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
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.
CA1: Applying knowledge and understanding related to problem identification and formulation of solutions, in the field of mechanical engineering, to set up, design, implement and verify systems and apparatus, even of high functional complexity, taking into account the implications related to environmental, economic and ethical aspects, employing well established methods.
CA3: Applying knowledge and understanding related to the choice and application of appropriate analytical and modelling methods, based on mathematical and numerical analysis, in order to better simulate the behavior of components and plants in order to predict and improve their performance.
CA8: Applying knowledge and understanding related to the appropriate interpretation of the results of experimental tests, verification calculations and complex theoretical simulation processes, through the use of the computer, applying the acquired experimental, modeling, mathematical and informatics bases.
CA9: Applying knowledge and understanding related to the critically assessment of data and results, drawing appropriate conclusions, aware of the degree of uncertainty that may affect them.
CA10: Applying advanced knowledge and understanding to operate effectively, individually and as members of a group, having a clear understanding of the context of engineering problems and of the interdisciplinary implications that characterize mechanical engineering.
CA11: Applying improved knowledge and understanding to present in written, verbal and, if necessary, multimedia form, their arguments and the results of their own study or work, with characteristics of organic and technical rigour.
CA12: Applying adequate knowledge and understanding to understand English texts.
CA15: Applying knowledge and understanding to achieve adequate preparation for tertiary level university studies (frequency to post-master's degree courses and doctoral schools) in order to further deepen knowledge and skills in research.
CC1: In-depth knowledge and understanding of the theoretical-scientific aspects of engineering, with a specific reference to mechanical engineering, in which students are able to identify, formulate and solve, even in an innovative way, complex and/or interdisciplinary problems. The ability to understand a multidisciplinary context in the engineering field and to work with a problem solving approach
CC2: In-depth knowledge and understanding of the theoretical-scientific aspects of mathematics and other basic sciences. To be able to use this knowledge to interpret and describe complex and/or interdisciplinary engineering problems.
CC3: Knowledge, understanding and use of scientific (computer and other) tools specific to the field of mechanical engineering design.
CC4: Knowledge and understanding of numerical methods for the design and verification of mechanical components and/or systems, including numerical models for the correct representation of material behaviour. Knowledge of analysis types necessary to carry out the aforesaid design and verification activity according to the most recent requirements of the industrial world.
CC5: Knowledge and understanding of materials and their behaviour in the various loading conditions found in design practice. Methods for characterising material behavior.
Theory classes and hands-on in computer room.
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.
- 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)