# 72769 - COMPUTATIONAL MECHANICS

### SDGs

L'insegnamento contribuisce al perseguimento degli Obiettivi di Sviluppo Sostenibile dell'Agenda 2030 dell'ONU.

## Conoscenze e abilità da conseguire

The course is an introduction to computational mechanics of solids and structures. The goal of the course is to provide the students with the fundamental concepts and operating tools to solve current structural problems using computer technology.

## Programma/Contenuti

Requirements/Prior knowledge

Fluent spoken English is a necessary pre-requisite: all lectures and tutorials, and all study material will be in English.

Course Contents

MODULE 1

1. Introduction

1.1 Strong and weak forms of the governing equations

1.2 The Galerkin method

2. The finite element method for static linear elasticity

2.1 Derivation and implementation of a basic 2D finite element code

2.2 Generalization of finite element procedures for linear elasticity: interpolation and numerical integration in 1D, 2D and 3D

2.3 Structural elements for finite element analysis

2.4 Analysis of the finite element method

MODULE 2

3. The finite element method for nonlinear problems

3.1 Origins of the nonlinearity in structural problems: material and geometric nonlinearity

3.2 Numerical solution of nonlinear problems: the Newton-Raphson method

3.3 Elastoplasticity: an illustration of material nonlinearity

3.4 Some comments on instabilities and bifurcation problems

Depending on the time available and on the students' background:

4.a The finite element method for dynamic problems in linear elasticity or 4.b An introduction to domain decomposition strategies

## Testi/Bibliografia

- Lecture slides and notes (available on the web site https://iol.unibo.it/ )

- Introduction to Finite Element Methods, C. Felippa , University of Colorado at Boulder, Chs 1-3, 2010, http://www.colorado.edu/engineering/CAS/courses.d/IFEM.d/Home.html

- Thomas J.R. Huges. The Finite Element Method. Dover Publications.

- M. Bonnet, A. Frangi, C. Rey. The finite element method in solid mechanics. McGraw-Hill Education.

- Antonio J. M. Ferreira. MATLAB codes for Finite Element Analysis. Springer.

During the lectures, some reading assignments will be made from selected papers in the published literature.

## Metodi didattici

The course content will be entirely covered by the lectures. The course includes some laboratory sessions, which will cover the practical aspects of the lectures. The instructors will tutor the students.

## Modalità di verifica dell'apprendimento

A final oral examination is planned, based on questions intended to assess the knowledge and understanding of the topics covered by the course. Furthermore, the student should present and discuss the solutions of some homework assignments (generally 4) and a final project.

To obtain a passing grade, students are required to at least demonstrate a knowledge of the key concepts of the subject and some ability for critical application.

A failing grade will be awarded if the student shows knowledge gaps in key-concepts of the subject and/or logic failures in the analysis of the subject.

## Strumenti a supporto della didattica

The teaching tools are the projector and the PC.

## Orario di ricevimento

Consulta il sito web di Stefano de Miranda

Consulta il sito web di Federica Daghia