Structural Analysis in Microelectronic and Fiber-Optic Systems

This book contains the fundamentals of a discipline, which could be called Structural Analysis in Microelectronics and Fiber Optics. It deals with mechanical behavior of microelectronic and fiber-optic systems and is written in response to the crucial need for a textbook for a first in-depth course on mechanical problems in microelectronics and fiber optics. The emphasis of this book is on electronic and optical packaging problems, and analytical modeling. This book is apparently the first attempt to select, advance, and present those methods of classical structural mechanics which have been or can be applied in various stress-strain problems encountered in "high technology" engineering and some related areas, such as materials science and solid-state physics. The following major objectives are pursued in Structural Analysis in Microelectronic and Fiber-Optic Systems: Identify structural elements typical for microelectronic and fiber-optic systems and devices, and introduce the student to the basic concepts of the mechanical behavior of microelectronic and fiber-optic struc­ tures, subjected to thermally induced or external loading. Select, advance, and present methods for analyzing stresses and deflections developed in microelectronic and fiber-optic structures; demonstrate the effectiveness of the methods and approaches of the classical struc­ tural analysis in the diverse mechanical problems of microelectronics and fiber optics; and give students of engineering, as well as practicing engineers and designers, a thorough understanding of the main princi­ ples involved in the analytical evaluation of the mechanical behavior of 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.