Numerical Methods

Learning Outcomes

Transferable and Generic Skills

Having successfully completed this module you will be able to:

• Logical thinking and conceptualisation of a problem for solution by computer algorithm.
• Time management and independent learning.
• Presentation of data and analysis results.
• Ability to use the MATLAB programming platform including built-in functions.
• Learning the use of commercial FE software.
• Critical analysis and judgment as to the quality of computer analysis output.

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• The significance, calculation and interpretation of numerical errors and methods to eliminate or mitigate their effects.
• The fundamental concepts of the FE method.
• The limitations of the FE method and appropriate choice of element type to suit the problem.
• Numerical analysis techniques available to solve a range of mathematical problems encountered in engineering (root finding, regression analysis, Taylor series, differentiation and integration, solution of ODEs)
• The key steps required to complete a FE simulation.
• The theory of the formulation and solution of finite element models.

Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Use a commercial FE package to solve practical 1D and 2D engineering problems (including understanding of the pre-processing, solution and post-processing phases of the process).
• Write, compile, execute and test programs using MATLAB to solve a range of problems numerically.
• Utilise user manuals and online help pages/tutorials to learn and gain familiarity with commercial software platforms.
• Use MATLAB built-in functions in a range of contexts relating to problem solving in numerical analysis.

Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

• Recognise engineering problems that may be solved numerically.
• Demonstrate the accuracy of typical numerical and FE results.
• Develop and solve FE simulations.
• Apply concepts of numerical analyses and FE models for analysis and solving of real-life engineering problems.
• Select the appropriate numerical solution technique to solve the problem.

Part 1: Numerical analysis for engineers

Types of errors and propagation of errors; Numerical solution of non-linear equations; Regression analysis/Curve fitting methods; Taylor series and applications; Numerical differentiation & integration (quadrature); Ordinary Differential Equation solvers; Partial differential equations

Part 2: Programming for engineers (MATLAB)

Writing, compiling and executing MATLAB codes to solve a range of practical numerical problems through a mixture of lectures and computer workshops.

Teaching and learning methods

Teaching methods include

• Lectures
• Tutorials
• Computer workshops

Learning activities include

• Worked examples
• Tutorial questions
• Coursework
• Problem assignments
• Private study

PowerPoint slides, tutorial sheets and solutions, worked examples and pre-recorded videos available from module Blackboard

Resources & Reading list

General Resources

ABAQUS. User manual

Internet Resources

Mathworks references (Mathworks is the official owner of Matlab).

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.

Repeat Information

Repeat type: Internal & External