References 11 Exercises 12 - Thermoelasticity 12.1 Heat conduction and the energy equation 12.2 General uncoupled formulation 12.3 Two-dimensional formulation 12.3.1 Plane strain 12.3.2 Plane stress 12.4 Displacement potential solution 12.5 Stress function formulation 12.6 Polar coordinate formulation 12.7 Radially symmetric problems 12.8 Complex variable methods for plane problems References 12 Exercises 13 - Displacement potentials and stress functions: applications to three-dimensional problems 13.1 Helmholtz displacement vector representation 13.2 Lamé's strain potential 13.3 Galerkin vector representation 13.4 Papkovich–Neuber representation 13.5 Spherical coordinate formulations 13.6 Stress functions 13.6.1 Maxwell stress function representation 13.6.2 Morera stress function representation References 13 Exercises 14 - Nonhomogeneous elasticity 14.1 Basic concepts 14.2 Plane problem of a hollow cylindrical domain under uniform pressure 14.3 Rotating disk problem 14.4 Point force on the free surface of a half-space 14.5 Antiplane strain problems 14.6 Torsion problem References 14 Exercises 15 - Micromechanics applications 15.1 Dislocation modeling 15.2 Singular stress states 15.3 Elasticity theory with distributed cracks 15.4 Micropolar/couple-stress elasticity 15.4.1 Two-dimensional couple-stress theory 15.5 Elasticity theory with voids 15.6 Doublet mechanics 15.7 Higher gradient elasticity theories References 15 Exercises 16 - Numerical finite and boundary element methods 16.1 Basics of the finite element method 16.2 Approximating functions for two-dimensional linear triangular elements 16.3 Virtual work formulation for plane elasticity 16.4 FEM problem application 16.5 FEM code applications 16.6 Boundary element formulation References 16 Exercises A - Basic field equations in Cartesian, cylindrical, and spherical coordinates Strain–displacement relations Cartesian coordinates Cylindrical coordinates Spherical coordinates Equilibrium equations Cartesian coordinates Cylindrical coordinates Spherical coordinates Hooke's law Cartesian coordinates Cylindrical coordinates Spherical coordinates Equilibrium equations in terms of displacements (Navier's equations) Cartesian coordinates Cylindrical coordinates Spherical coordinates B - Transformation of field variables between Cartesian, cylindrical, and spherical components Cylindrical components from Cartesian Displacement transformation Stress transformation Spherical components from cylindrical Displacement transformation Stress transformation Spherical components from Cartesian Displacement transformation Stress transformation C - MATLAB® Primer C.1 Getting started C.2 Examples References D - Review of mechanics of materials D.1 Extensional deformation of rods and beams D.2 Torsion of circular rods D.3 Bending deformation of beams under moments and shear forces D.4 Curved beams D.5 Thin-walled cylindrical pressure vessels Index A B C D E F G H I K L M N O P R S T U V W Y Z Back Cover