Structural modelling of deformable screens for large door openings
Keywords:MISG, mathematical modelling, deformable, screen, membrane
AbstractThe mathematical modelling of deformable, permeable screen doors was explored to assess their behaviour under wind loading. A load-response model was proposed whereby the wind load was modelled using a simplified approach that allowed it to be approximated as a uniformly distributed pressure load with empirical modification factors applied to relate it to the real case of a door on a building. Several approaches were adopted to model the mechanical behaviour of the door system in response to load, including discrete models based on mass-spring systems, continuum models based on the membrane equations (including tension modulation in some cases), and computational models using finite element packages. The primary aim of the work was to determine the distribution of wind load to the door's supporting `tabs' and estimate a failure wind speed. The mass-spring model and the membrane models without tension modulation both generated unrealistic deflection magnitudes in response to wind load, but could be calibrated in future work, and then used to obtain an estimate of the total force on the tabs. A tension-modulated version of the membrane model performed better with regards to deflected shape and magnitude, but time constraints meant that the load on the tabs was not calculated. Preliminary validation experiments were undertaken and deflected shape and magnitude were successfully measured in response to given wind speeds. References
- Standards Australia. AS/NZS1170.2–-Structural design actions part 2: Wind actions, 2011.
- F. Avanzini and R. Maronga. A modular physically based approach to the sound synthesis of membrane percussion instruments. IEEE Transactions on Audio, Speech, and Language Processing, 18(4):891–902, 2010. doi:10.1109/TASL.2009.2036903
- B. Bank. Energy-based synthesis of tension modulation in strings. In Proceedings of the 12th International Conference on Digital Audio Effects (DAFx-09), 2009. http://dafx09.como.polimi.it/proceedings/papers/paper_76.pdf
- Bert Blocken. 50 years of computational wind engineering: Past, present and future. Journal of Wind Engineering and Industrial Aerodynamics, 129(0):69–102, 2014. doi:10.1016/j.jweia.2014.03.008
- Demetres Briassoulis, Antonis Mistriotis, and Anastasios Giannoulis. Wind forces on porous elevated panels. Journal of Wind Engineering and Industrial Aerodynamics, 98(12):919–928, 2010. doi:10.1016/j.jweia.2010.09.006
- John Cheung and William Melbourne. Wind loading on porous cladding. In 9th Australasian fluid mechanics conference, 1986. http://people.eng.unimelb.edu.au/imarusic/proceedings/9/CheungMelbourne.pdf
- John Holmes. Wind Loading of Structures. Spon Press, 2001.
- P. D. Howell, G. Kozyreff, and J. R. Ockendon. Applied Solid Mechanics. Cambridge University Press, 2009.
- C.W Letchford. Wind loads on rectangular signboards and hoardings. Journal of Wind Engineering and Industrial Aerodynamics, 89(2):135–151, 2001. doi:10.1016/S0167-6105(00)00068-4
- Wojciech Okrasinski and \T1\L ukasz Plociniczak. A nonlinear mathematical model of the corneal shape. Nonlinear Analysis: Real World Applications, 13(3):1498–1505, 2012. doi:10.1016/j.nonrwa.2011.11.014
- D. W. Oplinger. Frequency response of a nonlienar stretched string. Journal of the Acoustical Society of America, 32(12):1529–1538, 1960. doi:10.1121/1.1907948
- Xavier Provot. Deformation constraints in a mass-spring model to describe rigid cloth behaviour. In Graphics interface, pages 147–147. Canadian Information Processing Society, 1995. http://kucg.korea.ac.kr/education/2005/CSCE352/paper/provot95.pdf
- P.J Richards and M Robinson. Wind loads on porous structures. Journal of Wind Engineering and Industrial Aerodynamics, 83(13):455–465, 1999. doi:10.1016/S0167-6105(99)00093-8
- A.P. Robertson, Ph. Roux, J. Gratraud, G. Scarascia, S. Castellano, M. Dufresne de Virel, and P. Palier. Wind pressures on permeably and impermeably-clad structures. Journal of Wind Engineering and Industrial Aerodynamics, 90(45):461–474, 2002. Bluff Body Aerodynamics and Applications. doi:10.1016/S0167-6105(01)00210-0
- T. Tolonen, V. Valimaki, and M. Karjalainen. Modeling of tension modulation nonlinearity in plucked strings. IEEE Transactions on Speech and Audio Processing, 8(3):300–310, 2000. doi:10.1109/89.841212
Proceedings of the Mathematics in Industry Study Group