Finite Elements

Recommended Prerequisites

The curricular units recommended are: Mathematic Analysis; Linear Algebra; Mechanics of Materials; Theory of Structures. There is necessary knowledge about the following subjects: differential equations; integral computations; matrix calculations; behaviour of materials; structural equilibrium by energetic formulation.

Teaching Methods

Theoretical-practical lessons composed by detailed explanations of the syllabus and resolution of practical applications to supply all the needs to guidelines the students on the matter. Tutorials help and guide the students to solve the proposed work.

Learning Outcomes

To knowledge the main concepts and theoretical bases required to the formulation of the finite element method for resolution of structural problems. To provide the knowledge of important elements used in the structural analysis.

Work Placement(s)

No

Syllabus

1. Main Concepts Required
The weighting residuals method: continuum approximating functions. The points for computation in the sub-domains. The Galerkin´s method.
Approximated solution for differential equations in the domain and at the boundaries. Weak formulations. Approximated discrete functions: the finite element method.
2. The Finite Element Method
Shape functions: continuity requirements. Linear and high degree shape functions. Lagrange and Serendipity elements. Mapping and numerical integration. Parametric and isoparametric mapping. Integrating at the Gauss points.
3. The Finite Element Method in the Structural Analysis
Equilibrium equation formulation. Problems in linear elasticity. Bar and Timoshenko beam elements. Bi-dimentional elements in elasticity. Shell elements.

Head Lecturer(s)

Maria Helena Freitas Melão Barros Gomes Pereira

Assessment Methods

Continuous
Synthesis work: 50.0%
Exam: 50.0%

Bibliography

1. O. C. Zienkiewicz, (1989) The Finite Element Method- VolI- Basic Formulation and Linear Problems.

2. E. Hinton, R. Owen (1977) Finite Element Progamming . Academic Press.

3. K C Rockey, H R Evans, Griffiths, D. A. Nethercot, (1979) Finite element Method -A basic introduction.

4. Y. K Cheung, Y Yeo (1979) A practical introduction to the finite element analysis.

5. J. N. Reddy, (2006) An introduction to the finite element method, MacGraw-Hill.

6. A. Portela, A. Charafi, (2002) Finite elements using MAPLE, Springer.