The paper presents a study of minimum energy forms of prestressed cable nets and membranes. Attention is directed towards accuracy and efficiency of numerical form-finding of stable minimal surfaces represented by soap-film models. The models are used to verify the correctness of the numerical approach. Within the numerical algorithm, which is based on a Dynamic Relaxation method, the performance of linear and triangular types of surface discretisations is examined.
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References
1.
MattheckC., ‘Why they grow, how they grow: the mechanics of trees’, AB Academic Publishers, Arboricultural Journal14, 1990, pp. 1–77.
2.
HildebrantS., and TrombaA., ‘Mathematics and optimal form’, Scientific American Library1985.
3.
IsenbergC., ‘The Science of soap films and soap bubbles’, Tieto Ltd.1978.
4.
OttoF., and TrostelR., ‘Zugbeanspruchte Konstruktionen’, M.I.T. Press, Cambridge1 (241) 1962.
5.
BachK., BurkhardtB. and OttoF., ‘Forming bubbles’, IL (Institute of Lightweight Structures, Stuttgart) Publication No. 18, 1987.
6.
BarnesM., ‘Non-linear numerical solution methods for static and dynamic relaxation’, IL Publication No. 15, 1982, pp. 150–166.
7.
LewisW.J., ., ‘Dynamic relaxation analysis of the non-linear static response of pretensioned cable roofs’, Computers and Structures, 18, No. 6, 1984, pp. 989–997.
8.
GrundigL., ‘The force-density approach and numerical methods for the calculation of networks’, Proceedings 3rd Int. Symposium Weitgespannte Flachentragwerke, University of Stuttgart, 1985, pp. 99–105.
9.
BuchholdtH.A., An introduction to cable roof structures’, Cambridge University Press, 1985.
10.
LewisW.J., ‘The efficiency of numerical methods for the analysis of prestressed nets and pin-jointed frame structures’, Computers & Structures, 33, No. 3, 1989, pp. 791–800.
11.
WakefieldD.S., ‘Pretensioned networks supported by compression arches’, PhD thesis, City University, April1980.
12.
IronsB., and AhmadS., ‘Techniques of finite elements’, Ellis Horwood Limited, 1980.
13.
LewisW.J., and GoslingP.D., ‘Computer modelling of stable minimal surfaces’, Research Report CE32, Department of Engineering, University of Warwick, 1990.
14.
AngelE., ‘Computer graphics’, Addison-Wesley, 1990, pp. 394–425.
15.
GoslingP.D., and LewisW.J., ‘Application of constant strain triangular membrane elements to the investigation of minimal energy forms’, Research Report CE36, Department of Engineering, University of Warwick, 1991.