# Numerical Methods in Mechanical Engineering

## Module summary

Module code: MECH1066
Level: 6
Credits: 15
School: Engineering and Science
Department: Engineering
Module Coordinator(s): Abdelhafid Belaidi

## Specification

None.

### Aims

The aim of the Module is help students develop the necessary skills and learn the concepts of computer-aided solutions to typical Mechanical Engineering problems. It also helps them formulate mechanical, fluid and heat transfer problems ready for computer simulation using industry standard software.

### Learning outcomes

On successful completion of this module a student will be able to:
1 Identify the type of analysis suitable for the solution of an engineering problem.
2 Recognise and explain equations governing typical engineering problems
3 Formulate a problem ready for computer simulation and drive commonly used industrial software
4 Analyse and validate simulated results against benchmarks

### Indicative content

Introduction of Finite Element Analysis (FEA), Revision on matrix manipulation, flexibility method, stiffness method, interpolation functions, the shape function, element selection, discretisation of a domain, analysis type selection, building an FEA model, one dimensional FEA.

FEA with higher order elements, 2D plane stress element, node coupling, using symmetry features and reduction of model size, loads and constraints, comparison of full model size results against reduced model size results

2D truss elements, supressing degrees of freedom in an element, section properties, boundary conditions, 2D displacement of a truss framework

Introduction to Computational Fluid Dynamic (CFD), flow models, forms of flow governing equations, integral approach, differential approach, conservation and non-conservation forms of the transport equations, discretisation methods

Main stages in a CFD simulation, use of symmetry conditions, boundary conditions, uniform/non-uniform mesh distribution, mesh optimisation, convergence testing,

### Teaching and learning activity

The Module introduces students to the basic concepts of Finite Element Analysis (FEA) and Computational Fluid Dynamics (CFD). Students will learn how to analyse engineering problems, identify the type of analysis warranted and formulate problems ready for computer simulation. Theoretical concepts will be introduced through formal lectures and re-enforced through weekly laboratory sessions, working on real engineering problems. Students will be set an overarching multi-physics challenge that covers stress analysis, fluid flow and heat transfer. This will involve the design and optimisation of an engineering system.

### Assessment

Portfolio - 50%
LO - 1, 3, 4.
Pass mark - 40%
1500 words.
Portfolio of research and lab activities on Design and optimisation of engineering systems.

Exam - 50%
LO - 1, 3.
Pass mark - 40%
2 hours.
Unseen closed book exam.

All elements of summative assessment must be passed to pass the module.

Nature of FORMATIVE assessment supporting student learning:
A programme of laboratory sessions will give the chance to students to work on real problems individually. Because of the nature of these sessions, each student will have the chance to ask questions and receive individual feedback. Time will be set aside in lectures, during the assignment period, to monitor progress, discuss problems and give feedback.