Analysis of Shells and Plates

1. Introduction.- 1.1 Role of the Theory of Elasticity.- 1.2 Engineering Theories.- 1.3 Load Resistance Mechanisms.- 1.4 References.- 1.5 Exercises.- 2. Geometry.- 2.1 Curvilinear Coordinates.- 2.2 Middle Surface Geometry.- 2.3 Unit Tangent Vectors and Principal Directions.- 2.4 Second Quadratic Form of the Theory of Surfaces.- 2.5 Principal Radii of Curvature.- 2.6 Gauss-Codazzi Relations.- 2.7 Gaussian Curvature.- 2.8 Specialization of Shell Geometry.- 2.9 References.- 2.10 Exercises.- 3. Equilibrium.- 3.1 Stress Resultants and Couples.- 3.2 Equilibrium of the Shell Element.- 3.3 Equilibrium Equations for Shells of Revolution.- 3.4 Equilibrium Equations for Plates.- 3.5 Nature of the Applied Loading.- 3.6 References.- 3.7 Exercises.- 4. Membrane Theory.- 4.1 Simplification of the Equilibrium Equations.- 4.2 Applicability of Membrane Theory.- 4.3 Shells of Revolution.- 4.4 Shells of Translation.- 4.5 References.- Appendix 4A. Summary of Surface Loading and Stress Resultants for Quasistatic Seismic Loading on Hyperboloidal Shells of Revolution.- 4.6 Exercises.- 5. Deformations.- 5.1 General.- 5.2 Displacement.- 5.3 Strain.- 5.4 Strain-Displacement Relations for Shells of Revolution.- 5.5 Strain-Displacement Relations for Plates.- 5.6 References.- 5.7 Exercises.- 6. Constitutive Laws, Boundary Conditions, and Displacements.- 6.1 Constitutive Laws.- 6.2 Boundary Conditions.- 6.3 Membrane Theory Displacements.- 6.4 References.- 6.5 Exercises.- 7. Energy and Approximate Methods.- 7.1 General.- 7.2 Strain Energy.- 7.3 Potential Energy of the Applied Loads.- 7.4 Energy Principles and Rayleigh-Ritz Methods.- 7.5 Galerkin Method.- 7.6 References.- 7.7 Exercises.- 8. Bending of Plates.- 8.1 Governing Equations.- 8.2 Rectangular Plates.- 8.3 Circular Plates.- 8.4 Plates of OtherShapes.- 8.5 Energy Method Solutions.- 8.6 Extensions of the Theory of Plates.- 8.7 Instability and Finite Deformation.- 8.8 References.- 8.9 Exercises.- 9. Shell Bending and Instability.- 9.1

Dr. Phillip L. Gould was the Harold D. Jolley Professor of Civil Engineering from 1981 until 2010 and is now a Senior Professor at Washington University in St.Louis. His research activities have centered on shell analysis with applications to finite element modeling, biomedical engineering, earthquake engineering, and the structural design of thin-shell structures. Dr. Gould is the author of numerous papers and several books and is the founding editor of the prestigious journal, Engineering Structures. He has served as a consultant to industry and to governmental organizations and has received numerous awards for his research, professional and educational activities.