Title:  Elasticity and Stress Analysis 
Long Title:  Elasticity and Stress Analysis 
Field of Study: 
Mechanical Engineering

Valid From: 
Semester 1  2016/17 ( September 2016 ) 
Module Coordinator: 
MATTHEW COTTERELL 
Module Description: 
This module will cover Unified Theory Elasticity Analysis and Design, from first principles, of Mechanical Engineering Cartesian and Polar Coordinate Applications and Elasticity Solution of Advanced Thin Plate/Shell and Torsion Design. 
Learning Outcomes 
On successful completion of this module the learner will be able to: 
LO1 
Analyse the governing relations of the unified design theory of advanced elasticity. 
LO2 
Solve, utilizing stress function techniques, stress distribution/concentration problems in cartesian / polar coordinates. 
LO3 
Analyse critical design parameter variation in advanced elasticity applications. 
LO4 
Demonstrate teamwork through investigation and presentation of advanced elasticity applications. 
Prerequisite learning 
Module Recommendations
This is prior learning (or a practical skill) that is strongly recommended before enrolment in this module. You may enrol in this module if you have not acquired the recommended learning but you will have considerable difficulty in passing (i.e. achieving the learning outcomes of) the module. While the prior learning is expressed as named CIT module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s). 
10447 
MECH6031 
Mechanics of Materials 2 
Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module. You may not earn additional credit for the same learning and therefore you may not enrol in this module if you have successfully completed any modules in the incompatible list. 
No incompatible modules listed 
Corequisite Modules

No Corequisite modules listed 
Requirements
This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. You may not enrol on this module if you have not acquired the learning specified in this section.

No requirements listed 
Module Content & Assessment
Indicative Content 
Introduction to Elasticity Theory
Introduction to Unified Theory of Elasticity. Translational and Rotational Equilibrium of 3D Infinitesimal Element in Cartesian Coordinates. Direct and Shear Strains in terms of Displacements. 3D Equations of Compatibility. Body Forces. Potential Functions. StressStrain and StrainStress Relations. Airy Stress Function. Biharmonic and Laplacian Equation Development for Plane Stress/Strain. Plane Stress to Plane Strain Transformations. Effect of Nonuniform Temperature Field in an Elastic Body.

Elasticity Solution Methods  Cartesian Coordinate System
Integrated Elasticity Application Solutions using Airy Stress Function Approach. Inverse, SemiInverse, Combination of Polynomials of Various Order. Boundary Condition, Equilibrium and Compatibility Criteria Achievement for Cartesian Coordinate Applications. Solution Initiation Assumptions. Comprehensive Stress and Deflection Elasticity Calculation. Comparison with Strength of Materials Solutions.

Elasticity Approach using Polar Coordinates
Equations of Equilibrium, Compatibility, Stress/Strain Relations, Biharmonic and Laplacian equations development in Polar Coordinates. Cartesian/Polar Transformations. Stress Function Solutions in Polar Coordinates. Axisymmetric and Asymmetric Applications – Curved Beams, Solid Shafts, Thick Cylinders. Comparison of Elasticity and Strength of Materials Solutions. Stress Concentration in a Circular Hole in a Tension Field. Stress Concentration Factors. Concentrated Load Line Solutions. Wedge subjected to Axial and Transverse Loads. Neubers Nomograph Design Approach. Unreinforced and Reinforced CutOut Stress Analysis. Design of Neutral Holes.

Contact Stress Elasticity Analysis – Hertzian Theory
SemiInfinite Solid Contact Stress Variation Analysis. Calculation of Contact Area Shape and Size and Maximum Contact Pressure. Cylinders in Contact. Determination of Relative Displacement, Contact Area and Maximum Stress. Pin in Concave. Cylinder on Flat Surface. Hertz Solution for 3D Variable Curvature Contacting Bodies. Sphere to Sphere, Sphere to Flat, Sphere to Concave Contact Design Solutions.

Thin Plate Elasticity Theory
Small Deflection Theory for Homogeneous Uniform Plates. Stress, Curvature and Moment Relations. The Differential Equation of Plate Deflection. Boundary Conditions. Simply Supported Rectangular Plates. Navier’s Solution. Infinite Beam. Applied Solutions including Reaction Distribution Solution and Assumption Assessment. Axisymmetrically Loaded Circular Plates. Elasticity Solutions for various Boundary Conditions, Shape and Loading Configurations. The Finite Difference Solution. The Grid Representation Method. The Finite Element Solution. Assessment of Numerical Methods to achieve Converged Solutions for various Boundary Conditions, Shape, Loading Configurations and Mesh Densities.

Thin Shell Elasticity Theory
Assumptions and Development of Thin Shell Theory. Simple Membrane Action. Bending versus Membrane Stresses as Load Carrying Mechanisms. Local Buckling. Geometry of Shells of Revolution. Meridional and Tangential Equilibrium and Stress and Deflection Analysis of Symmetrically Loaded Shells of Revolution. Comparison of Elasticity and Strength of Material Solutions for spherical, conical and cylindrical shells. Advanced Elasticity Applied Solutions The Finite Element Solution for various Boundary Conditions, Shape, Loading Configurations and Mesh Densities.

Torsion Elasticity Theory
Torsion of Prismatic Bars of Arbitrary Crosssection. General Solution of the Torsion Problem. Displacement / Strain / Stress Relations. Development of Equations of Equilibrium and Compatibility. Prandtl Stess Function. Poisson’s Equation. Traction Boundary Conditions for Sold and Multiply Connected Members. Torsion Stress Surface and Contours. Relationship between Torque and Stress. Torsion Elasticity Solution for Elliptical Member. Shear Stress, Angle of Twist and Warpage Determination. Prandtl’s Membrane Analogy. Experimental Application. Torsion of Thin Walled Members of Open Crosssection. Torsion of Multiply Connected Thin Wall Members. Membrane Analogy for Thin Walled Members. Development and Application of Bredt’s Formulae. Fluid Flow Analogy. Torsion of Restrained Thin Walled Members of Open Crosssection. The Finite Element Solution.

Assessment Breakdown  % 
Course Work  20.00% 
End of Module Formal Examination  80.00% 
Course Work 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Short Answer Questions 
Unified Theory Fundamentals 
1,2 
10.0 
Week 5 
Presentation 
Advanced Elasticity Applications 
2,3,4 
10.0 
Week 9 
End of Module Formal Examination 
Assessment Type 
Assessment Description 
Outcome addressed 
% of total 
Assessment Date 
Formal Exam 
EndofSemester Final Examination 
1,2,3 
80.0 
EndofSemester 
Reassessment Requirement 
Repeat examination
Reassessment of this module will consist of a repeat examination. It is possible that there will also be a requirement to be reassessed in a coursework element.

The institute reserves the right to alter the nature and timings of assessment
Module Workload
Workload: Full Time 
Workload Type 
Workload Description 
Hours 
Frequency 
Average Weekly Learner Workload 
Lecture 
Theoretical Development and Analysis 
3.0 
Every Week 
3.00 
Tutorial 
Worked Examples and Problems 
1.0 
Every Week 
1.00 
Independent & Directed Learning (Noncontact) 
Self directed study 
3.0 
Every Week 
3.00 
Total Hours 
7.00 
Total Weekly Learner Workload 
7.00 
Total Weekly Contact Hours 
4.00 
This module has no Part Time workload. 
Module Resources
Recommended Book Resources 

 Boresi A.P., Chong K., Lee J.D. 2010, Elasticity in Engineering Mechanics, 3rd Edition Ed., John Wiley and Sons [ISBN: 0470402555]
 Ugural A.C., Fenster S.K. 2011, Advanced Mechanics of Materials and Applied Elasticity, 5th Edition Ed., Prentice Hall [ISBN: 0 1370 79206]
 Hearn E.J. 1997, Mechanics of Materials, Volume 2, 3rd Edition Ed., Butterworth Heinemann [ISBN: 0 7506 3266 6]
 Supplementary Book Resources 

 Goodno B.J., Gere J.M. 2014, Mechanics of Materials, 8th Edition Ed., Engage Learning [ISBN: 0495081315247]
 Bisplinghoff L., Ashley H. 2013, Principles of Aeroelasticity, 2nd Edition Ed., Dover [ISBN: 0 4864 9500]
 Solecki R., Conant R.J. 2003, Advanced Mechanics of Materials, 1st Edition Ed., Oxford University Press [ISBN: 0 1951 4372 0]
 Cook R.D., Malkus D.S., Plesha M.E. 2007, Concepts and Applications of Finite Element Analysis, 4th Edition Ed., Wiley [ISBN: 8126513365]
 Craig R.R. 2011, Mechanics of Materials, 2nd Edition Ed., Wiley [ISBN: 0 4704 81811]
 Dally J.W., Riley W.F. 2005, Experimental Stress Analysis, College House Enterprises [ISBN: 0 9762 4130 7]
 Timoshenko S.P. 1983, History of Strength of Materials, Revised Edition Ed., Dover [ISBN: 0 4866 1187 6]
 Benham P.P., Crawford R.J., Armstrong C.G. 1996, Mechanics of Engineering Materials, 2nd Edition Ed., Longman [ISBN: ISBN 0 5822 5164 8]
 This module does not have any article/paper resources 

Other Resources 

 Website: Engineering Fundamentals  Mechanics of
Materials Website
 Website: Engineers Edge  Mechanics of Materials
Website
 Website: ANSYS Finite Element Website
 Website: Finite Element Demonstration Room

Module Delivered in
