# Module Information

Module Identifier
MA33410
Module Title
Theory of Elasticity
2024/2025
Co-ordinator
Semester
Semester 1
Pre-Requisite
Pre-Requisite
Exclusive (Any Acad Year)
Other Staff

#### Assessment

Assessment Type Assessment length / details Proportion
Semester Exam 2 Hours   Written Examination  100%
Supplementary Exam 2 Hours   Written Examination  100%

### Learning Outcomes

On successful completion of this module students should be able to:

Give the definitions of strain and stress and explain the relations connecting them

Manipulate tensors

Formulate simple problems in 2D elasticity and provide appropriate boundary conditions

Demonstrate the ability to employ coordinate systems appropriate to the situation being modelled

Derive analytic solutions to one and two-dimensional problems in linear elasticity

### Brief description

The aim of this module is to introduce the mathematical theory of linear elasticity in its 2D formulation. It will start from a broad framework in which a model of the deformation of a solid body undergoing external loading is derived by analyzing the internal stresses and the related strain deformation. The 2D theory will be developed as a system of differential equations and applied to selected practical problems. The analytical techniques required to tackle such problems will be presented.

### Content

• Introduction: Vectors, Matrices, Tensors, Tensor algebra.
• Analysis of strain. The infinitesimal strain tensor. Strain compatibility.
• The traction vector and the stress tensor. Equations of motion.
• Stress-strain relations for elastic and linearly elastic materials; isotropic materials.
• Formulation of boundary value problems of linear elasto-statics.
• One-dimensional problems. A selection of soluble problems (which are effectively one-dimensional) in Cartesian, cylindrical polars and spherical polar coordinates.
• Two-dimensional problems in theory of elasticity.
• Torsion. Laplace’s equation and methods of its solution.
• Plane strain problems. Theory of plane strain, Airy stress function. A selection of soluble two-dimensional problems using plane-strain theory.

### Module Skills

Skills Type Skills details
Application of Number hroughout
Communication Written answers to questions must be clear and well-structured, and should communicate students’ understanding
Improving own Learning and Performance Students are expected to develop their own approach to time-management regarding the completion of Example sheets on time, assimilation of feedback, and preparation between lectures.
Information Technology Use of blackboard.
Problem solving Throughout
Research skills Students will be encouraged to independently find and assimilate useful resources.
Subject Specific Skills Students will become accomplished at solving problems in a major area of applied mathematics.
Team work Students will be encouraged to work together on questions in workshops and on Example sheets.

### Notes

This module is at CQFW Level 6