This module aims to provide you with a sound basis in a variety of numerical techniques which will benefit the understanding and solution of engineering problems. The module provides a sound basis for post graduate research and work in industry. 

The techniques presented are general in nature and the feasibility of applying the techniques across a wide range of engineering applications is emphasised.  The module covers basic Finite Element Method (FEM) and Finite Difference Method (FDM).  

LO1. Derive the stiffness matrices of the commonly used 1D and 2D elements, understand the features of finite element shape functions and the physical interpretation of stiffness matrix. 

LO2. Demonstrate the following skills: assembling the global stiffness matrix, applying the boundary conditions, condensing the global matrix equation, and obtaining the solution for an engineering problem using finite element software.  

LO3. Systematically understand the physical interpretations and different engineering applications (e.g. temperature, water level and stress distribution) of different types of governing differential equations.  

LO4. Implement the finite difference approximations for first and second order differentials to solve simultaneous first order differential equations, higher order differential equations, and some practical 1D and 2D engineering problems (e.g. temperature distribution, water level in a river or a lake, torsional/shear stress in the cross-section of a rod). 

Face to face lecture and example classes are combined to explain the basic principles of numerical techniques and show how these can be applied to solve engineering problems. Some optional learning opportunities are provided, e.g. some websites are given for students to watch youtube videos about how to use a commercial finite element software to create and analyse typical engineering structures.  
 
Students are expected to work their way through all the lecture notes and tutorial sheets provided. Weekly module maps are provided to guide their learning.  It is only through such a study of the subject that the fundamental techniques and principles will be absorbed and the learning outcomes can be achieved. 

Independent and critical thinking - You will need to: 

• use your critical judgement to identify appropriate methods and analyse complex numerical problems 

• demonstrate intellectual curiosity in engaging with the complex ideas and principles  

Within this module you will also develop the following subject specific skills: 

• Solve ordinary and partial differential equations using numerical methods. 

• Formulate simple finite difference expressions using Taylor series. 

• Apply the principles of finite element and finite difference methods to a range of common engineering problems involving ordinary and partial differential equations and to predict distributions of key variables. 

• Develop computer programs using common spreadsheet software to solve typical field problems (e.g. fluid flow, heat transfer). 

• Peer learning and collaboration (informal) 

The assessment is assessed by an exam (LO 1-4), which covers both finite element method (FEM) and finite differences method (FDM). 

Formative assessment is provided through tutorials which are delivered throughout the semester.  

THE OPPORTUNITY FOR REASSESSMENT IN THIS MODULE:  

There is a potential for re-assessment in this module which may result in a 100% written assessment during the August Resit period.  

Opportunities for re-assessment is only permitted provided you have not failed more credit than in the resit rule adopted by your programme.  If the amount of credit you have failed is more than permitted by the relevant resit rule, you may be permitted to repeat study if you are within the threshold set for the Repeat rule adopted by your programme.  You will be notified of your eligibility to resit/repeat any modules after the Examining Board in the Summer period.  

All resit assessments will be held in the Resit Examination period, prior to the start of the following academic session.  

FEM: 
Finite Elements of a Continuum 

Bar elements, 2D truss and beam elements 
Virtual Work 
Weighted Residual Approach 

Triangle elements 

Shape Functions 

Numerical integration 

Square elements 
Plane stress/Strain elastic project 
 
FDM: 
Backward, Forward and Central Differences 

Initial and boundary value problems 

Simultaneous linear differential equations 

Higher order ordinary differential equations 

Partial differential equations 

Elliptic equations and applications 
Parabolic equations and applications (1D and 2D thermal, water and stress problems)