• 3D elasticity equations. Plane strain. Plane stress. Axial symmetry.
• Coordinate transformation. Derivation of the equations of 2D elasticity. Airy stress function, principles of solution of 2D elasticity.
• Plates. Kirchhoff's theory of thin plates. Mindlin's theory of thick plates.
• Plate equation - numerical methods of solution. Solution by the finite difference method.
• Shells. Rotationally symmetric shells. Membrane and bending theory of shells.
• Nature of failure of materials and failure criteria.
• Plasticity - introduction to mathematical theory of finite deformations. Tensor calculus.
• Plasticity criteria, notation, incremental theory of plasticity.
• Numerical methods of solution. Direct stiffness method. Solution of beam structures.
• Numerical methods - overview. Variational principles in mechanics and dynamics.
• Finite element method. Principle of the method, principles of spatial and time discretization, convergence of the method.
• Types of FEM elements, overview. Stiffness matrix and element mass matrix, derivation.
• Non-linear problems and methods of their solution. Principles of iterative methods.
Calendars at the Faculty of Transportation Sciences, CTU in Prague