A computational compensation method for fabric panels of tensioned membrane structures using a shape optimization method based on gradientless algorithms. (1st May 2017) - D. Dinh, T.; Rezaei, A.; Linthout, T.; Mollaert, M.; Van Hemelrijck, D.; Van Paepegem, W.
Abstract: Tensioned fabric membrane structures, in which a coated fabric material is used as both cladding and supporting structure, are classified as unconventional structures and demand a dedicated design method. In this paper, we propose a method to combine different stages in design and analysis of these structures within the shape optimization framework. The proposed method facilitates the incorporation of various sources of nonlinearities in the analysis of tensioned membrane structures. Especially, the amount of fabric panels compensation when using simple material model for the coated fabric, i.e., linear orthotropic elasticity, as is widely used in practice, is presented. The novelty of the proposed method lies on the postulation of a stress-free 3-D intermediate configuration, which is built from flat fabric panels. The goal is to find an optimum shape of this 3-D intermediate configuration such that the stress distribution in the resulting structure, which is formed by deforming the 3-D intermediate configuration, remains at desired levels. A nonlinear finite element analysis is employed to identify these stress fields in the resulting structures. In this analysis, material and geometrical nonlinearities are taken into account. Moreover, the nonlinear kinematical interaction between the boundary cables and the membrane is also considered. Hence the stress fields on the resulting structures are expected to be reliable and close to the physical ones. In this work, different gradientless optimization algorithms, viz., genetic algorithm, pattern search, and Bayesian, are considered. The obtained results show that the stress levels in the resulting structures obtained from the proposed method are close to the desired ones, and the Bayesian optimization algorithm has the best performance among the considered algorithms.