Structural applications of finite elements

Recommended Prerequisites

Mathematic Analysis; Algebra; Numerical Methods; Statistic; Vectorial Mechanics; Theory of Structures; Mechanics of Materials.

Teaching Methods

Presentation of the methodologies, its context, and resolution of implementation problems in the lectures.
Scheduling of practical works distributed in class.
Discussion / clarification of questions regarding the study conclusion of or work in the contact hours.

Learning Outcomes

It is intended that the students learn and control a numerical technique to approximate the differential equations (behaviour) of a continuous system through a set of algebraic equations, based on a finite number of variables (displacements). This tool should be understood as a numerical procedure for obtaining approximate solutions to problems of the continuum mechanics.
Subsequently, the aim is to understand and control the commercial tools of analysis of structures.

Work Placement(s)

No

Syllabus

• Introduction to FEM. Procedures in FEM;
• Theory of linear elasticity (review);
• Principle of virtual work. Formulation of the FEM;
• Finite Element of bi-articulated Bars (bar or tie) 2D and 3D;
• Finite Element of Beams. 2D theories of  Euler-Bernoulli and Timoshenko;
• Two-Dimensional Elasticity. 3-node and 4-node Finite Elements;
• Finite Element Analysis of Slabs. Thin slabs by Kirchhoff theory. Thick slabs by Reissner-Mindlin theory;
• Three-Dimensional Elasticity. 8-node Finite Element;
• Introduction to parameterization. Procedures in the parameterization. Numerical integration;
• Convergence and Error. Initial considerations. Convergence. Error analysis. Richardson extrapolation.

Assessment Methods

Continuous assessment
Continuous assessment: 100.0%

Bibliography

1. Eugenio Oñate, Calculo de Estructuras por el Metodo de Elementos Finitos, CIMNE, 1992

2. Zienkiewicz, O.C. Taylor, R.L.,, The finite element method, London : McGraw-Hill, 1989-1991.

3. Bathe and E. Wilson, Numerical Methods in Finite Element Analysis, Prentice-Hall,1976