Aims

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.

Objectives

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.

Content

Introduction to finite element analysis (1L Dr B Liu)

• Overview and key ideas
• Modelling and applicability

Elastic rods and beams (3L Dr B Liu)

• Strong and weak equations of static 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 Prof F Cirak)

• 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 Dr B Liu)

• Model analysis and critical time step
• Error estimates and convergence of finite element method

Time dependent problems (2L Dr B Liu)

• Strong and Weak formulation for time-dependent problems
• Consistent and lumped mass matrix
• Explicit and Implicit time integration

Aims

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.

Objectives

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.

Content

Introduction to finite element analysis (1L Dr B Liu)

• Overview and key ideas
• Modelling and applicability

Elastic rods and beams (3L Dr B Liu)

• Strong and weak equations of static 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 Prof F Cirak)

• 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 Dr B Liu)

• Model analysis and critical time step
• Error estimates and convergence of finite element method

Time dependent problems (2L Dr B Liu)

• Strong and Weak formulation for time-dependent problems
• Consistent and lumped mass matrix
• Explicit and Implicit time integration

Aims

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.

Objectives

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.

Content

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

Aims

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, covers its theoretical foundations, and presents some illustrative applications.

Objectives

As specific objectives, by the end 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.

Content

Introduction to finite element analysis (1L Prof 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 J Li)

• 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 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

This syllabus contributes to the following areas of the UK-SPEC standard:

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Last modified: 18/09/2018 11:43

Aims

The aims of the course are to:

• Explain some fundamental principles necessary for understanding the common water issues in the world.
• Introduce the basic topics in water resources, open channel flows and groundwater flows.
• Allow students to grasp essential concepts and procedures for analysing hydro-environmental processes and develop skills to solve practical water engineering problems.
• Highlight some of the most pressing water-related global challenges, such as freshwater scarcity, soil erosion, water quality deterioration and flooding, and stress the need for sustainable and integrated management of water resources.

Objectives

As specific objectives, by the end of the course students should be able to:

• Comprehend the scope of water-related topics in civil and environmental engineering
• Appreciate the environmental, social, political and economic implications of water engineering and hydraulic engineering projects
• Understand the hydrologic cycle and the water budget
• Promote nature-based and nature-friendly solutions to water-related problems
• Understand the soil properties and simple models of ground infiltration
• Determine the steady seepage patterns in the porous media
• Evaluate potentials, pore water pressures, and flow quantities in the ground by constructing flow nets
• Calculate the seepage below concrete dams and through embankment & earth dams
• Analyse topics on excavations and seepage, cofferdams and stability
• Draw parallels between groundwater flow and heat flow in porous media
• Understand river hydraulics
• Solve steady flows using the equations of mass, energy and momentum conservations

Content

Hydrology and Water Resources (3L) 2 lectures/week, weeks 1-2 (Dr Borgomeo)

• Global water issues
• Hydrologic cycle
• Water resources

Groundwater, Seepage and Heat Flow in Granular media (8L), 2 lectures/week, weeks 2-6 (Prof SPG Madabhushi)

• Concept of porous media and bulk properties.
• Definitions of potential head, pressure head and pore pressure.
• Groundwater flow and seepage
• Theory of flow nets
• Anisotropic soils and flow nets
• Darcy's law and Hydraulic conductivity
• Laboratory and in situ measurements
• Seepage below concrete dams
• Seepage through embankments and earth dams
• Stability and seepage around excavations
• Coffer dams and their stability
• Fourier’s law and heat flow in porous media
• Parallels between ground water flow and heat flow
• Ground source heat pumps
• Storage and extraction of heat from ground

Open Channel Flows (5L) 2 lectures/week, weeks 6-8 (Prof D. Liang)

• Boundary layer and turbulence
• Flow resistance
• Steady flow in open channels
• Backwater curves
• Water surface profiles in non-uniform flows 

This syllabus contributes to the following areas of the UK-SPEC standard:

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Last modified: 07/10/2025 02:46