The course is introductory to finite element method. Nonetheless students will learn all the necessary information to independently create models to carry out the most relevant analyses in the mechanical sector.
- "PROGETTAZIONE ASSISTITA DAL CALCOLATORE A.A. 2013-2014", McGraw-Hill Create
- Slides of the course
- Models provided for the hands-on sessions
Learning Objectives
The course aims to:
- teach theoretical bases of both for linear and non-linear finite element formulations;
- teach finite element modeling techniques;
- develop students' capabilities to perform a critical analysis of the results (a number of examples will be jointly developed in a computer room);
- teach the use of a pre-/post-processing software;
- teach the use of finite element solvers based on textual model input.
Prerequisites
None
Teaching Methods
Theory classes and hands-on in computer room.
Further information
-
Type of Assessment
Written test comprised of: preparation of a finite element model, given a CAD model; set up of one of the analysis explained during the course; analysis of the results. In case of positive evaluation (18/30 score in the Italian system), an interview on the theoretical topics of the course will follow.
Course program
Theory:
- Introduction to finite elements
- Finite element formulation
- general concepts on finite elements;
- integral formulation;
- assembly of system matrix;
- shape fucntions and isoparametric elements;
- natural coordinate systems and numerical integration;
- parameters to check mesh quality;
- Discretization with finite elements:
- calculation of stiffness matrix;
- calculation of mass matrix (lumped and consistent);
- load modeling (load lumping and work equivalent);
- constraint modeling (master-slave, Lagrange, and penalty methods);
- error estimate and convergence.
- Time domain
- semi-discretization (modal analysis and frequency response function);
- time discretization (concepts and algorithms).
- Solution algorithms based on residual methods
Activity in computer room:
- verification and simplification of a geometric model;
- mesh generation with 0D, 1D, 2D, and 3D elements;
- mesh quality check;
- setup of linear and non-linear analyses (static, modal, frequency response function, thermostatic, thermo-mechanical, non-linear quasi static and non-linear dynamic)