surface fitting approach for tensile membranes design - Tecnun

Other details, regarding surface fitting parameters, material properties, applied forces, visualization ofnormal vectors, can be defined.The external distributed forces applied can also vary, and the new membrane shape is calculated inreal-time. Figure 9 shows several membrane shapes obtained for different external applied loads,without changing the boundary conditions.5 ConclusionsFigure 9.- Load Sequence, using the same boundary conditionsThe proposed combined method complies with the requirements given for the design process. It is quitesimple to generate and modify shapes in real-time, assign material, loads or modify the boundaryconditions of the model. A non specialized designer can get used to the application in a short time.As said before, membrane structures shapes are easy to represent using parametric surfaces, and notmany points are needed to obtain a smooth surface. Geometry of common membranes structures is notsubject to important changes in curvature or local applied loads as shown in figure 7.Finally, we should highlight again the existing compromise between computation time and precisionneeded. The designer should have enough criteria to decide in which cases each is required.References[SHE74] H.J. Sheck, (1974) “The force density method for form-finding and computations of generalnetworks,Mahadevan”, Computer Methods in Applied. Mechanics and Engineering, p.115,134.[MAU98] B. Maurin & R. Motro (1998) “The surface stress density method as a form-finding tool fortensile membranes”, Engineering Structures, Vol 20, nº8, p.712-719.[BAR97] M.R. Barnes (1999) “Form Finding and Analysis of Tension Structures by DinamicRelaxation”, International Journal of Space Structures, Vol 14, nº2.[ROG89] D.F.Rogers, N.G.Fog (1989) “Constrained B-spline curve and surface fitting”, ComputerAided Design, Vol 21, No 10, p.641-648[PIE00] L.Piegl, W. Tiller. (2000) “Curve Interpolation with Arbitrary End Derivatives”, Engineeringwith Computers, Vol 16, p.73-79[ROG01] D.F.Rogers (2001) “An Introduction to Nurbs”, Academic Press.[PIE97] L.Piegl, W. Tiller. (1997) “The Nurbs Book”. Second Edition. Springer-Verlag, New York[PIE91] L.Piegl. (1991) “On Nurbs: A survey”, IEEE Computer Graphics & Applications, Vol 11,No 1, p.55-71