Postgraduate Course: Finite Element Analysis for Solids (MSc) (PGEE10006)
Course Outline
School  School of Engineering 
College  College of Science and Engineering 
Credit level (Normal year taken)  SCQF Level 10 (Postgraduate) 
Availability  Not available to visiting students 
SCQF Credits  10 
ECTS Credits  5 
Summary  The finite element method (FEM) (also called finite element analysis or FEA) originated from the need to solve complex problems in solid mechanics. FEM is used to obtain approximate numerical solutions to a variety of equations of calculus. Today it is used in a wide range of disciplines. This course is an introduction to FEA as applied to elasticity problems in solid and structural mechanics. The mathematical equations are developed using the virtual work basis of FEM and this is used to develop equations for one, two and three dimensional elements. As FEA is a computational tool this course includes practical exercises using the commercial package ABAQUS. A number of tutorials involving hand calculations are provided to aid understanding of the technique. 
Course description 
L1 Introduction
Course outline; areas of application of the finite element (FE) method; examples of some problems for which FE analysis has been used.
L2 FE terminology and steps
Introduction to FE terminology; steps of the analysis using an assumed displacement field approach for linear elastic analysis of structures.
L3 Input to and Output from a FE program 1
Feeding a finite element program (ABAQUS) with geometric, physical and loading information.
L4 Input to and Output from a FE program 2
Understanding and interpreting results from a FE program.
L5 FE Modelling
Introduction to plane stress, plane strain, axisymmetric, and plate bending problems; degrees of freedom; stressstrain and straindisplacement relations.
L6 Virtual Work Basis of Finite Element Method: 1
Definition of generic displacements, body forces, nodal displacements, and nodal actions; displacement shape functions with simple examples; relating generic displacements, strains, and stresses to nodal displacements.
L7 Virtual Work Basis of Finite Element Method: 2
Derivation of FE equilibrium equations using the virtual work principle; examples of derivation of stiffness and equivalent load vector for a two node truss element.
L8 Quadrilateral Elements 1
Normalised coordinates; shape functions for the bilinear and quadratic elements; Isoparametric concept; examples
L9 Quadrilateral Elements 2
Evaluation of element matrices; the Jacobian matrix; examples of specific cases.
L10 Quadrilateral Elements 3
Numerical integration; examples of numerical evaluation of element matrices
L11 Quadrilateral Elements 4
Examples of numerical and closed form evaluation of stiffness and load matrix terms
L12 Triangular elements 1
Natural coordinates; shape functions of constant and linear strain triangular elements; isoparametric mapping; examples
L13 Triangular elements 2
Evaluation of element matrices; the Jacobian matrix; examples of specific cases.
L14 Triangular elements 3
Numerical integration; examples of numerical evaluation of element matrices
L15 Beam elements 1
FE basis of Euler Bernoulli beam elements; FE matrices and shape functions
L16 Beam elements 2
Straindisplacement and stressstrain relations for Euler Bernoulli beams; evaluation FE matrices; limitations; examples
L17 Beam elements 3
FE basis of thick (Timoshenko) beam elements; shape functions
L18 Beam elements 4
Generalised straindisplacement and generalised stressstrain relations; evaluation of FE matrices; reduced integration
L19 Revision

Entry Requirements (not applicable to Visiting Students)
Prerequisites 

Corequisites  
Prohibited Combinations  
Other requirements  Structural Analysis/Mechanics 
Additional Costs  None 
Course Delivery Information
Not being delivered 
Learning Outcomes
On completion of this course, the student will be able to:
 describe the analytical methods and procedures which the finite element programs use to analyse elastic solid structures;
 be able to use the computer based finite element methods to solve simple problems by hand calculations
 identify and understand all the various matrix operations involved in the process;
 use computer programs to analyse elastic structures, present results in appropriate graphical formats, carry out checks to assess the correctness of the output, and interpret results properly.

Reading List
Recommended texts:
1. Cook, RD; Malkus, DS; Plesha, ME; Witt, RJ. Concepts and Applications of Finite Element Analysis, Wiley, 2002.
2. Zienkiewicz, OC; Taylor, RL. The Finite Element Method for Solid and Structural Mechanics, ButterworthHeinemann, 2005.
3. Bathe, KJ. Finite Element Procedures, Prentice Hall, 1996.
4. Smith, IM; Griffiths, DV. Programming the Finite Element Method, Wiley, 2004. 
Additional Information
Graduate Attributes and Skills 
Application of Mathematical concepts.
Computer Modelling skills.
Interpreting design problems. 
Keywords  Numerical methods,solid mechanics,elasticity,computational modelling 
Contacts
Course organiser  Dr Pankaj Pankaj
Tel: (0131 6)50 5800
Email: Pankaj@ed.ac.uk 
Course secretary  Miss Margaret Robertson
Tel: (0131 6)50 5565
Email: margaret.robertson@ed.ac.uk 

