ELASTICITY

CHAPTER 1 BASIC ASSUMPTIONS AND MATHEMATICAL PRELIMINARIES1.1 Introduction1.2 Basic Assumptions1.3 Coordinate Systems and Transformations1.4 Vector and Matrix Notations and Their Operations1.5 Divergence TheoremProblems/Tutorial QuestionsCHAPTER 2 STRESSES2.1 Stress and the Stress Tensor2.2 Equilibrium Equations2.3 Traction Boundary Conditions2.4 Stresses on an Oblique Plane2.5 Principal Stresses2.6 Stationary and Octahedral Shear Stresses2.7 Equilibrium Equations in Curvilinear CoordinatesProblems/Tutorial QuestionsCHAPTER 3 STRAINS3.1 Strains3.2 Finite Deformations3.3 Strains in a Given Direction and Principal Strains3.4 Stationary Shear Strains3.5 Compatibility3.6 Kinematic and Compatibility Equations in Curvilinear Coordinates3.7 Concluding RemarksProblems/Tutorial QuestionsCHAPTER 4 FORMULATION OF ELASTICITY PROBLEMS4.1 Strain Energy Density Function4.2 GeneralisedHooke's Law4.3 Initial Stresses and Initial Strains4.4 Governing Equations and Boundary Conditions4.5 General Solution Techniques4.6 St. Venant's PrincipleProblems/Tutorial QuestionsCHAPTER 5 TWO-DIMENSIONAL ELASTICITY5.1 Plane Strain Problems5.2 Plane Stress Problems5.3 Similarities and Differences Between Plane Strain/Plane Stress Problems5.4 Airy Stress Function and Polynomial Solutions5.5 Polar Coordinates5.6 Axisymmetric Stress Distributions5.7 Rotating Discs5.8 Stresses Around a Circular Hole in a Plate Subjected to Equal Biaxial Tension-Compression £¨Pure Shear in the 45¡ã Direction£©5.9 Stress Concentration Around a Circular Hole in a Plate Subjected to Uniaxial Tension5.10 Concluding RemarksProblems/Tutorial QuestionsCHAPTER 6 TORSION OF BARS6.1 Torsion of Bars in Strength of Materials6.2 Warping6.3 Prandtl's Stress Function6.4 Torque6.5 Bars of Circular and Elliptical Cross-Sections6.6 Thin-Walled Structures in Torsion6.7 AnalogiesProblems/Tutorial QuestionsCHAPTER 7 BENDING OF BARS7.1 Bending Theory in Strength of Materials7.2 Elasticity Formulation of Bending of Bars7.3 Stress Resultants and Shear Centre7.4 Bending of a Bar of a Circular Cross-Section7.5 Bending of a Bar of an Elliptical Cross-Section7.6 AnalogiesProblems/Tutorial QuestionsCHAPTER 8 THE STATE SPACE METHOD OF 3D ELASTICITY8.1 Concept of State and State Variables8.2 Solution for a Linear Time-Invariant System8.3 Calculation of e[A]t8.4 Solution of Linear Time-Variant System8.5 State Variable Equation of Elasticity8.6 Application of State Space Method8.7 ConclusionsProblems/Tutorial QuestionsCHAPTER 9 BENDING OF PLATES9.1 Love-KirchhoffHypotheses9.2 The Displacement Fields9.3 Strains and Generalised Strains9.4 Bending Moments9.5 The Governing Equation9.6 Generalised Forces9.7 Boundary Conditions9.8 Rectangular Plates9.9 Circular PlatesProblems/Tutorial QuestionsCHAPTER 10 ENERGY PRINCIPLES10.1 Introduction10.2 Work, Strain Energy and Strain Complementary Energy10.3 Principle of Virtual Work10.4 Application of the Principle of Virtual Work10.5 The Reciprocal Law of Betti10.6 Principle of Minimum Potential Energy10.7 Principle of Virtual Complementary Work10.8 Principle of Minimum Complementary Energy10.9 Castigliano's Theorems10.10 Application of the Principles of Minimum Strain Energy10.11 Rayleigh-Ritz MethodProblems/Tutorial QuestionsCHAPTER 11 SPECIAL TOPICS FOR ELASTICITY11.1 Thermal Elasticity11.2 Propagation of Elastic Waves11.3 Strength Theory, Crack and FractureProblems/Tutorial QuestionsREFERENCES