Nonlinear analysis of structures

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.

Work Placement(s)

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