This subject introduces important mathematical methods required in engineering such as manipulating vector differential operators, computing multiple integrals and using integral theorems. A range of ordinary and partial differential equations are solved by a variety of methods and their solution behaviour is interpreted. The subject also introduces sequences and series including the concepts of convergence and divergence.

Topics include: Vector calculus, including Gauss’ and Stokes’ Theorems; sequences and series; Fourier series, Laplace transforms; systems of homogeneous ordinary differential equations, including phase plane and linearization for nonlinear systems; second order partial differential equations and separation of variables.

AIMS

This subject consists of three distinct and fundamentally related topics -

• An introduction to the fundamentals of materials science will be given on atomic structure and bonding, crystal structures and defects, elastic and plastic deformation, dislocations and strengthening and failured (fast fracture, fatigue and creep)
• The mechanics of materials section will extend the concepts of material mechanical behaviour by detailing elastic/inelastic behaviour and introducing the concepts of stress and strain analysis. Topics covered may include the definition of principal stresses, plane stress, plane strain, two-dimensional stress and strain analysis, torsion, pure bending, transverse loading, Mohr’s circle, failure criteria, inelastic behaviour, residual stress
• This subject will also provide an introduction to finite element analysis (FEA) and its application for stress-strain analysis. Particular emphasis will be placed on the fundamental mechanisms by which materials fail under loading.

INDICATIVE CONTENT

• Mechanics: the definition of principal stresses, plane stress, plane strain, two-dimensional stress and strain analysis, torsion, pure bending, transverse loading, Mohr’s circle, failure criteria, inelastic behaviour, residual stress.
• Materials: atomic structure and bonding, crystal structures and defects, elastic and plastic deformation, dislocations and strengthening and failure (fast fracture, fatigue and creep).
• Finite element analysis (FEA): FEA procedure, application of FEA to discrete systems and continuous bodies.

AIMS

This course is an introduction to basic principles of fluid mechanics and thermodynamics. These two subjects are introduced together in a single course, reflecting the large degree of cross-over in applications and basic first principles between the two subjects.

Fluid mechanics is a very important core subject, influencing a diverse range of engineering systems (aircraft, ships, road vehicle design, air conditioning, energy conversion, wind turbines, hydroelectric schemes to name but a few) and also impacts on many biological (blood flow, bird flight etc) and even meteorological studies. As engineers, we are typically concerned with predicting the force required to move a body through a fluid, or the power required to pump fluid through a system. However, before we can achieve this goal, we must start from fundamental principles governing fluid flow.

Thermodynamics could be defined as the science of energy. This subject can be broadly interpreted to include all aspects of energy and energy transformations. Like fluid mechanics, this is a hugely important subject in engineering, underpinning many key engineering systems including power generation, engines, gas turbines, refrigeration, heating etc. This unit again starts from first principles to introduce the basic concepts of thermodynamics, paving the way for later more advanced units

This course aims to develop a fundamental understanding of thermodynamics and fluid mechanics, based on first principles and physical arguments. Real world engineering examples will be used to illustrate and develop an intuitive understanding of these subjects.

INDICATIVE CONTENT

Topics include:

Fluid Mechanics - fluid statics, static forces on submerged structures, stability of floating bodies; solid body motion; fluid dynamics; streamlines; pathlines and streaklines; conservation of mass, momentum and energy; Euler's equation and Bernoulli's equation; control volume analysis; dimensional analysis; incompressible flow in pipes and ducts; boundary layers; flow around immersed bodies; and drag and lift.

Thermodynamics - heat and work, ideal non-flow and flow processes; laws of thermodynamics; Carnot's principle; Clausius inequality; direct and reversed heat engines; thermal efficiencies; properties of pure substances; change of phase; representation of properties; steam and air tables; and vapour equation of state, ideal gases.

AIMS

Topics covered include: general approach to design problems; invention, analysis, decision making; terminologies such as ‘goal’, ‘objectives’, ‘criteria’ and ‘constraints’; strategies for synthesis and decision making; technical, ergonomic and economic factors; appraisal of benefit and cost; fault and failure analysis; probability, uncertainty, and assessment of risk; and interfacing geometric and mathematical models, sensitivity analyses, combinatorial search, structured approaches to material selection; failure modes for engineering systems, failure predictors for engineering components under multi-axial stress conditions; rational assessment of safety factors and maximum credible accident; integrity of structures and machines, design against failure; modelling of complex load-bearing systems in terms of simple engineering components; design of elements of structures and machines from first principles; and approaches to uncertainty in design problems, including those related to the environment.

INDICATIVE CONTENT

Introduction to strategies for creative idea generation in engineering design -

• The design process – specifying problems and generating solutions
• Making decisions – decision-making strategies, cost benefit analysis, economic and human factors
• Fault / failure analysis.

Introduction to engineering graphical communication -

• Sketching
• Orthographic (multiview), layout, assembly and detailed drawings
• Dimensioning.

Introduction to structural integrity in engineering design -

• Structural integrity and the nature of failure
• Structural distillation – decomposition of structural systems into elementary engineering components
• Estimation, units and calculation
• Failure predictors and factors of safety
• Fatigue – What is fatigue? Time-varying stresses, fatigue strength, design against failure. S-N diagram, A-M diagram. Shafts as an example of fatigue-based structural integrity design.

This subject will cover the modelling of a range of physical systems across multiple domains as ordinary differential equations, and then introduce the mathematical techniques to analyse their open loop behaviour.

Topics include:

• Development of low order models of a range of electrical, thermal, mechanical, pneumatic and hydraulic dynamic systems
• Different representations of these systems (time and, frequency domains) and transformations between them (Laplace, Fourier and Z-transforms)
• Representations of systems – transfer functions, Bode plots, state space, block diagrams, etc
• Identification of linear time invariant systems (least squares identification)
• Relation to time domain properties of open loop responses – stability, oscillations, etc.

MATLAB will be used throughout the course to complement the presented concepts.