Form-finding and patterning of fabric structures using shape optimization techniques Thomas Linthout Supervisors: Prof. dr. ir. Wim Van Paepegem, Dr. Ali Rezaei Counsellor: Tien Dung Dinh Master's dissertation submitted in order to obtain the academic degree of Master of Science in Civil Engineering Department of Materials Science and Engineering Chair: Prof. dr. ir. Joris Degrieck Faculty of Engineering and Architecture Academic year 2015-2016 Form-finding and patterning of fabric structures using shape optimization techniques Thomas Linthout Supervisors: Prof. dr. ir. Wim Van Paepegem, Dr. Ali Rezaei Counsellor: Tien Dung Dinh Master's dissertation submitted in order to obtain the academic degree of Master of Science in Civil Engineering Department of Materials Science and Engineering Chair: Prof. dr. ir. Joris Degrieck Faculty of Engineering and Architecture Academic year 2015-2016 Acknowledgements \Rome wasn't built in a day", and similarly, this dissertation is the result of a year of hard work and research. However, the completion of this dissertation would not have been possible without the advice and support of some people who I would like to thank. I would like to thank professor Van Paepegem for his efforts as supervisor, and for intro- ducing me to the wonderful world of optimization and tensile architecture. I am grateful for the advice of my counselor Tien Dung Dinh. Whenever I had a question about membrane materials, about optimization, or when a software bug slipped past my eye, he was always ready to assist. Special thanks to Ali Rezaei for helping me out numerous times. I am thankful for my friends, who provided distraction whenever I couldn't see the forest for the trees. And finally, I would like to thank my parents, for supporting me throughout my studies. Thomas Linthout, June 2016 Permission \The author gives permission to make this master dissertation available for consultation and to copy parts of this master dissertation for personal use. In the case of any other use, the limitations of the copyright law have to be respected, in particular with regard to the obligation to state expressly the source when quoting results from this master dissertation" Thomas Linthout, June 2016 Form-finding and patterning of fabric structures using shape optimization techniques by Thomas Linthout Master's dissertation submitted in order to obtain the academic degree of Master of Science in Civil Engineering Academic year 2015{2016 Supervisors: Prof. Dr. Ir. W. Van Paepegem, Dr. A. Rezaei Counsellor: M. Sc. T.D. Dinh Faculty of Engineering and Architecture Ghent University Department of Materials Science and Engineering Abstract Fabric materials used for tent structures are form-active, behave non-linearly and anisotrop- ically, and can only transfer loads through tension. Due to this, designing and modelling such structures is quite complicated and different from traditional structures. The so- called conventional method is the most frequently used design method for designing tensile structures. In this method, a form-finding is carried out, followed by the development of a cutting pattern on the surface. Another design method is the integrated method, in which flat panels are iteratively generated, assembled and subjected to tension, until a structure with a permissible stress distribution is reached. This thesis is a continuation on the method proposed by Dinh et al., based on the integrated approach. In this method, the shape of the assembled panels is iteratively adjusted until the final structure has a permissible stress distribution. It is assumed that the shape of the assembled panels, also called the intermediate configuration, is stress-free. Expressing the shape of the assembled panels by parameters, a SolidWorks model is created, which is then imported in Abaqus. After calculation, the stresses in the membrane, along with the forces in the boundary cables is compared to a specified stress and cable force, and the parameters are adjusted. This process is repeated until the stress and force deviations are minimal. Keywords Tensile architecture, shape optimization, fabric materials, Bayesian optimization, optimiza- tion Form-finding and patterning of fabric structures using shape optimization techniques Thomas Linthout Supervisors: Prof. Dr. Ir. Wim Van Paepegem, Dr. Ali Rezaei, M. Sc. Tien Dung Dinh Abstract Multiple methods exist to design fabric does not correctly represent the material. A material structures. The most commonly used method is the so- model was proposed by Dinh et al.[1], taking into called conventional method, which has some deficiencies. account these characteristics. However, time- However, an accurate method, taking into accounts the dependent behavior is not included in this model. This material characteristics of the membrane is non-existent. model is further referred to as the fabric plasticity In this thesis, a new method is proposed, taking into account the correct loading path the material follows. model. The proposed method assumes that the assembled panels form a similar shape as the final structure, albeit with a III. DESIGN METHODS smaller curvature. Using shape optimization, the shape of this intermediate shape is determined in such a way A. Conventional method that the stress distribution in the final structure is permissible. The most frequently used method in the industry is the so-called conventional method. The method Keywords Tensile architecture, shape optimization, consists of a form-finding step, in which a fictitious fabric materials, Bayesian optimization, optimization membrane material is subject to a prestress, resulting in an equilibrium shape. This shape is then subjected I. INTRODUCTION to a structural analysis, using the actual material For over 50 years, coated woven fabrics have been characteristics, in order to assess the impact of used in modern lightweight structures. However, clear environmental loads such as wind and snow loads. guidelines for such architecture do not exist, and their Finally, a cutting pattern is generated on the design is mainly reliant on experience. Fabric prestressed shape. This cutting pattern is then materials used for tent structures are form-active, flattened, resulting in flat panels. In this step, the behave non-linearly and anisotropically, and can only deformations caused by this flattening operation are transfer loads through tension. neglected. The shape of the stress-free panels is then The aim of this thesis is to propose a new method to determined by unloading these panels. Due to the non- design tensile structures, taking into account the linear behavior of the membrane and the difference characteristics of the material and the loading path it between the stress-strain curves for loading and follows. To this extent, shape optimization methods unloading, this is not straightforward. As such, a may provide an answer. linear orthotropic material model is often used in this step, and the shape of the panels is adjusted to II. MEMBRANE MATERIALS compensate for the inaccuracy of the model. Textile fabrics used for tensile structures are a Due to this compensation, and because deformations combination of a system of orthogonally woven yarns occurring during flattening are ignored, this method is and a coating applied to withstand weathering and less than optimal. ageing. The coating is applied continuously, by applying the liquid coating while the fabric is moving B. Integrated approach under a knife. During this process, the fabric moved While the conventional method starts with a through drums by pulling the warp fibres. Due to this, prestressed shape, the integrated approach includes the the warp fibres are more stretched than the fill fibres, influence of the cutting pattern in the form-finding and which will have an impact on the behavior of the analysis. Cutting patterns are iteratively adjusted such material. that, after applying the deformations resulting in the As a result of the production process and the final shape, the structure has a permissible stress- composite action, the fabric has a quite complex distribution, minimizing the difference between the material behaviour. The material behaves design prestress and the actual stress in the membrane. anisotropically, inelastically and nonlinearly. In a study conducted by Dinh et al.[2], a new design Additionally, the material behavior is dependent on method was proposed. This method is a variation of the load ratio between warp and fill threads. As a the integrated approach. In the method, the shape of result, a simple orthotropic elasticity material model the assembled panels is assumed to be flat, and three parameters describing the intermediate shape are The result of this optimization is a certain adjusted until the stress distribution in the final intermediate shape. As this shape consists of fabric construction is permissible. The method proposed in panels assembled together, this shape should be stress- this study is a continuation on this method. free. This assumption can be validated by cutting the three-dimensional intermediate shape into panels, IV. PROPOSED METHOD computationally flatten these panels using Rhino3D’s ‘Squish’ algorithm, and check the deformations. If A. Proposed design method these deformations are small enough to neglect, the In this case study, the proposed method is tested on method is deemed valid, and the panels can correctly a 4 m x 4 m hypar, with a height of 80 cm once assemble the hyperstructure. assembled and tensioned. First, the shape of the adjoined panels is considered. It is assumed that this B. Objective function intermediate stress-free shape will have a similar The objective function is used to convert the results shape of that of the final hypar, albeit with a smaller from the FEM analysis to one value, which is to be height. To describe this intermediate shape, a set of minimized. In order to do this, the average squared five state variables P is used, as seen in Figure 1. deviation from a predefined membrane stress and cable force is calculated. This results in two values, of which a weighted average is taken resulting in one value, which is the value of the objective function, as seen in the formulae below.