Structural Analysis in Microelectronic and Fiber-Optic Systems

1.1 Research Models in Mechanical Problems for Microelectronics and Fiber Optics.- 1.2 Theoretical Modeling.- 1.3 Analytical versus Numerical Modeling.- 1.4 Interaction with Experiment.- 1.5 Theoretical Modeling in Structural Analysis.- 1.6 Historical Sketch.- 1. Basic Principles of Engineering Elasticity.- 1. General Properties of Elastic Bodies.- 2. Equations and Conceptions.- 2.1 Stress.- 2.2 Stress Components.- 2.3 Stress Tensor.- 2.4 Equilibrium Conditions for an Elementary Tetrahedron.- 2.5 Equilibrium Conditions for an Elementary Parallelepiped.- 2.6 Principal Stresses and Stress Invariants.- 2.7 Normal Stress Surface and Stress Ellipsoid.- 2.8 Principal Shearing Stresses.- 2.9 Octahedral Stresses.- 2.10 Stress Deviator and Spherical Tensor.- 2.11 Displacements and Strains.- 2.12 Compatibility Equations.- 2.13 Strain Tensor, Principal Strains, and Strain Invariants.- 2.14 Hooke’s Law.- 2.15 Young’s Modulus and Poisson’s Ratio.- 2.16 Hooke’s Law with Consideration of Thermoelastic Strains.- 3. A View of Solution Procedures.- 3.1 Direct and Inverse Problems in Elasticity Theory.- 3.2 Semi-Inverse Method and Principle of Saint-Venant.- 3.3 Beltrami-Michell, Lamé, and Duhamel-Neumann Equations.- 4. The Elementary Problems.- 4.1 Pure Bending of a Prismatic Bar.- 4.2 Simple Torsion of a Circular Shaft.- 4.3 All-Round Uniform Compression.- 4.4 Prismatic Bar Subjected to Tension.- 4.5 Prismatic Bar Under Its Own Weight.- 4.6 Pure Bending of Plates.- 5. Strength Theories.- 5.1 Strain Energy.- 5.2 Classical Strength Theories.- 5.3 Some Modern Strength Theories.- 6. Two-Dimensional Problem in Rectangular Coordinates.- 6.1 Plane Strain and Plane Stress.- 6.2 Maurice Lévy Theorem.- 6.3 Stress (Airy) Function.- 6.4 Solution in Polynomials.- 6.5 Solution in Trigonometric Series.- 7. Two-Dimensional Problem in Polar Coordinates.- 7.1 Basic Relationships.- 7.2 Stresses and Displacements in a Circular Ring.- 7.3 A Circular Ring Loaded at Its Inner Boundary.- 7.4 Axisymmetric Problem.- 7.5 Thick-Walled Tube.- 7.6 Thermal Stress in Coaxial Cylinders.- 8. Torsion.- 8.1 Saint-Venant’s Torsion Function.- 8.2 Prandtl’s Stress Function.- 8.3 Prandtl’s Formula.- 8.4 Prandtl’s Formula for a Multiply Connected Region.- 8.5 Torsion of an Elliptical Shaft.- 8.6 Torsion of a Rectangular Shaft.- 8.7 Bredt’s Theorem.- 8.8 Torsion of a Closed Thin-Walled Section.- 8.9 Torsion of a Multiconnected Section.- 9. Fracture Mechanics.- 9.1 The Griffith Theory.- 9.2 Irwin’s Stress Intensity Approach.- 9.3 KIC Tests.- 9.4 Fracture Toughness.- 10. Plasticity.- 10.1 Uniaxial Plastic Deformation.- 10.2 Multiaxial Plastic Deformation: Small Elastoplastic Strains.- 10.3 Elastoplastic Bending of Beams.- 10.4 Theory of Plastic Flow.- 11. Viscoelasticity.- 11.1 Viscoelastic Materials.- 11.2 Time Effects.- 11.3 Mathematical Models of Prerupture Deformation of Plastics.- 11.4 Theory of Linear Viscoelasticity.- 11.5 Thermodynamics of Viscoelastic Deformation.- Questions and Problems.- 2. Fundamentals of Structural Analysis.- 12. Bending of Beams.- 12.1 Basic Definitions, Hypotheses, and Relationships.- 12.2 Solutions Based on Direct Integration of the Equation of Bending.- 12.3 Method of Initial Parameters.- 12.4 Reference Tables for Beam Deflections.- 12.5 Shear Deformations.- 12.6 Beams on Elastic Foundations.- 12.7 Effect of Shear on the Bending of Beams on Elastic Foundations.- 12.8 Beams Under Combined Action of Lateral and Axial Loads.- 12.9 Nonlinear Bending Under Combined Action of Lateral and Axial Loads.- 12.10 Large Deflections of Bent Beams (the Elastica).- 12.11 Thermal Bending of Beams.- 13. The Variational and Energy Methods, and Some General Principles of Structural Analysis.- 13.1 Variational Methods.- 13.2 Variational Principles of Structural Analysis.- 13.3 The Rayleigh—Ritz and Bubnov—Galerkin Methods.- 13.4 Finite-Element Method.- 14. Bending of Frames.- 14.1 Frame Structures, Simplest Frames.- 14.2 Complex Frames.- 14.3 Force Method and Deformation Method.- 15. Bending of Plates.- 15.1 Major Definitions and Assumptions.- 15.2 Bending of Rectangular Plates.- 15.3 Bending of Circular Plates.- 16. Buckling.- 16.1 Buckling of Bars.- 16.2 Buckling of Plates.- 17. Numerical Methods.- 17.1 Finite Differences.- 17.2 Collocation Method.- 17.3 Finite Elements.- 18. Experimental Techniques.- 18.1 Introductory Remarks.- 18.2 Bonded Strain Gauges.- 18.3 Photoelastic Analysis.- 18.4 Moiré Method.- Questions and Problems.- Appendix: Tables of Beam Deflections.