Structural Mechanics

Recommended Prerequisites

Linear Algebra, Mathematical Analysis, Numerical Analysis, Continuum Mechanics, Strength of Materials and Structural Analysis (at the level of a master's degree).

Teaching Methods

The traditional blackboard lecture style is used for (1) the motivation and detailed exposition of the fundamental ideas, concepts and methods and (2) the application and illustration of the theory, by working through selected examples in detail. The student is then expected to solve, under the supervision of the instructor, a collection of systematically arranged problems; the aim is (1) to suggest to him useful lines of disciplined thought in dealing with more complex problems and (2) to promote his autonomy.

Learning Outcomes

A) To understand some of the lower-dimensional mathematical models commonly used to describe the linear mechanical behaviour, under quasi-static loads, of beams (1D models) and plates (2D models), including their relation to the linear theory of elasticity (3D).

B) To have a reasonably in-depth knowledge of the finite element method (FEM), in its conventional displacement-based variant.

C) To apply the FEM to the numerical analysis of the lower-dimensional mathematical models referred to in A).

D) To critically assess the limitations of the mathematical and numerical models in A) and C).

Matters pertaining to the dynamic and non-linear behaviour of structures are addressed in other curricular units.

Work Placement(s)

No

Syllabus

1. Fundamentals of the finite element method (FEM)

2. One-dimensional (1D) models and their FE discretization

    2.1. Bending of planar beams - Euler-Bernoulli model and Timoshenko model (including an analysis of the shear locking phenomenon and techniques to avoid it)

    2.2. Bending and Saint Venant torsion of beams

    2.3. Bending and torsion of thin-walled beams - Vlasov and Benscoter models

3. Two-dimensional (2D) models and their FE discretization

    3.1. Membranes

    3.2. Bending of plates - Kirchhoff model (including conforming and non-conforming FE discretizations) and Reissner-Mindlin model (including an analysis of the shear locking phenomenon and techniques to avoid it)

Head Lecturer(s)

Anísio Alberto Martinho de Andrade

Assessment Methods

Assessment
Exam: 50.0%
Resolution Problems: 50.0%

Bibliography

K.D. Hjelmstad (2005), Fundamentals of Structural Mechanics (2nd edition), Springer.

P. Villaggio (1997), Mathematical Models for Elastic Structures, Cambridge University Press.

Gjelsvik A. (1981), The Theory of Thin Walled Bars, Wiley.

J.T. Oden, E.A. Ripperger (1981), Mechanics of Elastic Structures (2^nd edition), McGraw-Hill.

E. Oñate (2013), Structural Analysis with the Finite Element Method - Linear Statics, Volume 2: Beams, Plates and Shells, CIMNE/Springer.

F. Teixeira-Dias, J. Pinho-da-Cruz, R.A. Fontes Valente, R.J. Alves de Sousa (2010), Método dos Elementos Finitos – Técnicas de Simulação Numérica em Engenharia, ETEP.

T.J.R. Hughes (1987), The Finite Element Method – Linear Static and Dynamic Finite Element Analysis, Prentice-Hall.

E.B. Becker, G.F. Carey, J.T. Oden (1981), Finite Elements – An Introduction, Prentice-Hall.