Rijk de Rooij PhD Researcher Stanford University Department of Mechanical Engineering
Mechanics and Computation Group Stanford, CA 94305
U.S.A. rderooij@stanford.edu biomechanics.stanford.edu
Structural Modeling of Thin Membranes for Wind Energy Systems
Rijk de Rooij, Mostafa Abdalla
Faculty of Aerospace Engineering, Delft University of Technology Membrane structures have a rich history of use across
many disciplines and are widely used in aerospace and structural engineering applications. More recently, thin membranes are often applied in lighter-than-air wind en-ergy systems, such as in [1]. These membranes are es-pecially attractive to airborne wind energy systems for their low mass to surface ratio and their ability to take complex shapes. Although membranes can carry tensile loads very well, they tend to wrinkle under the slightest compressive load. These wrinkles affect the load carry-ing capabilities of the membrane, and thus the structural performance of the entire airborne system. It is there-fore important to accurately model the stress distribution in the membrane to assess its load carrying capabilities. To model the structural behaviour of wrinkles in a mem-brane, the mesh size in e.g. a finite element model needs to be at least as small as the wrinkles to detect them. Considering the small scale of the wrinkles with respect to the wind energy system as a whole, this requirement often results in unacceptably high computational costs.
In this work, we approached this problem by modelling the membrane wrinkles as a continuous in-plane contrac-tion of the membrane, using an interior-point implemen-tation [3]. This approach allows us to use a mesh size that is much greater than the size of individual wrinkles. The efficiency and robustness of the proposed method was proven mathematically and verified numerically. We val-idated our method by modelling an inflated, pressurized beam under applied bending loading and comparing the force-displacement curve with experimental data. This validation, together with the efficiency, robustness, and cost reduction of our method, show its great poten-tial for the structural modelling of large membrane struc-tures such as airborne wind energy systems.
References:
[1] Altaeros Energies. http://www.altaerosenergies.com/. Accessed 25 March 2015.
[2] KitePower. http://www.kitepower.eu/. Accessed 25 March 2015. [3] Rooij R. de, Abdalla M. M.: A finite element interior-point imple-mentation of tension field theory. Computers and Structures, Vol. 151, pp. 30–41 (2015)
