Theory of Elasticity

Cod y Modiwl: MA33410
Teitl y Modiwl: Theory of Elasticity
Blwyddyn Academaidd: 2026/2027
Semester: Semester 1
Cyd-gysylltydd y Modiwl: Dr Daniel Peck
Rhestr Ddarllen: Gweld ar Aspire
Rhagofynion: MA11210 neu MT11210
Rhagofynion: FG26020 neu PM26020
Anghymharus (Unrhyw Flwyddyn Acad): MAM3420
Staff Eraill sy'n Cyfrannu: Dr Daniel Peck; Professor Gennady Mishuris

Dulliau Asesu

Math o Asesiad	Manylion Asesiad	Hyd Asesiad	Cyfran
Arholiad Semester	Written Examination:	2 Awr	100%
Arholiad Ailsefyll	Written Examination:	2 Awr	100%

Canlyniadau Dysgu

Wedi cwblhau'r modiwl dylai'r myfyrwyr fedru:

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

Disgrifiad cryno

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.

Cynnwys

• 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.

Sgiliau Modiwl

Math o Sgiliau	Manylion Sgiliau
Cyfathrebu	Written answers to questions must be clear and well-structured, and should communicate students’ understanding
Datrys Problemau	Throughout
Gwaith Tim	Students will be encouraged to work together on questions in workshops and on Example sheets.
Gwella dysgu a pherfformiad ei hun	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.
Rhifedd	hroughout
Sgiliau pwnc penodol	Students will become accomplished at solving problems in a major area of applied mathematics.
Sgiliau ymchwil	Students will be encouraged to independently find and assimilate useful resources.
Technoleg Gwybodaeth	Use of blackboard.

Nodau

Mae'r modiwl hwn yn cydymffurfio a FfCChC Lefel 6