# Detailed module information

Module information on this degree can be found below, separated by year of study.

The module information below applies for the current academic year. The academic year runs from August to July; the 'current year' switches over at the end of July.

Students select optional courses subject to rules specified in the Mechanical Engineering Student Handbook,  for example at most three Design and Business courses. Please note that numbers are limited on some optional courses and selection criteria will apply.

### Module aims

This module introduces the student to fundamental elasticity and plasticity theory, problems and solutions. Stress function formulation and methods will be presented for plane stress, plane strain and torsional loading and the solution of a range of problems with be developed. The analysis of torsion will also be developed to treat thin walled sections of arbitrary but uniform, cross section. The Convolution Integral will be developed and used to analyse time dependent effects. A review of plasticity will be made and the Levy-Mises equations will be derived and used for problem solving.

ECTS units:    5

### Learning outcomes

On successfully completing this module, students will be able to:

1.Solve bi-harmonic and Laplace equations using stress functions for two dimensional problems and torsion

2. Explain the time dependent analysis using the Convolution integral

3. Explain the rationale behind the Levy-Mises equations

4. Assess, by appropriate consideration of boundary and equilibrium conditions, the applicability of a proposed stress function to the solution of a problem

5. Obtain exact solutions to stress analysis problems such as the bending of rectangular beams; loading of thick walled cylinders, split and curved rings; loaded wedges, holes in plates, discs between opposing loads and, approximately, the torsion of thin-walled non-circular section

6. Apply the Convolution Integral to the analysis of creep and relaxation phenomena in visco-elastic materials.

7. Solve residual stress problems and plasticity deformation problems using the Levy-Mises equations

### Module syllabus

Stress function methods in two dimensions

Torsion of non-circular sections

Convolution Integral

Plastic Deformation

### Pre-requisites

Pre-requisites: ME1-hSAN; ME2-hSAN

### Teaching methods

• Students will be introduced to the main topics through lectures (1 per week), supported by technology (PowerPoint, Panapto and Blackboard). Short activities (using interactive pedagogies) will occasionally be introduced in the classroom setting to reinforce learning, for example through mentimeter and the like. You will be provided with problem  sheets and should complete these as part of your independent study. Tutorials sessions (1 per week) will provide an opportunity for interaction with teaching staff where you can discuss specific problems.

### Assessments

 Assessment details Pass mark Grading method Numeric 50% Assessments Assessment type Assessment description Weighting Pass mark Must pass? Examination 3 Hour exam 100% 50% Y

### Supplementary

• #### Theory of elasticity

Timoshenko, Stephen, 1878-1972

3rd ed., Auckland ; London : McGraw-Hill

• #### Basic engineering plasticity [electronic resource] : an introduction with engineering and manufacturing applications

Rees, D. W. A.

1st ed., Elsevier/Butterworth-Heinemann

• #### Theory of Elasticity

Sitharam, T. G. author.

1st ed. 2021., Springer Singapore

• #### Stress analysis of polymers

Williams, J. G. (James Gordon).

2nd ed., Chichester : Ellis Horwood ; New York ; Chichesters ; Distributed by Wiley

• #### Elasticity /

Barber, J. R.

3rd rev. ed., Springer

• #### Elasticity

Barber, J. R.