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 Other Shapes.- 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 General.- 9.2 Circular Cylindrical Shells.- 9.3 Shells of Revolution.- 9.4 Shells of Translation.- 9.5 Instability and Finite Deformations.- 9.6 References.- 9.7 Exercises.- 10. Conclusion.- 10.1 General.- 10.2 Proportioning.- 10.3 Future Applications of Thin Shells.- 10.4 References.
The study ofthree-dimensional continua has been a traditional part of graduate education in solid mechanics for some time. With rational simplifications to the three-dimensional theory of elasticity, the engineering theories of medium-thin plates and of thin shells may be derived and applied to a large class of engi neering structures distinguished by a characteristically small dimension in one direction. Often, these theories are developed somewhat independently due to their distinctive geometrical and load-resistance characteristics. On the other hand, the two systems share a common basis and might be unified under the classification of Surface Structures after the German term Fliichentragwerke. This common basis is fully exploited in this book. A substantial portion of many traditional approaches to this subject has been devoted to constructing classical and approximate solutions to the governing equations of the system in order to proceed with applications. Within the context of analytical, as opposed to numerical, approaches, the limited general ity of many such solutions has been a formidable obstacle to applications involving complex geometry, material properties, and/or loading. It is now relatively routine to obtain computer-based solutions to quite complicated situations. However, the choice of the proper problem to solve through the selection of the mathematical model remains a human rather than a machine task and requires a basis in the theory of the subject.
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