Undergraduate Course: The Finite Element Method 5 (CIVE11029)
Course Outline
School 
School of Engineering 
College 
College of Science and Engineering 
Course type 
Standard 
Availability 
Available to all students 
Credit level (Normal year taken) 
SCQF Level 11 (Year 5 Undergraduate) 
Credits 
10 
Home subject area 
Civil 
Other subject area 
Mechanical 
Course website 
None

Taught in Gaelic? 
No 
Course description 
The finite element method is an indispensable tool for engineers in all disciplines. This course introduces students to the fundamental theory of the finite element method as a general tool for numerically solving differential equations for a wide range of engineering problems. A range of field problems described by the Laplace, Poisson and Fourier equations is presented first and all steps of the FE formulation is described. Specific applications in heat transfer and flow in porous media are demonstrated with associated tutorials. The application of the method to elasticity problems is then developed from fundamental principles. Specific classes of problem are then discussed based on abstractions and idealisations of 3D solids, such as plane stress and strain, EulerBernoulli and Timoshenko beams and Kirchoff and MindlinReissner plates and shells. 
Information for Visiting Students
Prerequisites 
This course can only be taken by students with prior experience of Advanced Structural Analysis. Visiting students must discuss their experience with the Course Organiser before they will be permitted to enroll on the course 
Displayed in Visiting Students Prospectus? 
Yes 
Course Delivery Information

Delivery period: 2010/11 Semester 1, Available to all students (SV1)

WebCT enabled: Yes 
Quota: 50 
Location 
Activity 
Description 
Weeks 
Monday 
Tuesday 
Wednesday 
Thursday 
Friday 
King's Buildings  Lecture   111  14:00  15:50     
First Class 
Week 1, Monday, 14:00  15:50, Zone: King's Buildings. Classroom 10, Alrick Building 
Exam Information 
Exam Diet 
Paper Name 
Hours:Minutes 
Stationery Requirements 
Comments 
Main Exam Diet S1 (December)  The Finite Element Method 5  1:30  12 sides / 2 x graph / Open Book / Double Desks  Double Desks  Resit Exam Diet (August)   1:30  12 sides / 2 x graph / Open Book  c/w P03269, Open Book 
Summary of Intended Learning Outcomes
By the end of the course, the student should be able to:
 demonstrate the ability to produce FEM based numerical discretisations of mathematical descriptions (differential equations) of simple problems in continuum mechanics;
 demonstrate the ability to use FEM for solving simple steady and transient field problems using a standard software package;
 demonstrate the ability to use FEM to produce a reliable prediction of displacements and stresses in linear elastic bodies of relevance to engineering practice using a standard software package;
 demonstrate the ability to make a critical assessment of the calculation. 
Assessment Information
The assessment will be made on the basis of: Intermittent assessment 30%. Degree examination 70% 
Special Arrangements
None 
Additional Information
Academic description 
Not entered 
Syllabus 
Lectures: Titles & Contents
L1 Introduction
Structure of the course. Aims of the course. References with comments. Recap of Direct Stiffness Method for frame type structures (members/elements, joint/nodes, joint or nodal dofs, free and restrained dofs, element stiffness matrix, assembly into structure stiffness matrix, rearranging of structures stiffness matrix into free and restrained parts, solution for free doffs, calculation of reactions at restrained dofs, calculation of member forces). Recap of the virtual work formulation based finite element formulation for framed structures and continua.
L29 Mathematical foundations of the finite element method and application to field problems
The finite element concept and its history. Mathematical preliminaries (Equations of calculus describing physical phenomena, exact solutions and approximate solutions). Strong and weak formulations of a problem. The finite element method will be introduced as a tool for discretising continuum equations of physics describing a problem of interest in engineering. A number of common types of differential equations of interest primarily in civil and mechanical engineering will be presented and their applications discussed. The methods of FEM used to achieve discretisation (variational and Galerkin weighted residual approaches) will be introduced and demonstrated using problems described by Laplace and Poisson equations (this includes steady heat conduction, flow in porous media etc.).
L1012 FEM for continuum elasticity problems and thermomechanics
Concepts developed in the previous lectures will be applied to continuum elasticity problems. The discretisation process will be described first for general 3D solids and then specialised to 2D idealisations of plane stress, plane strain and axial symmetry. This will finally be extended to show how thermomechanical effects may be accommodated in the formulations.
L1316 FEM for structural engineering idealisations
The specialist concepts and formulations required for structural engineering applications of FEM will be formally developed. This will begin with simple 1D bars to beams and plates and shells covering EulerBernoulli and Timoshenko beams and Kirchoff and MindlinReissner plates and shells. Special issues such as locking and the use of continuum 2D and 3D elements in modelling flexure dominated structural members will be discussed and their solutions presented.
L1718 Special topics
A number of special topics, such as skew boundary conditions, multiple point constraints and substructuring for large problems will be introduced with examples
Computing Tutorial
A deep and slender cantilever beam in a plane will be analysed first using continuum plane stress elements followed by beam elements of the EulerBernoulli and Timoshenko type to familiarise students with ABAQUS and to enable them to understand the differences of modelling a beam using continuum elements and the different types of beam elements. Students will be expected to complete this tutorial in 2 computing lab sessions of 2 hours. No submission will be required.
Computer Project
A computer project will be undertaken in one of the School Computing Labs using the commercial FE software ABAQUS. There will be 3 sessions of 2 hours duration. Students are encouraged to use ABAQUS Viewer post processing to present their results in a neat form. The tutorials should give experience and confidence in the use of finite element analyses and encourage good practice in computational analysis.
Analysis of a plate with hole and a hot disk in hole
This tutorial introduces nonrectangular elements in such a way that the orientation of the main stresses is understood in advance. This ensures that the student examines the principal stress as a means of understanding the behaviour. The stress concentration around the hole will require judicious mesh refinement to capture and provide useful experience. Assuming that the hole contains a disc of material at high temperature, the heat conduction into the plate will be analysed. The effect of thermally induced stresses caused by the thermally expanding disc will also be analysed.

Transferable skills 
Not entered 
Reading list 
Introduction to the Finite Element Method $ú Theory, Programming and Applications, Erik G. Thompson, John Wiley and Sons, 2005.
Finite Element Analysis  From Concepts To Applications, D.S. Burnett, AddisonWesley 1988
Concepts and Applications of Finite Element Analysis, Cook, Malkus, Plesha and Witt, Wiley 2002
The finite element method 4th Edition, Volume I: Basic Formulation and Linear Problems, O.C. Zienkiewicz and R.L. Taylor, McGraw Hill 1989Course Assessment
http://www.see.ed.ac.uk/~asif/Protected/CVFEM
http://homepage.usask.ca/~ijm451/finite/fe_resources/fe_resources.html
http://www.colorado.edu/engineering/CAS/Felippa.d/FelippaHome.d/Home.html
http://en.wikipedia.org/wiki/Finite_element_method

Study Abroad 
Not entered 
Study Pattern 
Not entered 
Keywords 
Not entered 
Contacts
Course organiser 
Dr Asif Usmani
Tel: (0131 6)50 5789
Email: Asif.Usmani@ed.ac.uk 
Course secretary 
Mrs Laura Smith
Tel: (0131 6)50 5690
Email: laura.smith@ed.ac.uk 

