Undergraduate Course: Computer Methods in Structural Engineering 3 (CIVE10018)
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 10 (Year 3 Undergraduate) |
Credits |
20 |
| Home subject area |
Civil |
Other subject area |
None |
| Course website |
None
|
Taught in Gaelic? |
No |
| Course description |
This course introduces computational matrix methods and the finite element method as a tool for numerical simulation with an introduction to the mathematics of matrices (Linear Algebra). |
Information for Visiting Students
| Pre-requisites |
Structural Mechanics/Analysis to 2nd year undergraduate level or similar |
| Displayed in Visiting Students Prospectus? |
No |
Course Delivery Information
| Not being delivered |
Summary of Intended Learning Outcomes
By the end of the course, the student should be able to:
- describe the basic steps and concepts of matrix methods of structural analysis and the finite element analysis of structures;
- identify and understand all the various matrix operations involved in the process;
- use the method in the solution of two dimensional simple elastic structural engineering problems, carry out checks to assess the correctness of the output, and interpret results. |
Assessment Information
| Coursework (40%) and degree examination (60%) |
Special Arrangements
| None |
Additional Information
| Academic description |
Not entered |
| Syllabus |
Segment 1 Matrix structural analysis
Lectures (4 hours per week); Tutorials (1 hour per week); Computer lab exercises, and computer lab projects (1 project in Segment 1 - Method Methods, and 2 projects in Segment 2 - Finite element method)
L1-2 Introduction to basic concepts; Basic matrix operations
L3-4 Fundamental structural analysis principles and indeterminacy
L5-6 Stiffness and flexibility; Flexibility method and beam example; Introduction to MASTAN (or a similar stiffness method-based structural analysis program)
L7-8 Stiffness method fundamentals; Stiffness method for beams with the unit displacement approach
L9-10 Stiffness method with unit displacement approach for beams (continued); Computer oriented direct stiffness method fundamentals
L11-12 Direct stiffness method for beams
L13-14 Direct stiffness method for trusses
L15-16 Direct stiffness method for frames
L17-18 Stiffness method with unit displacement approach for the trusses and frames.
Summary and revision
Segment - 2 Finite Element Method
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; stress-strain and strain-displacement 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 2D Rectangular Elements: 1
Lagrange and Serendipity family of elements; normalised coordinates; shape functions for the bi-linear element.
L9 2D Rectangular Elements: 2
Evaluation of element matrices; examples of specific cases.
L10 Isoparametric Elements: 1
Isoparametric concept; Mapping rectangular elements to distorted quadrilateral elements.
L11 Isoparametric Elements: 2
Derivation of element matrices; the need to use a Jacobian matrix.
L12 Isoparametric Elements: 3
Numerical integration for computing FE matrices.
L13 Practical Considerations in a FE Analysis
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.
L14 Revision
Segment 1 Matrix structural analysis
Tutorial 1 Static and kinematic indeterminacy & Flexibility and stiffness coefficients
Tutorial 2 Flexibility method problems
Tutorial 3 Stiffness method problems - beams
Tutorial 4 Stiffness method problems - beams (cont&©d) and simple trusses
Tutorial 5 Stiffness method problems - trusses and frames
Segment 2 Finite element method
Tutorial 1 Computer based exercise on Unix operating system; creating an ABAQUS input file.
Tutorial 2 Using ABAQUS to find the response of a cantilever subjected to a point load; using ABAQUS/viewer to display results; understanding and interpreting results from plots and output files.
Tutorial 3 Derivation of element matrices for rectangular elements using hand calculations.
Tutorial 4 Using ABAQUS to find the response of a column subjected to axial forces; using ABAQUS/viewer to display results; understanding and interpreting results from plots and output files.
Tutorial 5 Derivation of element matrices for distorted quadrilateral elements (including numerical integration) using hand calculations.
Computing Project 1: Using a frame analysis software (MASTAN or its equivalent)
Two frame problems will be set for the students to analyse. They will be asked to provide a report based on all the work carried out for the analyses and the assumptions made. They will be asked to present results in the form of graphs and diagrams (shear force, bending moment and deflection) and their interpretation of the results obtained.
Computing Project 2&3: Two small projects using the commercial FE package ABAQUS
Students are required to submit Tutorials 2 and 4 of Segment 2. They will be asked to present results in the form of graphs, interpret results obtained and answer specific questions.
Feedback Opportunities
Comments on marked computer project reports. In-class feedback during tutorial discussions.
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| Transferable skills |
Not entered |
| Reading list |
Reference texts:
McGuire W., Gallagher R.J. and Ziemian R.D. Matrix Structural Analysis John Wiley & Sons, 2000.
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| Study Abroad |
Not entered |
| Study Pattern |
Not entered |
| Keywords |
Not entered |
Contacts
| Course organiser |
Prof Yong Lu
Tel:
Email: Yong.Lu@ed.ac.uk |
Course secretary |
Ms Kathryn Nicol
Tel: (0131 6)50 5687
Email: kathryn.nicol@ed.ac.uk |
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