# The finite element method

Tags: research proposal, Prentice-Hall, Englewood Cliffs, Finite element method, O.C. Zienkiewicz, critical literature, Record Id, Engineering mathematics, lab reports, Module Assessment, independent research project, Civil and Structural Engineering, Module Description, lectures, Structural Analysis, element size, global stiffness matrix, element stiffness matrix, the Finite Element method, Unit Description, differential equations, finite element, dynamic aspects, Research Skills, individual research project, finite elements
Content: Civil and Structural Engineering Department Module Description : CIV8130
Module Title Credits Co-Ordinator Semester Unit Description Unit Aims Syllabus Learning Hours
Computational Structural Analysis and Research Skills
15
Christopher Keylock
Autumn
This module integrates two components. The first covers the theoretical and practical aspects of using the Finite Element Method in structural analysis. It starts with some basic concepts such as assembly and solving systems of equations. Next, weak forms and strong forms are discussed together with interpolation via finite element shape functions, so that general differential equations can be treated. Special emphasis is put on dynamic aspects such as different mass matrices and time integration algorithms. Part of the assessment is carried out via an individual piece of coursework that helps the student use professional finite element software.The second component will actually be taught first and is a self-contained 5 credit element on research skills. It combines lectures and a seminar with the primary learning objective to produce a pass-toprogress research proposal to support the semester 2 (MEng) or summer (MSc) individual research project. Gain (i) an understanding of the fundamentals and (ii) a working knowledge of the practicalities of the Finite Element method in static and dynamic structural analysis. Understand how to undertaken a piece of independent, academic research to a high level, and produce a research proposal that incorporates a critical Literature Review, explanation of detailed methodology and addresses health and safety issues. Part A: Introduction to Finite Element analysis Establishing the field equations of elasticityMoving from the continous system to a discretised systemFinite Element shape functionsIsoparametric Finite ElementsLinear and quadratic 3D continuum elementsNumerical integrationIntroduction to time domain dynamicsAppreciation of element size and time step selection procedures Part B:Introduction to research project formulationUndertaking a critical literature reviewWhy choose a particular methodology (Experiment, fieldwork, modelling)?Experimental designVerification, validation and software validationTime & Resource Management, and Health and SafetyLibrary study session on searching for resources and plagiarism
Activity Lectures
Learning Hours of the Unit Remarks
Hours 26
Tutorials
Computer Modelling
5
Tutorials
Practical Classes
5
Indepentant Study(including Prep
110
for Assessment)
Seminars
Seminars
2
Tutorials
2
Internet-based Research
teaching methods
Part A: 20 lectures to learn the fundamentals. 5 hours of tutorials to put fundamentals into practice. 5 hours of computer classes to learn how to use professional software.
Total Hours 150
H&S / risk management LEARNING OUTCOMES Assessment Methods
Part B: 6 lectures 1 Library skills tutorial 1 seminar to discuss research ideas with a member of staff. Aspects of H&S pertaining to research will be covered in lectures and will form a necessary aspect of the research proposal. 1. Derive the global Stiffness matrix from a mesh of finite elements and reduce according to the boundary conditions 2. Derive the element stiffness matrix for continuum finite elements from a governing differential equation 3. Use finite element shape functions for the interpolation of a variable and its gradient. 4. Perform numerical integration of the element stiffness integral equations 5. Use time integration to perform dynamic analysis 6. Appreciate time step and element size selection procedures 7. Develop greater understanding of how to undertake a piece of civil engineering research. 8. Improve capability to undertake a critical review of the relevant literature. 9. Produce a high quality engineering research proposal. Individual coursework (20%): This component tests the student's understanding of using finite element software, in particular the effects of element size on the accuracy of the solution. Written exam paper (80%): This component tests the student's understanding of the theory, fundamentals and applications of finite elements in statics and dynamics.
Assessment Philosphy
Pass-to-progress research proposal to set the student up appropriately to undertaken their independent research project in subsequent parts of their degree. The deadline for students on CIV4002 will be two weeks later for this (Fri. wk 12). A mixture of hands-on computer work without time constraints and an in-depth assessment of theory and fundamentals means that various skills are tested.
Assessment of the ability to understand the research process is best-accomplished by a research proposal.
Module Assessment
Type of Assessment
Fomative Assessment and Feedback
Assessment Type Individual Coursework, this includes lab reports, designs etc Written Exam Invigilated Individual Coursework, this includes lab reports, designs etc
Learning Outcomes (LO1) (LO2) (LO7,LO8,LO9)
Week Autumn Week 12 Autumn Week 15 Autumn Week 10
Written feedback on the coursework will be provided.
Day Monday
Percentage 20
Exam Period
80
Friday
0
Total Percentage 100%
Formative feedback on the research proposal will permit students to reshape it until it is of a sufficient high a quality.
Book 1 - Recommended Title: The finite element method. Author: O. C. Zienkiewicz Edition: 3rd ed. Publisher: London : McGraw-Hill, 1977 Identifier: ISBN 0070840725;ISBN 9780070840720 Format: xv,787p. Notes: 3rd expanded & revised ed. of "The finite element method in engineering science". Subjects: Finite element method; Engineering mathematics; Finite element method; Engineering mathematics; Engineering Mathematics Finite element methods Record Id: 21174322250001441 Book 2 - Recommended Title: The finite element method : linear static and dynamic finite elment analysis Author: Thomas J. R. Hughes Publisher: Mineola, NY : Dover Publications, 2000 Identifier: ISBN 0486411818;ISBN 9780486411811
Format: xxii, 682 p. : ill. ; 24 cm. Notes: Reprint. Originally published: Englewood Cliffs, N.J. : Prentice-Hall, 1987. The author has corrected minor errors inthe text and deleted the sections of Chapters 10 and 11 that are no longer necessary. Subjects: Finite element method; Boundary value problems Further Information: Thomas J.R. Hughes. Record Id: 21185361010001441 Book 3 - Recommended Title: Finite element procedures Author: Klaus-Jurgen Bathe Edition: 2nd ed. Publisher: Englewood Cliffs, N.J. ; London : Prentice-Hall, 1996 Identifier: ISBN 0133014584;ISBN 9780133014587 Format: 1037p ; 24 cm. Notes: Previous ed.: 1992. Subjects: Finite element method; Engineering mathematics Further Information: Klaus-Jurgen Bathe. Record Id: 21169332610001441 Book 4 - Recommended Title: The finite element method. Vol.1, Basic formulation and linear problems. Author: O. C. Zienkiewicz Other Contributors: R. L Taylor Edition: 4th ed. / O.C. Zienkiewicz and R.L. Taylor. Publisher: London : McGraw-Hill, 1989 Identifier: ISBN 0070841748;ISBN 9780070841741 Format: xx,648p : ill. ; 24 cm. Notes: Previous ed, 1977. 1st ed. pub. 1967 with title "The finite element method in structural and continuum mechanics". Subjects: Finite element method; Structural analysis; Finite element method; Engineering mathematics Record Id: 21192356380001441 Powered by TCPDF (www.tcpdf.org)

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