# ADAVANCED FINITE ELEMENTS ANALYSIS (MODULE 1) cod. 1006854

Academic year 2017/18
2° year of course - Second semester
Professor
Academic discipline
Scienza delle costruzioni (ICAR/08)
Field
A scelta dello studente
Type of training activity
Student's choice
21 hours
of face-to-face activities
3 credits
hub: -
course unit
in ENGLISH

Integrated course unit module: ADVANCED FINITE ELEMENT ANALYSIS

## Learning objectives

Knowledge and understanding:
The course aims to present concepts and tools for computational mechanics applied to generic solid structures beyond the linear behavior.
Furthermore the course intends to provide to the students the basis to perform numerical static or dynamic non-linear analyses of structures and enables them to read and understand computational mechanics books and to study autonomously the subject.

Applying knowledge and under standing:
At the end of course the student should be able to correctly develop a numerical model of structural elements or generic structures through the finite element technique in non-linear structural problems, both in static and dynamic problems.

Making judgments:
At the end of course the student should be able to correctly interpret the structural behavior of generic structures and to propose a proper numerical modeling.

Communication skills:
At the end of course the student should have a proper use of the terminology of the computational non-linear mechanics applied to structures and will be able to properly use it.

## Prerequisites

It is necessary to have at least attended to the following courses: Computational Mechanics and Mechanics of Structures.

## Course unit content

Non-linear problems in mechanics of solids and structures

Contents
1. Solutions of non-linear problems.
2. Mechanical non-linearity: basic concepts and a examples.
3. Introduction to plasticity of materials. Examples.
4. Solution of mechanical static and dynamic non-linear problems with finite elements.
5. Non-linear static and dynamic analysis of structures; examples and applications (seismic actions).
6. Geometrically non-linear problems. Examples.

## Full programme

1. Solutions of non-linear problems, iterative methods, convergence criteria.
2. Mechanical non-linearity: basic concepts of non-linear elastic behaviour and elastic-plastic behaviour of materials and structures. Examples.
3. Introduction to plasticity of materials. Examples.
4. Solution of mechanical non-linear problems with finite elements. Static and dynamic problems.
5. Non-linear static and dynamic analysis of structures; examples and applications (pseudo-static and dynamic analysis of structures under seismic actions).
6. An introduction to geometrically non-linear problems; large displacements, large strains, buckling analysis. Examples.

## Bibliography

• D.R.J. Owen, E. Hinton. Finite elements in plasticity: theory and practice. Pineridge Press, 1980
• P. Wriggers. Nonlinear Finite Element Methods. Springer, 2008.
• R. De Borst, M.A. Crisfield, J.J.C. Remmers, C.V. Verhoosel. Nonlinear Finite Element Analysis of Solids and Structures, 2nd Edition, Wiley, 2012.
• T. Belytschko, W.K. Liu, B. Moran, K. Elkhodary. Nonlinear Finite Elements for Continua and Structures, 2nd Edition, Wiley, 2013.
• R. Brighenti, Analisi numerica dei solidi e delle strutture: fondamenti del Metodo degli Elementi Finiti. Esculapio Editore (Bologna), 2014.
• Lecture notes provided by the teacher.
Teaching stuff:
- Stuff provided by the teacher (see the teacher’s website: http://www2.unipr.it/~brigh/index.htm) or from the Elly website of the Univ. of Parma.

All the suggested textbooks are available in the library of the Engineering school.

## Teaching methods

The course is organized in theoretical and practical lessons (by making use slides or other kind of computer presentations); the exercises are either developed by the teacher and autonomously in class also by making use of the computer and at home by the students.

For every topic, the practical activities are properly scheduled in order to provide the students the ability to solve the proposed problems on the basis of the previously explained theoretical concepts.

## Assessment methods and criteria

The final assessment consists in a single written test on all the topics covered by the course (with theoretical questions and simple numerical exercises). The students can also decide, on a voluntary basis, to improve the grading of their final exam by preparing a short report related to the non-linear analysis of a simple structure assigned by the teacher. Such a small project will contribute up to 30% of the final grading to the exam.

The evaluation of the final exam will be as follows:

- Only written test
Oral test (theoretical questions 50%, exercises 40%) (knowledge).
Clarity of presentation (Communication skills, 10%).

- Written test + project
An increment up to the 30% of the score obtained in the written test.

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