# Module descriptors - Advanced Computational Methods

The module descriptors for this programme can be found below.

Modules shown are for the current academic year and are subject to change depending on your year of entry.

Please note that the curriculum of this programme is currently being reviewed as part of a College-wide process to introduce a standardised modular structure. As a result, the content and assessment structures of this course may change for your year of entry. We therefore recommend that you check this course page before finalising your application and after submitting it as we will aim to update this page as soon as any changes are ratified by the College.

Find out more about the limited circumstances in which we may need to make changes to or in relation to our courses, the type of changes we may make and how we will tell you about changes we have made.

## Computational Mechanics

### Module aims

This module builds on the optional Finite Elements module and introduces advanced concepts in the application of the finite element method to the analysis of aerostructures. It explores the basics of non-linear structural analysis and relevant solution methods based on the finite element method and introduces the Boundary Element Method for two-dimensional potential, elastostatic and acoustic problems.

### Learning outcomes

On successfully completing this module, you should be able to: 1. Explain the concept of geometric and material non-linearity in structural analysis; 2. Appraise how non-linearity is treated within a finite element computer program;  3. Explain the fundamental concepts in the derivation of the boundary element method; 4. Implement advanced mathematical techniques to obtain problem-specific force-displacement relationships from the governing partial differential equations and associated boundary conditions; 5. Solve non-linear structural problems, selecting the appropriate modelling strategy for the effective analysis of structures; 6. Differentiate between domain type and boundary type computational methods; 7. Program the stiffness matrix for an isoparametric 2-D bending finite-element.  AHEP Learning Outcomes: SM7M, SM9M, EA6M, EA7M, P12M, P10m

### Module syllabus

Formulation Methods:  Governing equations, virtual work, potential energy and associated variational techniques, e.g. Hellinger-Reissner, illustrated using 1-D element modelling.  Boundary Element Method: An Introduction to the Boundary Element Method:  Overview of the boundary element method, main differences from the finite element method.  Boundary Element Method for 2-D Potential Problems: Derivation of the boundary element method, fundamental solutions, discretisation strategy, infinite and semi-infinite regions.  Boundary Element Method for 2-D Elastostatic Problems: Derivation of the boundary element method, fundamental solutions, evaluation of boundary and interior stresses.  Boundary Element Method for 2-D Acoustic Problems: Derivation of the boundary element method, fundamental solutions, eigenvalue analysis.  Finite-element modelling of plates and shells:  Eight-node isoparametric plate element; consistent pressure loading in fluid-structure interaction problems; modelling constraints.   Introduction to nonlinear problems in structural analysis:  Type of structural nonlinearities; geometrically-nonlinear beams; basic solution procedures based on the Newton-Raphson method.   Finite stress and finite strain: Green and Almansi strain; Cauchy and second Piola-Kirchhoff stress; Nonlinear static equilibrium; tangent stiffness matrix; buckling of rods using a finite-elements solution process.  Elastic-plastic Analysis: Stress invariants; Deviatoric stress; Yielding criteria; plastic flow.

### Pre-requisites

AERO70010 Finite Elements
(Students can only do Computational Mechanics if they have done Finite Elements in the Autumn term).

### Teaching methods

The module will be delivered primarily through large-class lectures introducing the key concepts and methods, supported by a variety of delivery methods combining the traditional and the technological.  The content is presented via a combination of slides, whiteboard and visualizer.Learning will be reinforced through tutorial question sheets.

### Assessments

This module presents opportunities for both formative and summative assessment.

You will be formatively assessed through progress tests and tutorial sessions.

You will have additional opportunities to self-assess your learning via tutorial problem sheets.

You will be summatively assessed by a written closed-book examination at the end of the module as well as through a coursework assignment.

 Assessment type Assessment description Weighting Pass mark Examination Closed-book written examination 85% 50% Coursework Coursework assignment 15% 50%

You will receive feedback following the coursework submission.

You will receive feedback on examinations in the form of an examination feedback report on the performance of the entire cohort.

You will receive feedback on your performance whilst undertaking tutorial exercises, during which you will also receive instruction on the correct solution to tutorial problems.

Further individual feedback will be available to you on request via this module’s online feedback forum, through staff office hours and discussions with tutors.

### Supplementary

• #### The boundary element method. Vol. 1, Applications in thermo-fluids and acoustics

Wrobel, L. C.

Wiley

Wiley

• #### Non-linear finite element analysis of solids and structures

2nd ed., Wiley

• #### Concepts and applications of finite element analysis

Cook, Robert D.

Fourth edition., Wiley

• #### Finite element procedures

Bathe, Klaus-JuÌˆrgen.

Prentice Hall

Fish, Jacob.

John Wiley