Università Roma Tre

The course topics cover several mechanical problems approached by the Finite Element Method (FEM), and specifically addressed to both 2D and 3D beam frame systems.
Since its first applications (late 1940s) FEM naturally plays an inter/multi-disciplinary role, where physical models can be implemented by simple modular schemes and iterative algorithms.

Through both theoretical presentations and practices, lectures will focus on the key-items of the numerical implementation for structural analysis (linear and modal analysis for elastic and dynamic structural characterization, respectively); connections between such aspects and those related to tools for parametric modeling of solid geometries will be regarded as crucial.
The equilibrium field equations will be also formulated in a general mathematical format, so as to have an overview of their use in general-purpose softwares, able to simulate generic physical problems.

The course program addresses the following issues:
1. Introduction to linear algebra and analysis;
2. Linear-elastic analysis of beam frame systems;
3. Modal (vibrational) analysis of beam frame systems;
4. Generalized FEM formulation for PDEs (Partial Differential Equations).

T.J.R. Hughes. The Finite Element Method. Dover Publications, 2000.
Nam-Ho Kim, Bhavani V. Sankar, Ashok V. Kumar. Introduction to Finite Element Analysis and Design (2nd ed.). Wiley.