Introduction to shell structures. An historical overview. Basic elements of differential geometry. Space curves, parametric representation. Surfaces as grid of families of space curves. First fundamental form. Applications. Assumptions of thin shell theories. Stress resultants per unit length. Equilibrium Equations. The general initial and boundary value problem of theory of shells. Statical indeterminacy of the general problem. Membrane theory assumptions. Cylindrical shells. General solution for the statically determinate problem. Strains and displacements. Applications. Use of symbolic language i.e. Maple or Mathematica for the solution of cylindrical shells for various loading cases and support conditions. Membrane theory of conical shells. Equilibrium equations. General solution. Applications. Use of symbolic language i.e. Maple or Mathematica for the solution of conical shells for various loading cases and support conditions. Membrane theory of Shells of revolution. Equilibrium equations. General solution for axisymmetric loading cases. Spherical Shell. Hyperbolic shells. Applications for open or closed spherical shells. Shells of revolution for arbitrary loading. Fourier series solution, symmetric and antisymmetric cases. Differential geometry notion of curvature. Second fundamental form. Gauss-Godazzi conditions. Bending theory of cylindrical shells. Axisymmetric loading. Beam on elastic foundation type of solution. Donnell theory. Applications for cylindrical shells with different boundary conditions. Comparison with numerical solutions with finite element method. Design provisions of Eurocode 3 for steel thin shell structures.
- Teacher: Βλάσιος Κουμούσης