# 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.

## Computational Continuum Mechanics A

### Module aims

The course is designed to introduce the fundamentals of continuum mechanics and to demonstrate how problems in continuum mechanics can be solved using numerical techniques. Particular attention is paid to the theory and implementation of the finite element method. The course provides the theoretical basis for Masters level courses on applications of finite element methods (FEAA) and finite volume method (CFD) and is a companion course to ME3 Fluid Mechanics (FMX) and ME3 Stress Analysis (SAN).

ECTS units:    5

### Learning outcomes

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

• Discuss the basic concepts of continua, and conservation and constitutive laws, in terms of deformation, strain and stress
• Restate simple problems - involving, e.g., heat transfer, stresses, deformation and/or flow - in continuum mechanics terms
• Describe the fundamentals of the Finite Element (FE) method
• Solve simple continuum mechanics problems using analytical methods
• Define more complex problems in a form suitable for solution using FE methods

### Module syllabus

• Basic concepts and definitions: Concept of a continuum, continuity, homogeneity and isotropy; Elements of vector and tension algebra.
• Deformation and flow: Length and angle changes: Strain tensor; Material and spatial description; Deformation; Motion and flow.
• Stresses: Body and surface forces; Stress tensor; Principal stresses, stress invariants, hydrostatic and deviatoric stresses.
• Fundamental laws of continuum mechanics: Mass conservation, conservation of linear and angular momentum, conservation of energy; Law of entropy production; Equations for large deformations.
• Constitutive relations: Ideal materials, constitutive relations and equations of state; Elastic solids; Newtonian fluids.
• Mathematical models: Linear elastic solids; Newtonian fluids; Initial and boundary conditions.
• Introduction to the Finite Element method: Principle of virtual work; Finite element discretisation; Linear elastic finite element model; Shape functions; Numerical quadrature; Mapping of elements; Solution of the finite element equations.

### Teaching methods

• Duration: Autumn term (11 weeks)
• Lectures: 1 x 2 hr per week

 Summary of student timetabled hours Autumn Spring Summer Lectures 22 — — Tutorials Details of tutorials to be advised by course leader during the course. Total 22 plus tutorials attended Expected private study time 3-4 hr per week, plus exam revision

### Assessments

 Written examinations: Date (approx.) Max. mark Pass mark Computational Continuum Mechanics (3hr) A Data and Formulæ Book and a Supplementary Formula Sheet are provided.   This is a CLOSED BOOK Examination. April/ May 200 n/a Coursework (including progress tests, oral presentations etc.) Submission date Max. mark Pass mark Submission Feedback None n/a n/a n/a n/a Total 200