Engineering Tripos Part IIB, 4D6: Dynamics in Civil Engineering, 2018-19
Module Leader
Lecturers
Prof G Madabhushi and Prof FA McRobie
Lab Leader
Prof FA McRobie
Timing and Structure
Lent term. 14 lectures + coursework. Assessment: 75% exam/25% coursework
Prerequisites
3D7, 3D2 and 3D4 useful
Aims
The aims of the course are to:
- introduce the behaviour and design of civil engineering structures subjected to time-varying loads.
- introduce earthquake-resistant design, dynamic soil-structure interaction, machine foundation design, blast effects on structures and the fundamentals of wind engineering.
Objectives
As specific objectives, by the end of the course students should be able to:
- identify cases where a static model of a structure is inadequate, and a dynamic model should be used
- produce a simple estimate of the natural frequency and fundamental natural mode of any linear-elastic structure.
- estimate linear-elastic spring parameters for a given foundation.
- compute the natural frequencies and natural modes of structures using the ABAQUS package and include simple soil models to account for soil-structure interaction.
- estimate the response of complex linear-elastic structures to earthquakes using modal superposition and the response spectrum.
- use elastic and inelastic design spectra, and to understand their form.
- perform simple designs for vibration isolation.
- perform simplified soil stiffness calculations accounting for partial liquefaction, and to use this approach in simple liquefaction resistant designs.
- describe some standard methods of seismic-resistant structural design.
- describe blast processes and their effects on structures.
- appreciate the factors involved in the estimation of wind climates and of structural response to wind.
- understand the various measures that characterise atmospheric turbulence.
- anticipate the circumstances under which aeroelastic phenomena may be problematic.
- estimate the dynamic response of a tall structure in a given wind environment
Content
LECTURE SYLLABUS
Structural dynamics (4L, Dr James Talbot)
Linear Elastic dynamics
á Introduction to dynamic loads in Civil Engineering; dynamic amplification factors.
á Approximate single-degree-of-freedom analysis of complex structures; sway frames; structures with distributed mass.
á Rayleigh's principle; natural frequency of simple systems using energy methods.
á Linear models to represent structures and their relevance; analysis in frequency domain; mode superposition method.
á Modal analysis of vibration; use of finite element packages.
Spectral Analysis & Earthquake Spectra (2L, Dr Matt DeJong)
á Introduction to spectral analysis
á Earthquake Spectra and Design Spectra, Design of linear systems
á Non-linear Spectral Analysis, Ductility in Structures
Application of dynamics in Civil Engineering Structures :
Part A: Soil-Structure Interaction (5L, Dr S.P.G.Madabhushi)
Non-linear Systems
á Sources of nonlinearity in structures and foundations.
á Analysis in time domain; numerical integration of equations of motion.
Seismic design
á Earthquake loading on structures; response and design spectra;
á Structures subject to ground motion; deformations due to lateral accelerations; Newmark's sliding block analysis; concept of threshold acceleration
á Foundations effects; stiffness of soil foundation and soil-structure interaction;
á Pore pressure build-up during earthquakes; partial liquefaction; degradation in soil stiffness; non-linear soil models.
á Liquefaction resistant design, simple examples.
á
Part B : Seismic resistant design, blast effects and wind engineering (3L, Prof F.A. McRobie)
Seismic Resistant Design
á Structural design and detailing considerations.
Blast Loading
á Physics of blasts; blast effects on structures; blast-resistant design.
Wind loading
á Nature of wind;
á Wind forces on structures.
á Response of structures to buffetting. Fluid-structure interaction (vortex-shedding, galloping and flutter). Long-span bridge case study.
Coursework
Seismic analysis of an existing tall building using the ABAQUS finite element package and a study of the effect of foundation softening on the overall structural response. Total time 8 hours.
| Coursework | Format |
Due date & marks |
|---|---|---|
|
[Coursework activity #1 title / Interim] Coursework 1 brief description Learning objective:
|
Individual/group Report / Presentation [non] anonymously marked |
day during term, ex: Thu week 3 [6/15] |
|
[Coursework activity #2 title / Final] Coursework 2 brief description Learning objective:
|
Individual Report anonymously marked |
Wed week 9 [9/15] |
Booklists
Please see the Booklist for Group D Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 13/12/2018 12:10
Engineering Tripos Part IIB, 4D6: Dynamics in Civil Engineering, 2017-18
Module Leader
Lecturers
Prof G Madabhushi, Dr J Talbot, Mr F A McRobie and Dr M DeJong
Lab Leader
Dr M DeJong
Timing and Structure
Lent term. 14 lectures + coursework. Assessment: 75% exam/25% coursework
Prerequisites
3D7, 3D2 and 3D4 useful
Aims
The aims of the course are to:
- introduce the behaviour and design of civil engineering structures subjected to time-varying loads.
- introduce earthquake-resistant design, dynamic soil-structure interaction, machine foundation design, blast effects on structures and the fundamentals of wind engineering.
Objectives
As specific objectives, by the end of the course students should be able to:
- identify cases where a static model of a structure is inadequate, and a dynamic model should be used
- produce a simple estimate of the natural frequency and fundamental natural mode of any linear-elastic structure.
- estimate linear-elastic spring parameters for a given foundation.
- compute the natural frequencies and natural modes of structures using the ABAQUS package and include simple soil models to account for soil-structure interaction.
- estimate the response of complex linear-elastic structures to earthquakes using modal superposition and the response spectrum.
- use elastic and inelastic design spectra, and to understand their form.
- perform simple designs for vibration isolation.
- perform simplified soil stiffness calculations accounting for partial liquefaction, and to use this approach in simple liquefaction resistant designs.
- describe some standard methods of seismic-resistant structural design.
- describe blast processes and their effects on structures.
- appreciate the factors involved in the estimation of wind climates and of structural response to wind.
- understand the various measures that characterise atmospheric turbulence.
- anticipate the circumstances under which aeroelastic phenomena may be problematic.
- estimate the dynamic response of a tall structure in a given wind environment
Content
LECTURE SYLLABUS
Structural dynamics (4L, Dr James Talbot)
Linear Elastic dynamics
á Introduction to dynamic loads in Civil Engineering; dynamic amplification factors.
á Approximate single-degree-of-freedom analysis of complex structures; sway frames; structures with distributed mass.
á Rayleigh's principle; natural frequency of simple systems using energy methods.
á Linear models to represent structures and their relevance; analysis in frequency domain; mode superposition method.
á Modal analysis of vibration; use of finite element packages.
Spectral Analysis & Earthquake Spectra (2L, Dr Matt DeJong)
á Introduction to spectral analysis
á Earthquake Spectra and Design Spectra, Design of linear systems
á Non-linear Spectral Analysis, Ductility in Structures
Application of dynamics in Civil Engineering Structures :
Part A: Soil-Structure Interaction (5L, Dr S.P.G.Madabhushi)
Non-linear Systems
á Sources of nonlinearity in structures and foundations.
á Analysis in time domain; numerical integration of equations of motion.
Seismic design
á Earthquake loading on structures; response and design spectra;
á Structures subject to ground motion; deformations due to lateral accelerations; Newmark's sliding block analysis; concept of threshold acceleration
á Foundations effects; stiffness of soil foundation and soil-structure interaction;
á Pore pressure build-up during earthquakes; partial liquefaction; degradation in soil stiffness; non-linear soil models.
á Liquefaction resistant design, simple examples.
á
Part B : Seismic resistant design, blast effects and wind engineering (3L, Mr F.A. McRobie)
Seismic Resistant Design
á Structural design and detailing considerations.
Blast Loading
á Physics of blasts; blast effects on structures; blast-resistant design.
Wind loading
á Nature of wind;
á Wind forces on structures.
á Response of structures to buffetting. Fluid-structure interaction (vortex-shedding, galloping and flutter). Long-span bridge case study.
Coursework
Seismic analysis of an existing tall building using the ABAQUS finite element package and a study of the effect of foundation softening on the overall structural response. Total time 8 hours.
| Coursework | Format |
Due date & marks |
|---|---|---|
|
[Coursework activity #1 title / Interim] Coursework 1 brief description Learning objective:
|
Individual/group Report / Presentation [non] anonymously marked |
day during term, ex: Thu week 3 [6/15] |
|
[Coursework activity #2 title / Final] Coursework 2 brief description Learning objective:
|
Individual Report anonymously marked |
Wed week 9 [9/15] |
Booklists
Please see the Booklist for Group D Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 19/01/2018 11:58
Engineering Tripos Part IIB, 4C9: Continuum Mechanics, 2018-19
Module Leader
Lecturers
Prof GN Wells and Dr GJ McShane
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3C7 assumed; 3D7 useful
Aims
The aims of the course are to:
- develop a more in-depth understanding of continuum solid mechanics, with particular emphasis on the distinction between linearised (i.e. infinitesimal strain) and nonlinear continuum mechanics;
- understand appropriate solution methods for particular boundary value problems, with a focus on elastic and visco-elastic materials.
Objectives
As specific objectives, by the end of the course students should be able to:
- show a working knowledge of tensor notation
- understand how to define deformation, stress and constitutive relationships, in both linear and nonlinear continuum mechanics
- use energy approaches to define constitutive relationships and solve problems in linear and nonlinear elasticity
- solve linear viscoelastic problems for arbitrary loading time-histories
- understand numerical solution methods for nonlinear continuum mechanics problems.
Content
This is an advanced course in continuum solid mechanics building on material covered in the Part IIA course 3C7. The aim of the course is to develop a more in-depth understanding of the techniques employed in continuum solid mechanics, for both small and large deformations, with particular emphasis on the response of elastic and visco-elastic bodies.
Preliminaries (2L, Dr GJ McShane)
- Introduction to indicial notation.
- Vectors, tensors and their manipulation.
Linearised Continuum Mechanics (6L, Dr GJ McShane)
- Kinematics: infinitesimal strains, compatibility.
- Conservation laws; stress and equilibrium.
- Linear elasticity: method of stationary potential energy.
- Linear viscoelasticity: constitutive equations; solving viscoelastic problems in 1D for arbitrary loading time-histories; viscoelastic analysis in 3D.
Nonlinear Continuum Mechanics (8L, Prof GN Wells)
- Nonlinear kinematics.
- Strain rates and stress measures.
- Nonlinear elasticity: stationary potential energy and hyper-elasticity.
- Numerical solution methods.
- Note that this part of the 4C9 course is new for 2018-19.
Examples papers
- Papers 1-2 - Preliminaries and linearised continuum mechanics.
- Papers 3-4 - Nonlinear continuum mechanics
Booklists
Please see the Booklist for Group C Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 03/08/2018 14:56
Engineering Tripos Part IIB, 4C9: Continuum Mechanics, 2024-25
Module Leader
Lecturers
Prof GN Wells and Dr GJ McShane
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3C7 assumed; 3D7 useful
Aims
The aims of the course are to:
- develop a more in-depth understanding of continuum solid mechanics, with particular emphasis on the distinction between linearised (i.e. infinitesimal strain) and nonlinear continuum mechanics;
- understand appropriate solution methods for particular boundary value problems, with a focus on elastic and visco-elastic materials.
Objectives
As specific objectives, by the end of the course students should be able to:
- show a working knowledge of tensor notation
- define deformation, stress and constitutive relationships, in both linear and nonlinear continuum mechanics
- use energy approaches to define constitutive relationships and solve problems in linear and nonlinear elasticity
- solve linear viscoelastic problems for arbitrary loading time-histories
- understand numerical solution methods for nonlinear continuum mechanics problems.
Content
This is an advanced course in continuum solid mechanics building on material covered in the Part IIA course 3C7. The aim of the course is to develop a more in-depth understanding of the techniques employed in continuum solid mechanics, for both small and large deformations, with particular emphasis on the response of elastic and visco-elastic bodies.
Preliminaries (2L, Dr GJ McShane)
- Introduction to indicial notation.
- Vectors, tensors and their manipulation.
Linearised Continuum Mechanics (6L, Dr GJ McShane)
- Kinematics: infinitesimal strains, compatibility.
- Conservation laws; stress and equilibrium.
- Linear elasticity: method of stationary potential energy.
- Linear viscoelasticity: constitutive equations; solving viscoelastic problems in 1D for arbitrary loading time-histories; viscoelastic analysis in 3D.
Nonlinear Continuum Mechanics (8L, Prof GN Wells)
- Nonlinear kinematics.
- Strain rates and stress measures.
- Nonlinear elasticity: stationary potential energy and hyper-elasticity.
- Numerical solution methods.
Examples papers
- Papers 1-2 - Preliminaries and linearised continuum mechanics.
- Papers 3-4 - Nonlinear continuum mechanics
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 31/05/2024 10:02
Engineering Tripos Part IIB, 4C9: Continuum Mechanics, 2017-18
Module Leader
Lecturers
Prof VS Deshpande and Dr GJ McShane
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3C7 assumed; 3D7 useful
Aims
The aims of the course are to:
- develop a more in-depth understanding of analytical techniques employed in continuum solid mechanics with particular emphasis on the response of elastic, visco-elastic and plastic bodies.
Objectives
As specific objectives, by the end of the course students should be able to:
- show a working knowledge of Cartesian tensor notation
- use the method of minimum potential energy to solve problems in linear elasticity
- understand how to solve viscoelastic problems in 1D and 3D for arbitrary loading time-histories
- know Drucker's stability postulate and understand the implications of convexity and normality
- understand the difference between deformation and flow theories of plasticity
- able to apply slip line field theory as well as upper and lower bound theorems for perfectly plastic solids
Content
This is an advanced course in continuum solid mechanics building on material covered in the Part IIA course 3C7. The aim of the course is to develop a more in-depth understanding of analytical techniques employed in continuum solid mechanics with particular emphasis on the response of elastic and plastic bodies.
Preliminaries (3L, Dr GJ McShane)
- Introduction to indicial notation
- Vectors, tensors and their manipulation
- Stress and equilibrium, strain and compatibility, constitutive relationships
Elasticity and Viscoelasticity (5L, Dr GJ McShane)
- Method of minimum potential energy
- Examples: application to elastic beams and plates in bending
- Deriving constitutive equations for linear viscoelasticity
- Solving viscoelastic problems in 1D for arbitrary loading time-histories
- Viscoelastic analysis in 3D
Plasticity (8L, Prof VS Deshpande)
- Constitutive relationships - Drucker's stability postulate, normality and convexity conditions, yield criteria, flow rules, strain-hardening materials, flow and deformation theories of plasticity;
- Limit analysis theorems;
- Slip-line field theory; the solution of boundary value problems - metal forming, contact problems, cracked bodies.
Examples papers
- Paper 1 - Preliminaries
- Paper 2 - Elastic and viscoelastic analysis
- Paper 3 - Plasticity 1
- Paper 4 - Plasticity 2
Booklists
Please see the Booklist for Group C Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 31/05/2017 09:12
Engineering Tripos Part IIB, 4C9: Continuum Mechanics, 2020-21
Module Leader
Lecturers
Prof GN Wells and Dr GJ McShane
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3C7 assumed; 3D7 useful
Aims
The aims of the course are to:
- develop a more in-depth understanding of continuum solid mechanics, with particular emphasis on the distinction between linearised (i.e. infinitesimal strain) and nonlinear continuum mechanics;
- understand appropriate solution methods for particular boundary value problems, with a focus on elastic and visco-elastic materials.
Objectives
As specific objectives, by the end of the course students should be able to:
- show a working knowledge of tensor notation
- define deformation, stress and constitutive relationships, in both linear and nonlinear continuum mechanics
- use energy approaches to define constitutive relationships and solve problems in linear and nonlinear elasticity
- solve linear viscoelastic problems for arbitrary loading time-histories
- understand numerical solution methods for nonlinear continuum mechanics problems.
Content
This is an advanced course in continuum solid mechanics building on material covered in the Part IIA course 3C7. The aim of the course is to develop a more in-depth understanding of the techniques employed in continuum solid mechanics, for both small and large deformations, with particular emphasis on the response of elastic and visco-elastic bodies.
Preliminaries (2L, Dr GJ McShane)
- Introduction to indicial notation.
- Vectors, tensors and their manipulation.
Linearised Continuum Mechanics (6L, Dr GJ McShane)
- Kinematics: infinitesimal strains, compatibility.
- Conservation laws; stress and equilibrium.
- Linear elasticity: method of stationary potential energy.
- Linear viscoelasticity: constitutive equations; solving viscoelastic problems in 1D for arbitrary loading time-histories; viscoelastic analysis in 3D.
Nonlinear Continuum Mechanics (8L, Prof GN Wells)
- Nonlinear kinematics.
- Strain rates and stress measures.
- Nonlinear elasticity: stationary potential energy and hyper-elasticity.
- Numerical solution methods.
Examples papers
- Papers 1-2 - Preliminaries and linearised continuum mechanics.
- Papers 3-4 - Nonlinear continuum mechanics
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 11/09/2020 19:52
Engineering Tripos Part IIB, 4C9: Continuum Mechanics, 2022-23
Module Leader
Lecturers
Prof GN Wells and Dr GJ McShane
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3C7 assumed; 3D7 useful
Aims
The aims of the course are to:
- develop a more in-depth understanding of continuum solid mechanics, with particular emphasis on the distinction between linearised (i.e. infinitesimal strain) and nonlinear continuum mechanics;
- understand appropriate solution methods for particular boundary value problems, with a focus on elastic and visco-elastic materials.
Objectives
As specific objectives, by the end of the course students should be able to:
- show a working knowledge of tensor notation
- define deformation, stress and constitutive relationships, in both linear and nonlinear continuum mechanics
- use energy approaches to define constitutive relationships and solve problems in linear and nonlinear elasticity
- solve linear viscoelastic problems for arbitrary loading time-histories
- understand numerical solution methods for nonlinear continuum mechanics problems.
Content
This is an advanced course in continuum solid mechanics building on material covered in the Part IIA course 3C7. The aim of the course is to develop a more in-depth understanding of the techniques employed in continuum solid mechanics, for both small and large deformations, with particular emphasis on the response of elastic and visco-elastic bodies.
Preliminaries (2L, Dr GJ McShane)
- Introduction to indicial notation.
- Vectors, tensors and their manipulation.
Linearised Continuum Mechanics (6L, Dr GJ McShane)
- Kinematics: infinitesimal strains, compatibility.
- Conservation laws; stress and equilibrium.
- Linear elasticity: method of stationary potential energy.
- Linear viscoelasticity: constitutive equations; solving viscoelastic problems in 1D for arbitrary loading time-histories; viscoelastic analysis in 3D.
Nonlinear Continuum Mechanics (8L, Prof GN Wells)
- Nonlinear kinematics.
- Strain rates and stress measures.
- Nonlinear elasticity: stationary potential energy and hyper-elasticity.
- Numerical solution methods.
Examples papers
- Papers 1-2 - Preliminaries and linearised continuum mechanics.
- Papers 3-4 - Nonlinear continuum mechanics
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 24/05/2022 13:10
Engineering Tripos Part IIB, 4C9: Continuum Mechanics, 2023-24
Module Leader
Lecturers
Prof GN Wells and Dr GJ McShane
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3C7 assumed; 3D7 useful
Aims
The aims of the course are to:
- develop a more in-depth understanding of continuum solid mechanics, with particular emphasis on the distinction between linearised (i.e. infinitesimal strain) and nonlinear continuum mechanics;
- understand appropriate solution methods for particular boundary value problems, with a focus on elastic and visco-elastic materials.
Objectives
As specific objectives, by the end of the course students should be able to:
- show a working knowledge of tensor notation
- define deformation, stress and constitutive relationships, in both linear and nonlinear continuum mechanics
- use energy approaches to define constitutive relationships and solve problems in linear and nonlinear elasticity
- solve linear viscoelastic problems for arbitrary loading time-histories
- understand numerical solution methods for nonlinear continuum mechanics problems.
Content
This is an advanced course in continuum solid mechanics building on material covered in the Part IIA course 3C7. The aim of the course is to develop a more in-depth understanding of the techniques employed in continuum solid mechanics, for both small and large deformations, with particular emphasis on the response of elastic and visco-elastic bodies.
Preliminaries (2L, Dr GJ McShane)
- Introduction to indicial notation.
- Vectors, tensors and their manipulation.
Linearised Continuum Mechanics (6L, Dr GJ McShane)
- Kinematics: infinitesimal strains, compatibility.
- Conservation laws; stress and equilibrium.
- Linear elasticity: method of stationary potential energy.
- Linear viscoelasticity: constitutive equations; solving viscoelastic problems in 1D for arbitrary loading time-histories; viscoelastic analysis in 3D.
Nonlinear Continuum Mechanics (8L, Prof GN Wells)
- Nonlinear kinematics.
- Strain rates and stress measures.
- Nonlinear elasticity: stationary potential energy and hyper-elasticity.
- Numerical solution methods.
Examples papers
- Papers 1-2 - Preliminaries and linearised continuum mechanics.
- Papers 3-4 - Nonlinear continuum mechanics
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 30/05/2023 15:28
Engineering Tripos Part IIB, 4C9: Continuum Mechanics, 2019-20
Module Leader
Lecturers
Prof GN Wells and Dr GJ McShane
Timing and Structure
Lent term. 16 lectures (including examples classes). Assessment: 100% exam
Prerequisites
3C7 assumed; 3D7 useful
Aims
The aims of the course are to:
- develop a more in-depth understanding of continuum solid mechanics, with particular emphasis on the distinction between linearised (i.e. infinitesimal strain) and nonlinear continuum mechanics;
- understand appropriate solution methods for particular boundary value problems, with a focus on elastic and visco-elastic materials.
Objectives
As specific objectives, by the end of the course students should be able to:
- show a working knowledge of tensor notation
- understand how to define deformation, stress and constitutive relationships, in both linear and nonlinear continuum mechanics
- use energy approaches to define constitutive relationships and solve problems in linear and nonlinear elasticity
- solve linear viscoelastic problems for arbitrary loading time-histories
- understand numerical solution methods for nonlinear continuum mechanics problems.
Content
This is an advanced course in continuum solid mechanics building on material covered in the Part IIA course 3C7. The aim of the course is to develop a more in-depth understanding of the techniques employed in continuum solid mechanics, for both small and large deformations, with particular emphasis on the response of elastic and visco-elastic bodies.
Preliminaries (2L, Dr GJ McShane)
- Introduction to indicial notation.
- Vectors, tensors and their manipulation.
Linearised Continuum Mechanics (6L, Dr GJ McShane)
- Kinematics: infinitesimal strains, compatibility.
- Conservation laws; stress and equilibrium.
- Linear elasticity: method of stationary potential energy.
- Linear viscoelasticity: constitutive equations; solving viscoelastic problems in 1D for arbitrary loading time-histories; viscoelastic analysis in 3D.
Nonlinear Continuum Mechanics (8L, Prof GN Wells)
- Nonlinear kinematics.
- Strain rates and stress measures.
- Nonlinear elasticity: stationary potential energy and hyper-elasticity.
- Numerical solution methods.
- Note that this part of the 4C9 course is new for 2018-19.
Examples papers
- Papers 1-2 - Preliminaries and linearised continuum mechanics.
- Papers 3-4 - Nonlinear continuum mechanics
Booklists
Please see the Booklist for Group C Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
Last modified: 24/05/2019 14:18
Engineering Tripos Part IIB, 4C8: Vehicle Dynamics, 2023-24
Module Leader
Lecturers
Prof D Cebon and Dr R L Roebuck
Lab Leader
Dr X Na
Timing and Structure
Lent term. 13 lectures + 2 examples classes + coursework
Prerequisites
3C5 and 3C6 useful
Aims
The aims of the course are to:
- introduce the forces generated by rolling wheels;
- show how these forces affect the lateral stability and steady cornering behaviour of road and railway vehicles;
- introduce some simple mathematical models and performance criteria for vehicle vibration;
- show how vehicle suspension parameter values can be tuned to optimise vibration performance;
- review vehicle suspension technology;
Objectives
As specific objectives, by the end of the course students should be able to:
- understand steady state creep forces and moments in rolling contact and be able to calculate them using the 'brush' model for a variety of simple cases;
- derive the equations of motion of a simple automobile and understand the basic concepts of automobile handling and lateral stability;
- derive the equations of motion of a two-axle rigid railway bogie and to understand the implications for the steady cornering and stability of railway vehicles;
- derive the equations of motion of simple vehicle models and calculate the vibration responses;
- understand the trade-offs involved in suspension design;
- explain the influence of vehicle and road parameters on vehicle vibration behaviour.
Content
Introduction (1L) Prof. D Cebon and Dr D J Cole
Vehicle dynamics (6L) (Prof. D Cebon)
- Introduction to the creep forces and moments generated by rolling wheels, using the 'brush' model.
- Steady state and transient response of a simple automobile model to steering and side force inputs.
- Introduction to understeer, oversteer, and handling diagrams.
- Stability and cornering of a single railway wheelset and a two-axle railway bogie.
Vehicle vibration (6L) (Dr D J Cole)
- Introduction to random vibration, description of road surface roughness.
- Performance criteria.
- Quarter-car model of vehicle vibration, natural modes, conflict diagrams.
- Pitch-plane model, natural modes, wheelbase filtering, suspension tuning.
- Roll-plane model, lateral tyre behaviour, parallel road profiles.
- Vehicle suspension technology.
Further notes
ASSESSMENT
Lecture Syllabus/Written exam (1.5 hours) - Start of Easter Term/75%
Coursework/Laboratory Report - End of Lent Term/25%
Examples papers
Examples paper 1, vehicle dynamics, issued in lecture 1.
Examples paper 2, vehicle vibration, issued in lecture 8.
Coursework
| Coursework | Format |
Due date & marks |
|---|---|---|
|
One laboratory experiment on behaviour of vehicle tyres, to be performed in pairs, essentially unsupervised. An online booking sheet will offer a wide range of possible times at which the experiment may be performed. A normal laboratory write-up is to be prepared, which will be assessed for the coursework credit. The aim of this experiment is to investigate, qualitatively and quantitatively, the characteristics of a model tyre under a variety of operating conditions. Although the model tyre is not dimensionally similar to a real tyre and is made of solid silicone rubber, it displays many of the important characteristics of road and railway wheels. Learning objectives:
|
Individual Report anonymously marked |
Submit online via Moodle before the feedback lecture. [15/60] |
Booklists
Please refer to the Booklist for Part IIB Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
IA2
Demonstrate creative and innovative ability in the synthesis of solutions and in formulating designs.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
E4
Understanding of and ability to apply a systems approach to engineering problems.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
US4
An awareness of developing technologies related to own specialisation.
Last modified: 30/05/2023 15:28
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