Dr F Cirak, Dr C Lestringant
Timing and Structure
Lent term. 16 lectures and coursework.
The aims of the course are to:
- Provide an introduction to the finite-element (FE) method, which is widely used to obtain numerical solutions to engineering problems.
- Explain the key ideas of the FE approach, cover its theoretical foundations, and present some illustrative applications.
As specific objectives, by the end of the course students should be able to:
- Develop the weak form of the governing equation for various problems.
- Explain the difference between strong and weak formulations.
- Compute shape functions in one, two and three dimensions for different elements.
- Obtain the stiffness and mass matrices and the right-hand side vector for different elements.
- Explain the idea and motivation behind isoparametric formulations.
- Apply numerical integration on different finite elements.
- Assemble the stiffness and mass matrices for a mesh.
- Explain how to apply various loadings and boundary conditions.
- Generate suitable meshes for different problems.
- Set up a finite element mesh, apply appropriate boundary conditions and solve the resulting system in a finite element program.
- Appreciate sources of errors associated with finite element analysis.
- Explain key features of different methods for time-dependent problems.
Introduction to finite element analysis (1L Prof G.N. Wells)
- Overview and key ideas
- Modelling and applicability
Elastic rods and beams (3L Prof G.N. Wells)
- Strong and weak equations of equilibrium for rods
- Linear shape functions in one dimension
- Assembly and application of boundary conditions
- Construction of higher-order shape functions
- Euler beams and Hermitian shape functions
Heat conduction and elasticity in two and three dimensions (8L C Lestringant)
- Strong and weak formulations for heat conduction
- Shape functions for two and three dimensional elements
- Isoparametric mapping and numerical integration
- Application of boundary conditions
- Assembly of element matrices and vectors
- Stability considerations
- Generalisation to elasticity
- Aspects of solid modelling and meshing
Modelling issues (2L Prof G.N. Wells)
- Practical issues: element selection, what can go wrong, when does it not work?
- Errors and convergence
- Stress recovery and post-processing
Time dependent problems (2L Prof G.N. Wells)
Strategies for time-dependent problems
Use of a finite-element package to solve a stress-analysis problem related to the experiment performed in Module 3C7.
Computational Stress Analysis
- Quantify the choice of elements on the obtained results.
- Identify the importance of the choice of boundary conditions.
- Compare finite element results with experimental and analytical results.
- Explore the influence of mesh refinement on computed results.
- The coursework can be completed remotely. Support session will he held online.
- This activity involves the installation/configuration of software. Instructions will be provided.
- 3C7 experimental data can be obtained from the Lab Leader.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Please refer to Form & conduct of the examinations.
Last modified: 18/08/2021 09:24