# Aeronautical Engineering (MEng)

## Computational Mechanics

### Module aims

·     To introduce advanced concepts in the application of the finite element method to the analysis of aerostructures.
·      To introduce the basics of non-linear structural analysis and relevant solution methods based on the finite element method.
·      To introduce the Boundary Element Method for two-dimensional potential, elastostatic and acoustic problems.

### Learning outcomes

Knowledge and understanding
On successfully completing this course unit, students will be able to:
•  understand the concept of geometric and material non-linearity in structural analysis.
•  understand how non-linearity is treated within a finite element computer program.
•  understand fundamental concepts in the derivation of the boundary element method.

Skills and other attributes
On successfully completing this course unit, students will be able to:
Intellectual skills
•  use advanced mathematical techniques to obtain problem-specific force-displacement relationships from the
governing partial differential equations and associated boundary conditions.
•  solve non-linear structural problems.
•  differentiate between domain type and boundary type computational methods

Practical skills
•  select the appropriate modelling strategy for the effective analysis of structures.
•  program the stiffness matrix for an isoparametric 2-D bending finite-element.

Transferable skills
•  Computer skills.

### 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

AERO96003 Finite Elements

### Teaching methods

Lectures and tutorials. There are class notes for this module.

### Assessments

Examined Assessment
2 hour written examination in January (85%),
one coursework assignment (15%)

Non-Examined Assessment
1 x Progress test (peer marked)

### 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

4th ed., Wiley

• #### Finite element procedures

Bathe, Klaus-JuÌˆrgen.

Prentice Hall

• #### First Course in Finite Elements

Fish, Jacob ; Belytschko, Ted

Wiley