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2014/15 Undergraduate Module Catalogue
MECH3730 Structural Mechanics
10 creditsClass Size: 100
Module manager: Prof David C Barton
Email: D.C.Barton@leeds.ac.uk
Taught: Semester 1 (Sep to Jan) View Timetable
Year running 2014/15
Pre-requisites
| MECH1230 | Solid Mechanics |
| MECH1520 | Engineering Mathematics |
| MECH2610 | Engineering Mechanics |
This module is mutually exclusive with
| MECH3900 | Finite Element Methods of Analysis |
Module replaces
MECH 3105 Fundamentals of Finite Element AnalysisMECH 3230 Engineering CFDMECH 3825 Computational Fluid MechanicsThis module is not approved as a discovery module
Objectives
On completion of this module, students should:1) have an understanding of the basic principles of structural analysis using finite element methods;
2) understand the principle of the minimum structural potential method and be able to apply this principle to derive equations for:
a) structures under point and distributed static loading,
b) the analysis of linear buckling of structures;
3) understand the concept of the shape function and be able to derive stiffness matrices for 1D and 2D elements under different modes of loading;
4) be able to analyse 2 and 3 dimensional structures under static loading by the construction of global stiffness matrices, application of boundary and symmetry conditions and extraction of unknown simultaneous equations;
5) be able to determine the critical forces for the buckling of simple 2D structures;
6) understand the computational processes used to solve such problems using Gaussian elimination and Choleski factorisation;
7) be familiar with a finite element software package, be able to use the software to construct models of structures under static loading and evaluate the results;
8) be able to identify and choose the correct loads and boundary conditions to represent symmetry and real-life problems;
9) understand the limitations of finite element modelling and understand how to interpret and validate the results;
10) understand the processes and assumptions that underpin the definition and development of a FEM to answer a specific engineering question.
Overall Grading/Criteria for marking:
70-100: Outstanding
- Demonstrates a high level of understanding of the modeling process.
- The reports are clearly laid out and the content has a high level of accuracy.
- Extensive and relevant checks are undertaken on all aspects of the modeling process and these are carefully taken into account in the presentation of the results and in the conclusions.
- Demonstrates a comprehensive understanding of the underpinning principles that can be synthesised and applied to new problems. Very few errors made in calculations and assumptions used are justified.
60-69: Very Good
- Demonstrates clear understanding of the modeling process with all of the key aspects reported.
- Most of the necessary checks have been undertaken and there is evidence of these having been taken into account in the results and conclusions.
- Demonstrates a clear understanding of the underpinning principles with correct use of equations in most cases.
- Some minor errors in calculations or assumptions made.
50-59: Good
- Shows a reasonable understanding of the modeling process and reports cover most of the basic issues.
- Content is generally accurate but not always clearly presented.
- Several checks are undertaken and some are taken into account in the conclusions.
- Demonstrates an understanding of the basic principles but with frequent errors and use of incorrect equations or false assumptions.
40-49: Satisfactory
- Shows evidence of having understood some of the key aspects of the finite element modeling process but reports contain some errors or omissions.
- Some limited evidence of checks undertaken is presented but these are not taken into account in the analysis of the results and conclusions.
- Demonstrates some understanding of the underpinning principles but approach to questions is unclear and unsystematic.
0-39: Fail
- Shows little understanding with limited or unclear evidence of the modeling process undertaken.
- Very limited if any report of checks undertaken on the models.
- Conclusions drawn are unclear or do not follow from results.
- Evidence of failure to understand basic finite or apply basic finite element principles.
- Calculations contain significant errors or the wrong use of equations and are frequently inaccurate.
Syllabus
- Matrix algebra
> Revision of matrix operations
> Methods for solving simultaneous equations using Gaussian elimination and Choleski factorisation.
- Fundamentals of the FE method for structural analysis
> Principle of minimum structural potential
> Derivation of potential equations
> Introduction to shape functions
> Finite element formulation
> Derivation of stiffness matrix
> Relationship between nodal displacements and stress/strain.
- Truss elements
> Derivation of shape function and stiffness matrix for truss element
> Derivation of body force vector
> Transformation in 2 and 3D of truss element
> Assembly of global stiffness matrix and load vectors
> Application of boundary conditions
> Solution of equations.
- Beam elements
> Derivation of shape function and stiffness matrix for beam element
> Derivation of distributed load force vector.
- 2D elasticity finite elements
> Plane stress, plane strain and axisymmetric stress states
> Constant strain triangle for plane stress: derivation of stiffness matrix
> Force vectors in 2D
> Constant strain triangle for plane strain: derivation of stiffness matrix
> Constant strain triangle for axisymmetric stress state: derivation of stiffness matrix.
- Buckling
> Derivation of structural potential for buckling analysis
> Derivation of geometric matrices for truss and beam elements
> Solution for simple structures to determine critical load.
Teaching methods
| Delivery type | Number | Length hours | Student hours |
| On-line Learning | 3 | 2.00 | 6.00 |
| Class tests, exams and assessment | 1 | 1.50 | 1.50 |
| Group learning | 1 | 10.00 | 10.00 |
| Lecture | 22 | 1.00 | 22.00 |
| Practical | 10 | 2.00 | 20.00 |
| Private study hours | 40.50 | ||
| Total Contact hours | 59.50 | ||
| Total hours (100hr per 10 credits) | 100.00 | ||
Private study
Independent learning - online self-assessment questions including some multiple choice questions with automated feedback and some with full worked solutions to provide active learning of theoretical aspects.Private study - writing reports for laboratory assessments and revision for exam.
Opportunities for Formative Feedback
Laboratory project on FE submitted and feedback given during first semester.Methods of assessment
Coursework
| Assessment type | Notes | % of formal assessment |
| Project | Short Lab Project utilising the finite element software package (weeks 6-11) | 40.00 |
| Total percentage (Assessment Coursework) | 40.00 | |
Students learn software package and undertake a series of lab tasks during weeks 2-6 (10%). Short Lab Project utilising the finite element software package is run during weeks 6-11 (30%).
Exams
| Exam type | Exam duration | % of formal assessment |
| Standard exam (closed essays, MCQs etc) | 1 hr 30 mins | 60.00 |
| Total percentage (Assessment Exams) | 60.00 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
Reading list
The reading list is available from the Library websiteLast updated: 16/04/2015
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