Cambridge University Department of Engineering

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ENGINEERING TRIPOS PART IIA 2012/2013

Module 3D7 - Finite Element Methods

Leaders:

Dr GN Wells

Timing	Lent

Structure:	16 lectures + coursework

AIMS

This course provides an introduction to the finite-element (FE) method, which is widely used to obtain numerical solutions to engineering problems such as finding stress/strain, temperature, pore pressure, etc. in a structure, mechanical component or foundation, for some specified boundary conditions. The course explains the key ideas of the FE approach, covers it's theoretical foundations, and presents some illustrative applications.

LECTURE SYLLABUS

Introduction to finite element analysis (1L Dr G.N. Wells)

Overview and key ideas
Modelling and applicability

Elastic rods and beams (3L Dr 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

Membranes, heat conduction and elasticity in two and three dimensions (8L Dr F. Cirak)

Strong and weak formulations for membranes and 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 Dr 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 Dr G.N. Wells)

Strategies for time-dependent problems

COURSEWORK

Use of a finite-element package to solve a stress-analysis problem related to the experiment performed in Module 3C7.

OBJECTIVES

On completion of the course students should be able to:

Develop the weak form of a governing equation for various problems.
Explain the difference between strong 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 ideas and motivations 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 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.

REFERENCE

Please see the Booklist for Part IIA Courses for references for this module.

Last updated: June 2012

teaching-office@eng.cam.ac.uk