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


Pre and co requisites



The aim of the course is help students develop the necessary skills and learn the concepts of computer-aided solutions to typical Mechanical Engineering problems to be able to formulate mechanical, fluid and heat transfer problems ready for computer simulation using industry standard FEA and CFD software.

Learning outcomes

On successful completion of this course a student will be able to:
1 Identify and explain equations governing typical fluid flow problems.
2 Identify the type of analysis suitable for the solution of a problem.
3 Formulate a problem for computer simulation.
4 Carry out FEA hand calculations for simple one-dimensional elastic problems.
5 Drive commonly used industrial computer software to simulate simple stress analysis, fluid flow and heat transfer problems.
6 Analyse and validate simulated results against analytical and experimental results.

Indicative content

Deformation of a tapered support column under tensile/compressive loading
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.

Overhead crane support plate
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

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

Mechanical integrity of a pressurised pipeline
Constant strain triangular element, elastic strain, 2D plain strain element, principal stresses, axisymmetric solid element,

Water supply pipeline
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

Fluid mixing in a process mixer
Main stages in a CFD simulation, use of symmetry conditions, boundary conditions, uniform/non-uniform mesh distribution, mesh optimisation, convergence testing, model duplication,

Teaching and learning activity

The course 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. Throughout the course students will be set challenges such as the design of pin jointed roof structures, cable anchoring steel plates, heat exchangers, pressurised pipelines and fluid mixers. Students will be set an overarching multi-physics challenge that covers, fluid flow and heat transfer. This will involves the optimisation of an air cooling system for computer microprocessors and electronic components.


Continuous assessment - 50%
LO - 2,3,4,5,6
Numeric grading.
Assignment + Challenges.

Examination - 50%
LO - 1,2,3,5
Numeric grading.
3 hour - Closed book examination

Pass mark - 30%, and 40% overall.

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

Nature of FORMATIVE assessment supporting student learning:
Students will be asked to work on real industrial problems to apply theory into practice. These will be set as group as well as individual challenges.