Finite Elements

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49047 Finite Element Applications in Structural Mechanics

The Finite Element Method (FEM) is a computer based analysis tool, used primarily in the field of structural mechanics, to solve stress and vibration problems. Other non-structural mechanics applications of the method include heat problems, diffusion of pollutants, fluid flow in porous medium, electrostatics and electro-magnetics. This subject extends understanding of Finite Element analysis techniques and their application to problems in engineering, particularly in solid and structural mechanics, and develops problem formulation and modelling skills in FEM. Topics include a review of matrix analysis methods; the derivation of element stiffness for plane elasticity and force matrices; Finite Element modelling techniques, limitations, errors and solution accuracy of the method. The subject is also oriented toward users of the FEM and requires the use of general purpose Finite Element programs in assignments and project work.

Course Name: Master of Engineering and other postgraduate courses in Engineering

Credit Points: 6 (3 hpw)

Modes of Presentation: Normal (3 hpw for one semester) or block release

Pre-requisites: 48349 Structural Analysis or  or equivalent as part of a completed first or higher degree in Engineering or a cognate discipline

Co-requisites: Nil

Content:

Introduction and overview of the Finite Element Method. Historiacl overview. Essential building blocks of FE models

Revision of Matrix Methods in the analysis of frame structures. Formulation of a simple Bar Finite Element. Concept of assembly and solution of system of equations of complete structure. Recovery of values inside the element from nodal solution.  

Introduction and overview of FE software. Computer Laboratory

Overview of important physical & mathematical concepts: Approximate solution using weighted residual and variational methods. Revision of elasticity theory and the principles of equilibrium and compatibility.

Finite Elements for Plane Elasticity: The derivation of stiffness and force matrices using total potential and assumed displacement fields. The isoparametric formulation. Numerical integration and higher order elements.

Plate and Shell Elements and general 3D Analyses : Isoparametric shell elements. Solid isoparametric element. Shells of revolution and axisymmetric elements. Fourier analysis.

FEA Modelling Skills and Techniques: Mesh design, convergence and the analysis of errors.  Quality of FE models. Element selection, Errors & Accuracy in Linear Analysis . Symmetry and anti-symmetry and other types of symmetry. Super-elements and sub-structuring techniques. 

Overview of advanced topics in FEA such as Dynamic and Non-Linear Analyses: The use of FEA to estimate normal modes and transient and steady state response. Buckling and large displacement analysis, material models. Examples of non-linear applications in structural and solid mechanics.

Extensive use of FEA programs in assignments and projects.

Method:

Formal lectures combined with tutorials are used in teaching the subject. The tutorials are aimed at providing a deeper insight in important topics and at reinforcing problem solving skills. Computing facilities are used to provide hands-on experience with Finite Element software and their application in engineering.

Assessment: Assignments 35%, Laboratory project 35%, Quiz 30%

Textbooks:

Cook, R.D. "Finite Element Modeling for Stress Analysis" Wiley, 1995.

References:

  1. Zienkiewicz, "The Finite Element Method", McGraw Hill. 1982

  2. Zienkiewicz & Taylor, "The Finite Element Method" 4th Ed, McGraw-Hill, Vol 1 1989, Vol 2 1991.

  3. Bathe, "Finite Element Procedures in Engineering Analysis". Prentice Hall. 1982

  4. Hughes, "The Finite Element Method", Prentice Hall, 1987.

  5. Cook, Malkus & Plesha, "Concept and Applications of Finite Element Analysis", 3rd Ed.Wiley. 1989.

  6. Cook, "Finite Element Modeling for Stress Analysis" Wiley, 1995.

  7. Reddy, "An Introduction to The Finite Element Method", 2nd Ed., McGraw Hill. 1993.

  8. Rockey, Evans, Griffith & Nethercroft, "The Finite Element Method", Granada. 1975.

  9. Pilkey & Wunderlich, "Mechanics of Structures, Variational & Computational Methods". CRC. 1994.

  10. Jennings & McKeown, "Matrix Computations" 2nd Ed. Wiley, 1992.

  11. Al-Khafaji & Tooley, "Numerical Methods in Engineering Practice". CBS 1986.