# Nonlinear analysis of structures

Year
5
2019-2020
Code
02006769
Subject Area
Structures and Structural Mechanics
Language of Instruction
Portuguese
Mode of Delivery
Face-to-face
Duration
SEMESTRIAL
ECTS Credits
6.0
Type
Elective
Level

## Recommended Prerequisites

Mechanics and Strength of Materials, Theory of Structures.

## Teaching Methods

Theory exposition by the teacher, followed by a proposal of pertinent exercises, whose resolution is  summarized by the teacher and detailed and programmed by the students with teacher support. The programming language “Octave” has been used.

## Learning Outcomes

After completing this unit, the student shall be familiar with the fundamental features of non-linear structural analysis, giving him a basis for theoretical and computational research on this area. Furthermore it shall give the student the necessary critical capacity for the use of third-party software on non-linear structural analysis.

No

## Syllabus

A. General considerations: review of fundamental concepts of Continuum Solid Mechanics; kinds of non-linearity; field of application of Non-linear Structural Analysis; numerical methods for the resolution of non-linear systems of equations, applied to the Displacement Method of Structural Analysis.
B. Material non-linearity: non-linear elastic behavior; elastoplastic material behavior in the one-dimensional case; extension to the three-dimensional case; time-dependent rheological behavior (visco-elasticity and visco-elasto-plasticity).
C. Geometrically non-linear behavior: stability analysis by means of the displacement method; taking into account the geometrical stiffness in the non-iterative computation of displacements; problems with large displacements and rotations and small deformations; introduction to large deformationsStructural design.

## Assessment Methods

Evaluation
For the evaluation there are three options available to the student: Midterm exams, at the end of each one of the three chapters, consisting in the analytical development of the solution of a proposed problem, followed by programming the developed algorithm; Exam; Synthesis work: 100.0%

## Bibliography

Dias da Silva, V. (2007), Introdução à Análise Não-Linear de Estruturas, DEC-FCTUC

Dias da Silva, V. (2005), Mechanics and Strength of Materials, Springer, ISBN 3-540-25131-6

M.A. Crisfield, Non-linear Finite Element Analysis of Solids and Structures, Volume 1: Essentials, John Wiley & Sons Ltd, 1991, ISBN 0-471-92956-5

T. Belytschko, W.K. Liu, B. Moran, Nonlinear Finite Elements for Continua and Structures, John Wiley & Sons Ltd, 2000, ISBN 0-471-98773-5