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 for solution of problems in solid/fluid mechanics, heat transfer, electromagnetism and acoustics. This course is an introduction to FEA as applied to elasticity problems in solid 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 |
¿ Introduction to FE terminology; steps of the analysis using an assumed displacement field approach for linear elastic analysis of structures.
¿ Feeding a finite element program (ABAQUS) with geometric, physical and loading information; understanding and interpreting results from a FE program.
¿ Introduction to plane stress, plane strain, axisymmetric, and 3D problems; degrees of freedom; stress-strain and strain-displacement relations.
¿ 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.
¿ Beam, Triangular and quadrilateral elements; normalised coordinates; shape functions.
¿ Isoparametric concept of mapping; derivation of element matrices; the need to use a Jacobian matrix; numerical integration for computing FE matrices.
¿ Factors influencing the choice of a model, element and order of Gauss integration; concept of reduced integration and zero energy modes; acceptable distortion of elements; choice of mesh; convergence requirements; adaptive meshing.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
| Additional Costs | None |
Course Delivery Information
| Not being delivered |
Learning Outcomes
By the end of the course, the student should 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.
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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, Butterworth-Heinemann, 2005.
3. Bathe, KJ. Finite Element Procedures, Prentice Hall, 1996.
4. Kim, NH; Sankar, BV. Introduction to Finite Element Analysis and Design, Wiley, 2009.
5. Smith, IM; Griffiths, DV. Programming the Finite Element Method, Wiley, 2004.
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | Numerical methods, solid mechanics, elasticity |
Contacts
| Course organiser | Dr Pankaj
Tel: (0131 6)50 5800
Email: Pankaj@ed.ac.uk |
Course secretary | Mr Craig Hovell
Tel: (0131 6)51 7080
Email: c.hovell@ed.ac.uk |
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