Translated from Danish lecture notes, with changes and additions.

Includes bibliographical references and index.

This account of the theory of plates and shells is written primarily as a textbook for graduate students in mechanical and civil engineering. The unified treatment of shells of arbitrary shape is accomplished by tensor analysis. This useful tool is introduced in the first chapter, and no knowledge of advanced mathematical methods is required. The general theory developed in the first eight chapters is applied in the remaining part to thin elastic plates and shells with special emphasis on engineering methods and engineering applications. A number of detailed examples illustrate the theory.

Print version record.

Front Cover; Shell Theory; Copyright Page; Dedication; Preface; Table of Contents; Introduction; Chapter 1. Tensor analysis; 1. Introduction; 2. Coordinate transformations; 3. Contravariant and covariant vectors; 4. Tensors; 5. Algebra of tensors; 6. The fundamental tensor; 7. Associated tensors; 8. Magnitude; 9. Covariant differentiation; 10. The Riemann-Christoffel tensor; 11. The order of covariant differentiation for tensors; 12. Contravariant differentiation; 13. Summary; Bibliography; Chapter 2. The geometry of the middle-surface; 1. Introduction.

2. The first fundamental form of a surface3. Normal coordinates; 4. Second fundamental form of a surface; 5. Invariants of curvature; 6. The inverse problem; 7. The equations of Codazzi; 8. Surface and volume element; 9. Coordinates of principal curvature; 10. Summary; Bibliography; Chapter 3. The kinematics of a surface; 1. Introduction; 2. Displacements; 3. Stretching of the middle-surface; 4. Rotation of an element of the shell; 5. Bending of the middle-surface; 6. Equations of compatibility; 7. Summary; Chapter 4. The statics of a shell; 1. Introduction; 2. An element of the shell.

3. The divergence theorem4. Statically equivalent forces and moments; 5. External loads; 6. Equations of equilibrium; 7. Summary; Chapter 5. Effective forces and moments; 1. Introduction; 2. The principle of virtual work; 3. Equations of equilibrium; 4. Summary; Chapter 6. Boundary conditions; 1. Introduction; 2. External forces; 3. Boundary conditions; 4. Stress-distribution; 5. Summary; Chapter 7. Stress-strain relations; 1. Introduction; 2. The elastic energy; 3. The mathematical problem; 4. Summary; Chapter 8. The static-geometric analogy; 1. Introduction.

2. Alternative measures of bending3. Static-geometric analogy; 4. Stress-functions; 5. Summary and discussion; Bibliography; Chapter 9. Plates; 1. Introduction; 2. Separation of the plate problem; 3. In-plane loaded plates; 4. Bending theory of plates; 5. Bending of plates in rectangular coordinates; 6. Corners; 7. Bending of a simply supported rectangular plate; 8. The clamped and uniformly loaded elliptical plate; 9. Vibrating plates; 10. Energy methods; 11. Bending of a clamped rectangular plate; 12. Lowest natural frequency of a skew plate; 13. Bending of plates in polar coordinates.

14. Axisymmetrical bending of a circular plate15. Free vibrations of a circular plate; 16. Behaviour at a corner of a simply supported plate; Bibliography; Chapter 10. The membrane state; 1. Introduction; 2. The membrane state in orthogonal coordinates; 3. Axisymmetrical shells; 4. Drop container; 5. Domes; 6. Conditions at the apex; 7. Conditions at the base; 8. Spherical dome of uniform thickness; 9. Dome of uniform strength; 10. Domes with given circumferential stresses; 11. Deformation of axisymmetrical shells in the membrane state.

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