Mechanical And Aerospace Engineering

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Research Output 1976 2020

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Conference contribution book
2019

Artificial intelligence for the early design phases of space missions

Berquand, A., Murdaca, F., Riccardi, A., Soares, T., Gerené, S., Brauer, N. & Kumar, K., 20 Jun 2019, 2019 IEEE Aerospace Conference. Piscataway, N.J.: IEEE, 20 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Artificial intelligence
Expert systems
Ontology
Concurrent engineering
Inference engines

Autonomous generation of observation schedules for tracking satellites with structured-chromosome GA optimisation

Greco, C., Gentile, L., Filippi, G., Minisci, E., Vasile, M. & Bartz-Beielstein, T., 10 Jun 2019, 2019 IEEE Congress on Evolutionary Computation. Piscataway, NJ: IEEE, p. 497-505 9 p. 8790101

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Chromosomes
Earth (planet)
Satellites
Space debris
State estimation

Creep fatigue life assessment of hydrogenation reactor manufactured of 2.25Cr-1Mo steel using the linear matching method framework

Ma, Z., Wang, X., Chen, H. & Xuan, F., 8 May 2019, ESIA15 & ISSI-2019 Joint Conference on Engineering Structural Integrity Assessment. Preston, UK, 11 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Hydrogenation
Creep
Fatigue of materials
Steel
Fatigue damage

Improved trailing edge noise prediction using a generalized Rapid-distortion theory approach

Afsar, M. Z., 18 May 2019, 25th AIAA/CEAS Aeroacoustics Conference. Reston, VA, 10 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Turbulence
Fluids
Prediction
Fluid
Hydrodynamics

Modeling supersonic heated jet noise at fixed jet Mach number using an asymptotic approach for the acoustic analogy Green’s function and an optimized turbulence model

Afsar, M. Z., Sescu, A. & Minisci, E., 18 May 2019, 25th AIAA/CEAS Aeroacoustics Conference. Reston, VA, 13 p. AIAA 2019-2731

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Turbulence Model
Turbulence models
Green's function
Mach number
Analogy

Robust optimisation of low-thrust interplanetary transfers using evidence theory

Di Carlo, M., Vasile, M., Greco, C. & Epenoy, R., 8 Feb 2019, 29th AAS/AIAA Space Flight Mechanics Meeting. Topputo, F., Sinclair, A. J., Wilkins, M. P. & Zanetti, R. (eds.). San Diego, CA, Vol. 168. p. 339-358 20 p. AAS 19-285

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Asteroids
Propulsion
Earth (planet)
Uncertainty

Solving multi-objective dynamic travelling salesman problems by relaxation

Ricciardi, L. A. & Vasile, M., 13 Jul 2019, GECCO '19 Proceedings of the Genetic and Evolutionary Computation Conference Companion. López-Ibáñez, M. (ed.). New York, p. 1999-2007 9 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Traveling salesman problem
Space applications
Transcription
Multiobjective optimization
Debris

Structured-chromosome GA optimisation for satellite tracking

Gentile, L., Greco, C., Minisci, E., Bartz-Beielstein, T. & Vasile, M., 30 Sep 2019, GECCO '19 Proceedings of the Genetic and Evolutionary Computation Conference Companion. Prague, Czech Republic, p. 1955-1963 9 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Chromosomes
Genetic algorithms
Earth (planet)
State estimation
Genes

The implications of constitutive model selection in hyperelastic parameter identification

Connolly, S., MacKenzie, D. & Gorash, Y., 20 Jun 2019, Constitutive Models for Rubber XI: Proceedings of the 11th European Conference on Constitutive Models for Rubber (ECCMR 2019), June 25-27, 2019, Nantes, France. Huneau, B., Le Cam, J-B., Marco, Y. & Verron, E. (eds.). London, 6 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Constitutive models
Identification (control systems)
Rubber

Towards new contact-less techniques for the control of inertial particles dispersed in a fluid

Lappa, M., 26 Feb 2019, 12th International Conference on Thermal Engineering: Theory and Applications, February 23-26, 2019, Gandhinagar , India. Toronto, 3 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Fluids
Hopf bifurcation
Crystallization
Fluid dynamics
Agglomeration
2018

Application of the CEL approach to consider FSI for the assessment of leak tightness for elastomeric seals

Gorash, Y., Bickley, A. & Gozalo, F., 15 Jul 2018, ASME 2018 Pressure Vessels and Piping Conference: Fluid-Structure Interaction. New York, Vol. 4. 10 p. PVP2018-84792

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Packers
Seals
Leakage (fluid)
Fluids
Fluid structure interaction
Open Access
File
Silanes
Shear strength
Glass fibers
Residual stresses
Composite materials

Comparison of the finite volume and discontinuous Galerkin schemes for the double vortex pairing problem using the SU2 software suite

Singh, K. K., Drikakis, D., Frank, M., Kokkinakis, I. W., Alonso, J. J., Economon, T. D. & van der Weide, E. T. A., 8 Jan 2018, 2018 AIAA Aerospace Sciences Meeting. Reston, VA., 14 p. 1833

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Mach number
Vortex flow
Galerkin methods
Finite element method

Cyclic plasticity behavior of 90° back-to-back pipe bends under cyclic bending and steady pressure

Cho, N-K. & Chen, H., 24 Oct 2018, 2018 26th International Conference on Nuclear Engineering. New York, 9 p. ICONE26-82386

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Plasticity
Pipe
Bearings (structural)
Nuclear industry
Piping systems

Evidence-based robust optimisation of space systems with evidence network models

Filippi, G., Vasile, M., Marchi, M. & Vercesi, P., 14 May 2018, (Accepted/In press) IEEE world congress on computational intelligence. Piscataway, N.J.: IEEE, p. 1-8 8 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Aerospace engineering
Systems engineering
Large scale systems
Uncertainty

Fatigue and corrosion fatigue life assessment with application to autofrettaged parts

Okorokov, V., MacKenzie, D. & Gorash, Y., 20 Jul 2018, ASME 2018 Pressure Vessels and Piping Conference: Volume 5: High-Pressure Technology; ASME Nondestructive Evaluation, Diagnosis and Prognosis Division (NDPD). New York, 6 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Corrosion fatigue
Fatigue of materials
Crack initiation
Plasticity
Crack propagation

Inside out: a shift in perspective for building exergy analysis

Bonetti, V., 21 Jun 2018, ECOS 2018: Proceedings of the 31st International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems. Guimarães, Portugal, 12 p. 220

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Exergy
Roofs
Energy efficiency
Sustainable development
Conservation

On the use of positive polynomials for the estimation of upper and lower expectations in orbital dynamics

Vasile, M. & Tardioli, C., 11 Feb 2018, Stardust Final Conference: Advances in Asteroids and Space Debris Engineering and Science. Vasile, M., Minisci, E., Summerer, L. & McGinty, P. (eds.). Cham: Springer, p. 99-107 9 p. (Astrophysics and Space Science Proceedings; vol. 52).

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
polynomials
Polynomials
orbitals
asteroid
Asteroids
2 Citations (Scopus)

Physical insight into a Mach 7.2 compression corner flow

Ritos, K., Kokkinakis, I. W. & Drikakis, D., 8 Jan 2018, 2018 AIAA Aerospace Sciences Meeting. Reston, VA

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Mach number
Boundary layers
Large eddy simulation
Turbulent flow
Momentum

Self-warning hybrid composite patches for repairing cracked aluminium panels

Jalalvand, M., Lok Wu, H. W. M., Sheibanian, F., Fotouhi, M. & Wisnom, M. R., 27 Jun 2018, ECCM18 - 18th European Conference on Composite Materials. 8 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Repair
Aluminum
Composite materials
Monitoring
Inspection
2017

3D micro-macro fluid-structure model of pressure relief valve leak tightness

Anwar, A. A., Dempster, W. (ed.) & Gorash, Y. (ed.), 17 Jul 2017, ASME 2017 Pressure Vessels and Piping Conference: Volume 5: High-Pressure Technology; ASME Nondestructive Evaluation, Diagnosis and Prognosis Division (NDPD). New York, Vol. 5. 10 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Pressure relief valves
Model structures
Macros
Fluids
Metals

A 'big data' approach to the application of building performance simulation to improve the operational performance of large estates

Clarke, J., Costola, D., Kelly, N. & Monari, F., 7 Aug 2017, Building Simulation 2017: The 15th Biennial Conference of the International Building Performance Simulation Association (IBPSA). [Vancouver, B.C.], 8 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Electronic data interchange
Calibration
Fault detection
Failure analysis
Control systems
2 Citations (Scopus)

A direct memetic approach to the solution of multi-objective optimal control problems

Vasile, M. & Ricciardi, L., 13 Feb 2017, 2016 IEEE Symposium Series on Computational Intelligence, SSCI 2016. Piscataway: Institute of Electrical and Electronics Engineers Inc., 7850103

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Optimal Control Problem
Nonlinear programming
Transcription
Rockets
Nonlinear Programming

Assessing policy constraints and technical feasibility of energy developments in cities

McGhee, R., Clarke, J. & Svehla, K., 2 Jul 2017, Design to Thrive: Proceedings of 33rd PLEA International Conference. Brotas, L., Roaf, S. & Nicol, F. (eds.). Edinburgh, Vol. 1. p. 1446-1453 8 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
energy
farm
policy
method
city

Combining mathematical modelling with in-vitro experiments to predict in-vivo drug-eluting stent kinetics

McGinty, S., McCormick, C., McKittrick, C. M., Kennedy, S., Oldroyd, K. G., Wheel, M., Scullion, B., Pontrelli, G., McKee, S., Nithiarasu, P. (ed.) & Robertson, A. M. (ed.), 10 Apr 2017, 5th International Conference on Computational and Mathematical Biomedical Engineering (CMBE2017). Swansea UK, p. 1011-1014 4 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Stents
Kinetics
Acrylics
Experiments
Mathematical models

Conceptual design analysis for a two-stage-to-orbit semi-reusable launch system for small satellites

Maddock, C., Toso, F., West, M., West, J., Kontis, K., Rengarajan, S., Evans, D., Milne, A. & McIntyre, S., 25 Sep 2017, 68th Proceedings of the International Astronautical Congress. Adelaide, South Australia, 14 p. IAC-17-D2.7.12

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Conceptual design
Orbits
Satellites
Aircraft carriers
Launch vehicles

Configurational optimizer of combined cycle propulsion using genetic programming

Mogavero, A., 13 Feb 2017, 2016 IEEE Symposium Series on Computational Intelligence, (SSCI). Piscataway: Institute of Electrical and Electronics Engineers Inc., 7850102

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Genetic programming
Conceptual Design
Conceptual design
Genetic Programming
Propulsion

Consideration of weld distortion throughout the identification of fatigue curve parameters using mean stress correction

Gorash, Y., Zhou, X., Comlekci, T., Mackenzie, D. & Bayyouk, J., 30 Jun 2017, FATIGUE 2017: Proceedings of the 7th Engineering Integrity Society International Conference on Durability & Fatigue. Bailey, P., Berto, F., Cawte, E. R., Roberts, P., Whittaker, M. T. & Yates, J. R. (eds.). Rutland, p. 366-377 11 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Welds
Fatigue of materials
Numerical methods
Identification (control systems)
Steel

Delamination detection and growth assessment in composite laminated beams through data-driven vibration structural health monitoring

García, D., Trendafilova, I. & Inman, D. J., 19 May 2017, 14th International Conference on Engineering Structural Integrity Assessment (ESIA14). Warrington

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Structural health monitoring
Laminated composites
Delamination
Spectrum analysis
Sensors

Dynamic exergy analysis for the built environment: fixed or variable reference?

Bonetti, V., 8 Jun 2017, Proceedings of the 9th Exergy, Energy and Environment Symposium: 14-17 May 2017, Split, Croatia. Nižetić, S., Šolić, P. & Milanović, Ž. (eds.). Split, Croatia, p. 924-939 16 p. 70

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Exergy
Water tanks
Dynamic analysis
Thermodynamics

Engineering procedure for positive displacement pump performance analysis based on 1D and 3D CFD commercial codes

Josifovic, A., Stickland, M., Iannetti, A. & Corney, J., 30 Jul 2017, Proceedings of the ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. New York, NY, 10 p. 67758

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Pump
Performance Analysis
Computational fluid dynamics
Pumps
Engineering
1 Citation (Scopus)

Finite-element formulation of a Jacobian-free solver for supersonic viscous flows on hybrid grids

Gao, S., Habashi, W. G., Fossati, M., Isola, D. & Baruzzi, G. S., 5 Jan 2017, 55th AIAA Aerospace Sciences Meeting. Grapevine, Texas, p. 1-28 28 p. (AIAA SciTech Forum).

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Viscous flow
Mach number
Supersonic flow
Newton-Raphson method
Linear systems

Implementation of plasticity model for a steel with mixed cyclic softening and hardening and its application to fatigue assessments

Okorokov, V., Comlekci, T., MacKenzie, D., van Rijswick, R. & Gorash, Y., 30 Jun 2017, Fatigue 2017 Proceedings of the 7th Engineering Integrity Society International Conference on Durability & Fatigue: Downing College, Cambridge, UK, 3-5 July 2017. Bailey, P., Berto, F., Cawte, E. R., Roberts, P., Whittaker, M. T. & Yates, J. R. (eds.). Rutland, UK, p. 72-81 10 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Plasticity
Hardening
Fatigue of materials
Compressive stress
Steel
1 Citation (Scopus)

Integrating life cycle assessment of space systems into the concurrent design process

Wilson, A. R. & Vasile, M., 27 Sep 2017, 68th International Astronautical Congress: Unlocking imagination, fostering innovation and strengthening security. Paris, 13 p. IAC-17-D1.4A.9

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Life cycle
Environmental impact
Solar power satellites
Satellites
Environmental management
1 Citation (Scopus)

New approaches to quantifying tensile strength variability and size effects in unidirectional composites

Wisnom, M. R., Cantera, M. A., Czél, G. & Jalalvand, M., 25 Oct 2017, 32nd Technical Conference of the American Society for Composites 2017. Pipes, R. B., Yu, W. & Goodsell, J. (eds.). Vol. 4. p. 2902-2909 8 p. 375

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Tensile strength
Carbon
Composite materials
Weibull distribution
Glass

New heuristics for multi-objective worst-case optimization in evidence-based robust design

Ortega, C. & Vasile, M., 5 Jul 2017, 2017 IEEE Congress on Evolutionary Computation (CEC). Piscataway, N.J.: Institute of Electrical and Electronics Engineers Inc., p. 1519-1526 8 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Distribution functions
Costs
Uncertainty

Novel piecewise trajectory shaping in Hill's canonical variables

Greco, C. & Vasile, M., 28 Sep 2017, 68th International Astronautical Congress (IAC) 2017. Paris, 11 p. IAC–17–C1,6,1,x41322

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Trajectories
Asteroids
Parameterization
Spacecraft
Orbits

Numerical modeling and simulation of supersonic flows in propulsion systems by open-source solvers

Hoste, J. J. O. E., Casseau, V., Fossati, M., Taylor, I. J. & Gollan, R. J., 3 Apr 2017, 21st AIAA International Space Planes and Hypersonics Technologies Conference, Hypersonics 2017. 17 p. 2411

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
supersonic combustion ramjet engines
supersonic flow
Supersonic flow
propulsion
Propulsion

Numerical simulations of the thermocapillary migration of a deformable Newtonian droplet in an Oldroyd-B matrix fluid in stokes flow conditions

Capobianchi, P., Lappa, M. & Oliveira, M. S. N., 19 May 2017, 30th Scottish Fluid Mechanics Meeting: Book of Abstracts. Glasgow, UK: University of Strathclyde, 1 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Fluids
Computer simulation
Thermal gradients
Shear viscosity
Liquids
2 Citations (Scopus)

Optimal trajectory planning for multiple asteroid tour mission by means of an incremental bio-inspired tree search algorithm

Vroom, A., Di Carlo, M., Martin, J. M. R. & Vasile, M., 13 Feb 2017, 2016 IEEE Symposium Series on Computational Intelligence (SSCI). Piscataway, NJ: IEEE, 8 p. 7850108

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Asteroids
Trajectory Planning
Optimal Trajectory
Trees (mathematics)
Tree Algorithms
3 Citations (Scopus)

Partial discharge detection using software defined radio

Mohamed, H., Lazaridis, P., Upton, D., Khan, U., Saeed, B., Jaber, A., Zhang, Y., Mather, P., Vieira, M. F. Q., Barlee, K., Atkinson, D. S. W. & Glover, I. A., 6 Jan 2017, 2016 International Conference for Students on Applied Engineering (ICSAE). Piscataway, NJ: IEEE, p. 373-376 4 p. 7810220

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Partial discharges
Software radio
Electric potential
Insulation
Wireless networks

Predicting the effect of changes to the urban environment on future electrical demand using building simulation and archetype models

Cowie, A., Kelly, N., McGhee, R., Samuel, A., Higgins, C. A. & Peat, W., 3 Mar 2017, (Accepted/In press) Building Simulation 2017: The 15th Biennial Conference of the International Building Performance Simulation Association (IBPSA). [Vancouver, B.C.], 10 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Electric vehicles
Electric power distribution
Energy efficiency
Time series
Loads (forces)

Return and abort trajectory optimisation for reusable launch vehicles

Toso, F. & Maddock, C., 2 Mar 2017, Proceedings of the 21st AIAA International Space Planes and Hypersonic Systems and Technologies Conference. Reston, VA, 11 p. AIAA 2017-2250. (International Space Planes and Hypersonic Systems and Technologies Conferences).

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Launch vehicles
Trajectories
Recovery
1 Citation (Scopus)

Stress linearization concepts and restrictions in elastic design by analysis

MacKenzie, D., 21 Mar 2017, (Accepted/In press) ASME 2017 Pressure Vessels and Piping Conference (PVP2017). New York, 8 p. PVP2017-65678

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Linearization
Load limits
Stress analysis
Pressure vessels
Stress concentration

Surface roughness 3D modelling and its association with leak tightness for a metal-to-metal contacting surface

Anwar, A. A., Dempster, W. (ed.), Gorash, Y. (ed.) & Nash, D. (ed.), 17 Jul 2017, ASME 2017 Pressure Vessels and Piping Conference: Volume 4: Fluid-Structure Interaction. New York, 7 p. PVP2017-65404

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Surface roughness
Metals
Computational fluid dynamics
Roughness measurement
Pressure relief valves

Taxonomy and analysis of issues facing post mission disposal concept

Kerr, E., Macdonald, M. & Voigt, P., 29 Sep 2017, 68th International Astronautical Congress, IAC 2017: Unlocking Imagination, Fostering Innovation and Strengthening Security. Paris, France, Vol. 6. p. 3735-3744 10 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
taxonomy
disposal
Taxonomies
Spacecraft
spacecraft

Thermal Marangoni migration of droplets in an Oldroyd-B fluid under creeping flow conditions

Capobianchi, P., Lappa, M. & Oliveira, M., 12 Feb 2017, The Society of Rheology: 88th Annual Meeting Program and Abstracts. Co, A. (ed.). Orono, ME., 1 p. NF1

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Elasticity
Computational fluid dynamics
Fluids
Hot Temperature

Thermoacoustic effects in high-speed compressible transitional and turbulent boundary layers

Ritos, K., Kokkinakis, I. W., Drikakis, D. & Spottswood, S. M., 9 Jan 2017, 55th AIAA Aerospace Sciences Meeting. Reston, VA, 14 p. 2017-0745

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Thermoacoustics
Boundary layers
Acoustics
Supersonic flow
Compressible flow
2 Citations (Scopus)

Vehicle and mission design of a future small payload launcher

Maddock, C. A., Toso, F., Ricciardi, L., Mogavero, A., Lo, K. H., Rengarajan, S., Kontis, K., Milne, A., Merrifield, J., Evans, D., West, M. & McIntyre, S., 2 Mar 2017, 21st AIAA International Space Planes and Hypersonic Systems and Technologies Conference. Reston, VA, 21 p. AIAA 2017-2224. (International Space Planes and Hypersonic Systems and Technologies Conferences).

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Aircraft carriers
Launch vehicles
Conceptual design
Orbits
Earth (planet)
2016
3 Citations (Scopus)

A comparative study of simulated and experimental results for an extruding elastomeric component

Connolly, S., Gorash, Y. & Bickley, A., 23 Feb 2016, 23rd International Conference on Fluid Sealing 2016. Bickley, A. (ed.). Cranfield, p. 31-41 11 p.

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

Open Access
File
Extrusion
Compression testing
Rubber
Boundary conditions
Finite element method