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

 AERO96003 Finite Elements

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.

 

Reading list

Supplementary

Module leaders

Professor Ferri Aliabadi