Introduction to the Theory of Shells

PrefaceI. Preludes The Lama Problem A Derivation of Beam TheoryII. The Theory of Surfaces The First Fundamental Form Curvature and the Second Fundamental Form The Gauss-Codazzi Conditions and the Fundamental Form The Surface of Revolution Some Terminology for SurfacesIII. The Construction of a Shell Theory The Basic Assumptions Shell Coordinates Strain-Displacement Relations Stress Resultants and Strain Energy Equations of Equilibrium Simplifications of the Strain Energy Functional and the Stress-Strain Relations The Kirchoff Boundary Conditions Appendix IIIA. Verification of Equation (56) Appendix IIIB. Strain-Displacement Relations in Curvilinear Coordinates Appendix IIIC. Verification of Equation (67) Appendix IIID. Alternate Derivation of the Equilibrium Equations Appendix IIIE. Strain Parameter Values for Rigid Body MotionsIV. Membrane Shells General Formulation of Membrane Theory Shells of Revolution with Straight Generators Some Examples of Axisymmetric Shells of Revolution Appendix IVA. Stresses in a Pressurized Oval Cylinder Appendix IVB. Stresses in an Ogival DomeV. The Bending of Circular Cylinders Basic Relations and Simplifications The Donnell, Sanders and Flügge Equations The Axisymmetric, Semi-Infinite Cylinder Decay Lengths and Edge Effects The Donnell Equation and Some of Its Solutions for Asymmetric Deformation Appendix VA. Cylinders with Variable Wall Thickness Appendix VB. Influence Coefficients for the Axisymmetric Cylinder Appendix VC. The Maxwell-Betti TheoremVI. Shells of Revolution General Formulation and Uncoupling Procedures The Reissner-Meissner Theory of Axisymmetric Shells of Revolution The Geckeler Approximation for Steep Shells The Reissner Theory for Shallow Shells Appendix VIA. The Shell Mating ProblemVII. Axisymmetric Vibrations of Circular Cylinders Free Vibrations-Frequencies, Mode Shapes, Orthogonality Forced Vibrations-Normal Modes Solution Forced Vibrations-Williams' Method for Time-Dependent Boundary ConditionsBibliographyIndex