Course title: Shells and Plates

Study: graduate program in Mechanical Engineering

Course director: Prof. Dr. Jurica Soric
Hours/Semester: 45
Semester: optional
 
Course syllabus:
Theory of surfaces. General theory of shells, Kirchhoff-Love's assumptions: deformation of shell, compatibility conditions, forces and moments, equilibrium equations, constitutive laws, boundary conditions, solution methods of shell problems. Basic equations of Reissner-Mindlin's shell theory. Membrane theory: basic equations, membrane theory of shells of revolution. Shells of revolution: differential equations, symmetrical deformation of shells of revolutions, integration of differential equation, internal forces and displacements. Symmetrical deformation of toroidal shells. Symmetrical deformation of conical shells. Bending of plates: equilibrium equations, constitutive equations, rectangular plates, circular plates, energy method solutions, finite difference method. Basic equations of geometrically nonlinear theories: Donnell-Marguerre's assumptions of small rotations, finite rotations, total Lagrangian formulations. Elastic stability of shells. Finite shell elements: formulations based on Kirchhoff-Love's and Reissner-Mindlin's assumptions, finite elements based on the shell theories, isoparametric finite elements, assumed strain finite element concept, basic equations for linear and nonlinear analyses.
Bibliography:

1.Novozhilov, V.,V., Thin Shell Theory, Noordhoff, Groningen 1964.

2.Gould, P. L., Analysis of Shells and Plates, Springer, New York 1988.

3. Basar, Y., Krätzig, W. B., Mechanik der Flächentragwerke, Vieweg, Braunschweig 1985.

4. Reismann, H., Elastic Plates, Theory and Application, John Wiley, New York 1988.

5. Bathe, K-J., Finite Element Procedures, Prentice Hall, New Jersey 1996.

6. Senjanovic, I., Theory of plates and shells. (In Croatian), FSB, Zagreb 1998.

7. Soric, J.: Shells and Plates, Inženjerski prirucnik (Handbook for Engineers), ŠSkolska knjiga, Zagreb 1996, 620-637, (In Croatian)