# Detailed module information

Module information on this degree can be found below, separated by year of study.

The module information below applies for the current academic year. The academic year runs from August to July; the 'current year' switches over at the end of July.

Students select optional courses subject to rules specified in the Mechanical Engineering Student Handbook,  for example at most three Design and Business courses. Please note that numbers are limited on some optional courses and selection criteria will apply.

## Finite Element Analysis and Applications

### Module aims

The aim of the course is to teach the students to use Finite Element programs in a practical way to solve problems in linear elastic stress analysis. A student who has studied the course should be able, in a later industrial setting, to undertake the analysis of real problems with a fair understanding of sensible modelling procedures. In support of this, the course is split into two stages:

1. Theoretical study of the Finite Element method, with emphasis on understanding what goes on inside a typical, modern, commercial program
2. Practical experience in analysis using an industry-standard, interactive, Finite Element program.

ECTS units:    5

### Learning outcomes

On successfully completing this module, students will be able to:

• Explain the basic theoretical principles of the Finite Element method
• Employ industry-standard software for interactive FE model generation, analysis and the post-processing of results
• Interpret the output from the software critically and intelligently in order to yield the required information
• Formulate the boundary conditions of a problem in a suitable form for correct analysis
• Assess alternative strategies (of element type, mesh design, boundary condition definition etc.) for economical and accurate FE modelling of specific 2D, 3D and axisymmetric structural problems

### Module syllabus

• Introduction: with application to static stress analysis. Context and history.
• Truss frame example: division into elements, selection of variables and shape functions, stiffness derivation, assembly of stiffness equations, application of boundary conditions, solution for displacements, computation of element stresses and strains.
• The constant strain triangle: Continuum model and role of continuum elements; Geometry of constant strain triangle (CST), nodal variables and shape functions, stiffness derivation (plane stress and plane strain), element stress and strain computation.
• Element forumulation: the need for more advanced and generalised procedures; element stiffness by virtual work; general procedure applied to CST; detailed derivation of linear rectangular element (Gauss quadrature, location of element integration points etc.); quadratic rectangular element, axisymmetric elements, 3-dimensional solid elements, truss and beam elements, membrane, plate and shell elements. Isoparametric elements, Jacobian mapping for arbitrarily shaped elements. Element performance: Stiffness and accuracy considerations. Nonconforming elements, reduced integration.
• Element libraries: elements offered by commercial programs (shapes, nodes, degrees of freedom, allowable load types, etc.). Materials, loads, supports and solution: analysis procedure for modern commercial programs (definition of structure and loads, supports and other constraints, solution, post-processing); material property definitions and matrices; geometric properties (thicknesses, cross-sectional areas etc.); load types (point forces and moments, pressure, body forces, thermal) and internal conversion to nodal loads; supports, prescribed displacements, rigid links; symmetric and antisymmetric boundary conditions and their application to reduce model size; stiffness transformations to model supports or loads at arbitrary angels; stiffness matrix assembly and solution, bandwidth and its minimisation; Other types of solution (structural dynamics, material plasticity, large deflections, contact problems, fracture mechanics).
• Guide to good modelling: Identification of appropriate domain of solution (2-/3-dimensional, axisymmetry, beams/shells etc.). Selection of elements, degrees of freedom, stress assumptions etc. Creation of mesh (refinement, shape, aspect ratios, curvature); Definition of material and geometric properties; application of loads and supports; pre-analysis checks; post-processing results - typical options; importance of verification, development of checking strategies; sources of inaccuracies and errors.

### Pre-requisites

ME1-HSAN; ME2-HSAN

### Teaching methods

• Duration: autumn and spring term (22 weeks)
• Lectures: lectures covering the theoretical material listed in the syllabus
• Tutorials: classroom and computer room, devoted mainly to tackling the four tasks listed in the syllabus, but including some general tutorial time. Students work in groups of 2 or 3. Results of practicals are reported on brief structured forms for assessment.
• Projects: Two tutorial sheets (not assessed), short project, both to be done mainly in own time.

### Assessments

 Written examinations: Date (approx.) Max. mark Pass mark Finite Element Analysis & Applications (3h) A Data and Formulae handbook is provided. This is a CLOSED BOOK Examination. April/ May 160 n/a Coursework (including progress tests, oral presentations etc.) Submission date Max. mark Pass mark Submission Feedback Practical task 1 Returned, with grade and written comments for discussion in tutorial Jan-March 10 n/a Practical task 2 Ditto Jan-March 10 n/a Practical task 3 Ditto Jan-March 10 n/a Practical task 4 Ditto Jan-March 10 n/a Total 200 n/a