Caricamento in corso...
Advanced topics in the finite element method
01QCEIW
A.A. 2024/25
Course Language
Inglese
Degree programme(s)
Doctorate Research in Ingegneria Aerospaziale - Torino
Course structure
| Teaching | Hours |
|---|---|
| Lezioni | 20 |
Lecturers
| Teacher | Status | SSD | h.Les | h.Ex | h.Lab | h.Tut | Years teaching |
|---|---|---|---|---|---|---|---|
| Esposito Marco | Ricercatore L240/10 | IIND-01/D | 12 | 0 | 0 | 0 | 3 |
Co-lectures
Context
| SSD | CFU | Activities | Area context |
|---|---|---|---|
| *** N/A *** |
The Finite Element Method (FEM) is a numerical approach to solve partial differential equations and is widely adopted both in the industrial world and for scientific research. The aim of the course is to provide an overview on advanced topics regarding FEM, usually not covered by MS courses and applicable to different fields of engineering. Nevertheless, main applications and examples will make reference to FEM for structural analysis.
Matrix analysis, basic concepts of FEM, programming
0. Basic concepts of FEM (for structural analysis)
Basic definitions and fundamental equations of the theory of elasticity (displacements, strains, stresses, governing equations, variational formulations, one-dimensional axiomatic approaches for beams)
Approximate solutions: the Rayleigh-Ritz method, the Finite Element Method (discretization, shape functions selection, assembly, solution)
1. Non-conventional shape functions
Shape functions for the solution of specific problems (the “shear-locking“ phenomenon)
Shape functions to improve convergence (“exact“ shape functions and “super-convergence“)
Shape functions to increase accuracy (p-elements)
Examples for rod and beam finite elements
2. FEM for high-frequency dynamic applications
The Spectral Element Method (SEM)
Examples for rod and beam finite elements
3. FEM for smoothing of functions
The Smoothing Element Analysis (SEA)
4. FEM for inverse problems
The inverse Finite Element Method (iFEM)
Applications to integration of functions on complex geometries and to “shape sensing”
On site
Written report presentation
P.D.2-2 - September