Description
Objectives
The three main objectives of Finite Elements (FE) are: To recapitulate and integrate the structural models; To introduce the Finite Element Method (FEM) and practice its application to linear structural analysis; To develop the skills necessary to interpret and check the solutions. The first part of the course combines the definition of each structural model to its FEM solution. Besides introducing the use of commercial codes, the main purpose is to use the numerical solutions to support the physical interpretation of the alternative structural models. The second part addresses the definition and the characterization of the finite elements developed for each structural model. In what regards the use of commercial codes, the focus now is on the interpretation of numerical results in terms of consistency with the finite element assumptions, to support the identification of input errors and adequacy of the approximation in terms of design requirements.
Syllabus
Definition of the compatibility, elasticity and equilibrium conditions of the 3D elastic-linear model. Assumptions for 2D models (plane stress and plane strain states), plate and beam models, with and without shear deformation, and the bar model. Definition of field variables and equations by particularization of the 3D model. Fundamental concepts of the FEM displacement model: Domain decomposition; approximation of displacements; definition of compatible solutions. Use of a FE program; data definition and interpretation of results. Definition and interpretation of the FEM elementary and global equilibrium equations. Elements with C0 continuity: 1D, 2D (triangular and quadrangular) and 3D (tetrahedral and hexahedral) elements; applications, analysis of FE solutions and convergence with h and p refinements. Isoparametric elements and numerical evaluation of the elementary matrices. Elements with C1 continuity: Application to beams and plates with negligible shear deformation.
Cross Competence Component
The course supports the development of the following soft skills in the framework of the project (50% of the final assessment): Critical thinking (namely strategic thinking and problem solving approaches); Interpersonal and intrapersonal skills (oral, organizational and teamwork, self-discipline, perseverance, self-motivation); Information and media literacy (ability to locate and access information, as well as to analyse and evaluate media content).
Programming And Computing Component
The success of applying the FEM to the most diverse fields of engineering and science follows from its versatility and generality, as it can be applied to any problem defined by a system of partial differential equations, and the ease with which the procedures leading to the solution can be systematized. This simplicity led to the offering of software packages commonly used in the design of structural systems. A program is used in the course to describe the design of FE codes and to identify its capabilities in the analysis of complex structural applications. Moreover, all students participate in FEM-based group projects targeting one of two main objectives. The first is to develop skills on the application of structural design codes and the second targets the development of programming skills through the implementation of software for linear-elastic 2D or 3D structural applications.
Ethical Principles
All members of a group are responsible for the group's work. In any assessment, every students shall honestly disclose any help received and sources used. In an oral assessment, every students shall be able to present and answer questions about the entire assignment and solution.