87253 - Computer Aided Design of Mechanical Structures m

Learning outcomes

The course aims to illustrate the main analytical and numerical methods for structural calculation, particularly suited for computer use. The student will be able to develop calculation programs based on different numerical methods, understand the mathematical foundations of the most common commercial software, and use them for the structural analysis of mechanical components. After covering the main concepts of continuum mechanics and numerical calculation, the student will be able to delve into the main simulation techniques based on the Displacement Method, the Finite Element Method, and the Finite Difference Method. The student will therefore acquire the following skills:

• Ability to set up finite element calculations for mechanical structures.
• Ability to perform advanced finite element analyses of mechanical structures.
• Knowledge of the structure of a finite element calculation code.

Course contents

Review of Structural Mechanics.

Differential equations of main physical phenomena.

Analytical solution of ordinary and partial differential equations.

Numerical solution methods for thermo-structural problems.

Variational calculation and finite element.

Frame modeling with beam elements for static, dynamic, and critical load analysis: calculation of the linear and geometric stiffness matrix, the mass matrix, and the load vector.

Modeling of planar and axisymmetric structures with two-dimensional C0 finite elements: triangular and quadrilateral elements.

Modeling of three-dimensional structures: solid and shell finite elements.

Mesh generation methods.

Readings/Bibliography

G.M. Santi, F. Cesari; Il Metodo degli Elementi Finiti nella modellazione meccanica delle strutture - Teoria e applicazioni, Clueb, 2024

Teaching methods

Lectures on theory and exercises, plus additional exercises assigned to be completed independent

Assessment methods

Students are encouraged to form groups of 2-3 people.

During the lessons, exercises with questions are given to check the understanding of the subject matter.

Exercises performed using a calculation program are collected in a notebook to be presented at the exam.

The exam will take place in two phases. In the first phase, students will be given an oral question in written form, for which they will have 30 minutes to answer on paper. After submitting their responses, the professor will grade the papers, and only those who pass the written question will proceed to the oral exam. The oral exam will consist of theoretical questions and a review of the exercise notebook completed during the year.

Office hours

See the website of Gian Maria Santi