The objective of this UC is to introduce the Finite Element method (FEM) and its application to solve problems in structural mechanics, heat transfer and fluid mechanics. The basic concepts of the FEM are presented and commercial software packages are used to give students some practical experience in FEM modelling. On successful completion of the course students will be able to: i) discuss the strengths and weaknesses of the FEM; ii) to solve simple problems by the FEM using analytical techniques; iii) to know the computational implementation of the FEM; iv) to perform finite element analysis using commercial software packages; v) to analyze the obtained numerical results.
Second order differential equations. Strong and weak formulation. Galerkin approximation.
1D problems: Domain discretization; Finite element and shape function. Linear and quadratic elements. Higher-order elements. Applications: Unidimensional bars; Heat transfer; Laminar flow. Discrete systems.
2D problems Triangular and rectangular elements. Two-dimensional shape functions. Linear and quadratic elements.
Standard element. Coordinate transformation. Numerical Integration. Isoparimetric elements. Applications: Heat transfer, Potential flow; torsion in shafts with non-circular section. Elastic membranes. Finite element for twodimensional elasticity.
Finite elements for plane truss structures. Beam element. Frame element.
Error estimation. Modelling 2D problems: errors; admissible elements; mesh refinement.
Three-dimensional problems. Development of a Finite Element program. Finite element modelling and analysis using commercial software packages.
The assessment is based on a final written exam and one project. The final grade is obtained as follows: Project = 60%;
Final Exam = 40%. The project is developed by groups of three students. Approval in the discipline requires that the
final test has a minimal grade of 7.5 (out of 20) and a final grade equal or above 9.5. The project may have an oral presentation and discussion.
"Introduction to the Finite Element Method", J.N Reddy, 2018, 4th Edition, McGraw-Hill
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