COURSES

• Solid Mechanics, Level 2 - BEng & MEng (core)
• Structural Optimisation, Level 3 - BEng & MEng (option)
• Finite Element Methods, Level 3 - BEng (option), Level 4 - MEng (core), MSc
• Residential Field Course at Whitby (shared with other members of staff), Level 3 - BEng & MEng (core)
• Final year projects, Level 3 - BEng, Level 4 - MEng (core)

SOLID MECHANICS

Module: 181504M

Prerequisites: Structures - Trusses, Structures - Beams, Redundant Structures or equivalent, Mathematics 2 or equivalent.

Co-requisites: None

Lecture hours: 24

Tutorial hours: 12

Non-contact hours: 64

Outline syllabus:

• Fundamental assumptions of solid mechanics. Concept of the continuum. Examples of three-dimensional behaviour of actual materials and structural elements.
• Stress state. Stress vector, its normal and shear components. Stress tensor. Principle of complementary shear stress. Determination of stresses corresponding to a given orientation of an imaginary cutting plane. Stress tensor invariants. Principal stresses, determination of their values and directions. Maximum shear stress, orientation of corresponding plane. Differential equations of motion and equilibrium. Two-dimensional stress states. Plane stress. Mohr's circle of stress.
• Displacements and strain state. Displacement vector. Concept of the strain tensor. Assumptions of linearisation. Direct and shearing strains. Relations between strains and displacements. Compatibility equations. Strain tensor invariants, principal strains and their directions. Two-dimensional strain states. Plane strain. Mohr's circle of strain. Measurements of displacements and strains. Strain rosettes.
• Stress - strain relations. Testing of materials. Typical stress - strain diagrams. Concepts of elasticity and plasticity. Brittle and ductile behaviour of materials. Effect of creep. Linear elasticity. Isotropic and anisotropic behaviour of materials. Poisson's effect. Hooke's law. Plane stress and plane strain situations.
• Potential energy of deformation. Strain energy, dilatational and distortional components. Spherical stress tensor and stress deviator. Work of external loads. Total potential energy.
• Failure criteria. Concept of the equivalent stress. Maximum principal stress and strain criteria. Maximum shear stress criterion. Distortional strain energy criterion.
• Principle of minimum potential energy. Rayleigh-Ritz method, applications to structural analysis. Discrete form of Rayleigh-Ritz method, concept of the finite element method. Applications to the stability analysis of axially compressed bars. Potential energy of the transformation to an alternative equilibrium state. Rayleigh-Ritz method for the determination of the critical load and buckling mode.

Coursework:

1. Stress state.
2. Strain state and Hooke's law.

Directed study and indicative reading:

• Baxter Brown, J.McD. (1973): Introductory Solid Mechanics. John Wiley & Sons. (Library Class No. X 624.04 BRO)
• Boresi, A.P. (1965): Elasticity in Engineering Mechanics. Prentice-Hall International, Inc. (Library Class No. M539.3 BOR)
• Chou, P.C.; Pagano, N.J.(1967): Elasticity. Tensor, Dyadic, and Engineering Approaches. D. van Nostrand Company, Inc. (Library Class No. M539.3 CHO)
• Douglas, R.A. (1963): Introduction to Solid Mechanics. Sir Isaac Pitman & Sons Ltd. (Library Class No. T620.17 DOU)
• Fenner, R.T. (1989): Mechanics of Solids. Blackwell Scientific Publications (Library Class No. T620.17 FEN)
• Fenner, R.T. (1986): Engineering Elasticity. Application of Numerical and Analytical Techniques. Ellis Horwood Ltd. (Library Class No. T620.17 FEN)
• Ross, C.T.F. (1987): Applied Stress Analysis. Ellis Horwood Ltd. (Library Class No. T620.17 ROS)
• Ross, C.T.F. (1987): Advanced Applied Stress Analysis. Ellis Horwood Ltd. (Library Class No. T620.17 ROS)
• Shames, I.H. (1989): Introduction to Solid Mechanics. Prentice-Hall International, Inc. (Library Class No. T620.17 SHA)
• Timoshenko, S.P.; Goodier, J.N. (1970): Theory of Elasticity. McGraw-Hill International. (Library Class No. M539.3 TIM)
• Ugural, A.C.; Fenster, S.K. (1975): Advanced Strength and Applied Elasticity. American Elsevier Publishing Company, Inc. (Library Class No. T620.17 UGU)
• Venkatraman, B., Patel S.A. (1970): Structural Mechanics with Introductions to Elasticity and Plasticity. McGraw-Hill, Inc. (Library Class No. X 624.04 VEN)

Staff involved:

Module co-ordinator: Dr VV Toropov

Other staff: Mr H Ravaii (PG demonstrator)

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STRUCTURAL OPTIMISATION

Prerequisites: Structures - Redundant Structures, Solid Mechanics, Mathematics 2, Computing 2.

Co-requisites: None

Aim: To acquaint the students with the formulation of a structural optimisation problem, modern methods of nonlinear mathematical programming and interpretation of the results. To introduce the basic concepts of structural design sensitivity analysis and structural identification, formulated as an optimisation problem. The emphasis is made on the application of modern optimisation techniques linked to the numerical methods of structural analysis, particularly, the finite element method.

Lecture hours: 24

Computer laboratory hours: 12

Non-contact hours: 64

Outline syllabus:

• Criteria of structural efficiency. Formulation of an optimisation problem as a nonlinear mathematical programming problem.
• Choice of design variables and an objective function. Formulation of typical constraints imposed on structural behaviour.
• The relationships between fully-stressed and minimum weight structures. Maxwell-Michell structural continua. Topology optimisation.
• Global and local optima. Kuhn-Tucker optimality conditions.
• Classification of structural optimisation problems. Constrained and unconstrained problems. Multi-objective problems. Pareto optimum solutions. Basic approaches to the formulation of a combined criterion.
• Numerical optimisation techniques. Local and global one-dimensional optimisation. Unconstrained multi-parameter optimisation techniques. Linear programming. Geometric programming. General constrained optimisation techniques. Random search, genetic algorithms, neural networks.
• Approximation techniques. Local, mid-range and global approximations, used in conjunction with the finite element structural analysis.
• Design sensitivity analysis based on the finite element modelling of structural behaviour. Analytical, semi-analytical and finite difference techniques.
• Structural identification problems: finite element model identification, material parameter identification, structural damage recognition. Formulation of an identification problem as a general optimisation problem.
• Real-life examples of structural optimisation and identification. Availability of commercial software.

Coursework:

1. Formulation and graphical interpretation of a structural optimisation problem.
2. Penalty function approach to a structural optimisation problem.

Assessment:

80% examination (2 hour examination) and 20% coursework (2 assignments).

Directed study and indicative reading:

• Adeli, H. (1994): Advances in Design Optimization. Chapman & Hall. (Library Class No. X624.04:517.27 ADE)
• Atrek, E.; Gallagher, R.H.; Ragsdell, K.M.; Zienkiewicz, O.C. (1984): New Directions in Optimum Structural Design. Wiley & Sons (Library Class No. X624.04 ATK)
• Bunday, B.D. (1984): Basic Optimisation Methods. Edward Arnold. (Library Class No. L517.27 BUN)
• Gallagher, R.H.; Zienkiewicz, O.C. (1973): Optimum Structural Design. Theory and Applications. Wiley & Sons (Library Class No. X624.04 GAL)
• Haftka, R.T.; Gürdal, Z. (1992): Elements of Structural Optimization. 3rd ed., Kluwer Academic Publishers (Library Class No. T 620.17 HAF)
• Hemp, W.S. (1973): Optimum Structures. Clarendon Press, 1973 (Library Class No. X624.04 HEM)
• Kamat, M.P (1993): Structural Optimization : Status and Promise, Washington, DC: American Institute of Aeronautics and Astronautics (Library Class No. X 624.04:517.27 KAM)
• Kirsch, U. (1993): Structural Optimization: fundamental and applications. Springer-Verlag. (Library Class No. X 624.04:517.27 KIR)
• Majid, K.J.(1974): Optimum Design of Structures. Newness-Butterworth, (Library Class No. X624.04 MAJ)
• Vanderplaats, G.N.(1984): Numerical Optimization Techniques for Engineering Design. McGraw-Hill, New York

Staff involved:

Module co-ordinator: Dr VV Toropov

Other staff: none

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FINITE ELEMENT METHODS

Module: 180504M

Pre-requisites: Structures - Trusses, Beams and Redundant Structures, Solid Mechanics, Mathematical Techniques, Applicable Mathematics and Mathematics 2 or equivalent.

Co-requisites: None

Aim: To demonstrate the use and usefulness of the finite element method for the solution of engineering problems, and acquaint students with a typical commercial software package.

Lecture hours: 18

Computer laboratory hours: 18

Non-contact hours: 64

General comments:

As it is an introductory course focusing on the basic principles of generating a finite element model and interpreting the results, only linear problems are considered.

To enable students to become competent finite element analysts, the main body of the course focuses on the application of a single system. However, a review of the range of software available is undertaken.

Outline syllabus:

• A concept of considering an engineering structure as an assembly of elements whose properties are pre-defined. The integration of this concept with the matrix displacement/stiffness/finite element method.
• The basic steps in a finite element analysis.
• Introduction to the commercial system ANSYS.
• Use of ANSYS to analyse structures comprised of one-dimensional bar and beams elements:
• pin-jointed plane frames,
• rigid-jointed plane frames,
• generalised plane frames,
• use of symmetry and skew symmetry.
• Exact and approximate solutions; consideration of roundoff, discretisation and approximation errors.
• Use of ANSYS to solve the following categories of two-dimensional and a quasi-two-dimensional stress analysis problems:
• structures in a state of plane stress,
• structures in a state of plane strain,
• axisymmetric structures,
• plates in bending.
• Use of ANSYS to solve two-dimensional steady state field problems.

Coursework:

1. Finite element modelling of structures comprising of one-dimensional elements.
2. Finite element modelling of two-dimensional structures.

Directed study and indicative reading:

• Bathe, KJ. (1982) Finite Element Procedures in Engineering Analysis, Prentice-Hall, (Library Class No. 624.04.519.6).
• Dawe, DJ. (1984) Matrix and Finite Element Displacement Analysis of Structures, Clarendon Press, (Library Class No. 624.04.519.6).
• Hinton, E. Owen, DRG. (1979) An Introduction to Finite Element Computations, Pinerinde Press, (Library Class No.L519.63 HIN).
• Segerlind, LJ. (1976) Applied Finite Element Analysis, Wiley, (Library Class No.L519.63 SEG).
• ANSYS/ED Workbook for Revision 5.0. (1993) Swanson Analysis Systems Inc.
• Getting Started with ANSYS Program (1992) Swanson Analysis System Inc.

Staff involved:

Module co-ordinator: Dr VV Toropov

Other staff: none

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RESIDENTIAL FIELD COURSE AT WHITBY

Module: 187001H

Pre-requisites: Surveying 1 or equivalent, Surveying 2, Soil Mecahnics 1, Engineering Geology, Communication Skills or equivalent (report writing skills), Concrete, Hydrology & Water Supply or equivalent (principles of group working)

Co-requisites: None

Aim: To provide experience of a realistic working environment in the field of civil engineering by undertaking relevant group activity work; to obtain field data of a quality sufficient to enable the subsequent design of appropriate civil engineering works to promote an integrated link with the Civil Engineering Design modules.

Fieldwork hours: 50

Outline syllabus:

• Group and inter-group organisation and co-ordination.
• Theory, design and measurement of control surveys.
• Location of local surface details using modern surveying techniques.
• Use of a CAD package to produce a topographical map.
• Geotechnical surveying techniques; applications of geotechnical cross sections.
• Site investigation.

Coursework: 1 report

Assessment: 100% coursework

Directed study and indicative reading:

• Notes from Surveying 1 and 2.
• Bannister & Raymond (1986) Surveying, Longman (Library Class No. X528 BAN).

Staff involved:

Module co-ordinator: Dr JC Boot

Other staff: Dr BC Chapman, Dr VV Toropov, Dr KV Horoshenkov, Dr Y Chen, Dr AA Javadi

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FINAL YEAR PROJECTS

OPTIMISATION OF TRUSS AND FRAME STRUCTURES USING THE FINITE ELEMENT PACKAGE “ANSYS”

Number of students: one

Type: computational

A typical truss or frame optimisation problem is formulated as follows: to find the set of design parameters (cross-sectional areas, second moments of area, etc.) which corresponds to the best value of a chosen objective function (typically, weight or cost) subject to conditions imposed on the values of stresses and displacements. Project is to apply a finite element package ANSYS, analyse and optimise truss and frame structures and analyse the results.

Number of students: one

Type: computational

The project is to develop a series of subroutines in FORTRAN-like built-in language of the general finite element structural analysis package ANSYS in order to create a user-friendly plane frame analysis software to be used by Civil and Structural Engineering students.

Number of students: one

Type: computational

The project is to develop a series of subroutines in FORTRAN-like built-in language of the general finite element structural analysis package ANSYS in order enhance the package for finding the layout of reinforcement corresponding to the maximum strength of masonry walls.

Number of students: one

Type: computational

In order to analyse masonry structures, it is necessary to know material parameters (Young’s modulus, Poisson’s ratio, etc.) for plain and reinforced masonry. Material properties of masonry depend strongly on manufacturing conditions and cannot be easily identified from usual tests. To determine unknown material parameters, a structural response predicted by the analysis (e.g. displacements or strains in a specimen) will be compared to the response observed in the course of a laboratory experiment. Project is to apply a finite element package ANSYS, analyse specimens used in laboratory experiments and compare results with the available experimental data.

Number of students: one

Type: mainly experimental, partly computational

The damage recognition problem is formulated as follows: find the location of damage in a portal frame by minimising the difference between the dynamic response (frequencies of vibrations) predicted by the analysis and the response observed in the course of laboratory experiments. Project is to learn the fundamentals of dynamic testing and then participate in the experimental programme carried out in the Heavy Structures laboratory, analyse the frame and assess the results.

Number of students: one

Type: computational

A typical frame optimisation problem is formulated as follows: to find the set of design parameters (second moments of area, etc.) which corresponds to the best value of a chosen objective function (typically, weight or cost) subject to conditions imposed on the values of stresses and displacements. Project is to learn the fundamentals of genetic algorithms based on the numerical modelling of Darwin’s theory of survival of the fittest, apply a simple genetic algorithm (under continuous development at the Department) coupled to the existing finite element program, and analyse the results.

• All aspects of structural analysis
• Finite element structural analysis
• Structural optimisation
• Dynamic testing
• Structural damage recognition
• Material parameter identification

Final year students are welcome to propose their own project related (not necessarily very closely) to any of those areas.

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