A Trigonometry Based Linear Form- Finding Method For Irregular Multi-Layer Prism Tensegrity - Moghaddas, Mohammad (2017)
Prism tensegrity is one type of tensegrity system, is suitable for possible application in the field of civil and architectural engineering. The form-finding process of an irregular prism tensegrity is normally nonlinear due to the reason that the number of force equilibrium equations are less than the number of unknown parameters. The review of previously proposed methods of form-finding shows that none of them is practical for the form-finding of irregular prism tensegrity with a large number of members. Therefore, this study was carried out with the aim of presenting a practical form-finding method which is fast, accurate and able to satisfy designers’ requirements. Moreover, self-weight and external loads are known to affect final configuration of prism tensegrity which is neglected in the form-finding analysis. Prism tensegrities applied in the field of civil and architectural engineering are subjected to specified practical requirement of structure displacement and member deflection. Hence, this study also aimed at investigating the effect of initial stress and configuration on deformation of prism tensegrity under self-weight. In this research, trigonometry relation is used to connect length relation condition and force equilibrium equations in order to establish a linear approach of form-finding called trigonometry approach. The novel trigonometry approach for form-finding of irregular single layer prism tensegrity is firstly introduced. Then, the concept of connection and conjunction polygons necessary for form-finding of multi-layer prism tensegrity are presented, where a connection polygon is used to connect single layer prism tensegrities to form a multi-layer prism tensegrity. The established trigonometry approach for the form- finding of the single layer prism tensegrity is extended to form-finding of multi-layer prism tensegrity. A computational Excel tool for form-finding is developed based on the trigonometry approach. Eight numerical examples for irregular single layer and ten numerical examples for irregular multi-layer prism tensegrity were designed successfully using the developed computational Excel tool. In all of these examples, new configurations of prism tensegrities are presented for the first time and most of them are unsolvable by other available approaches. Nine numerical examples with variable configurations were designed by using the trigonometry approach proposed in this study and analysed using the Robot Structural Analysis. The self-weight and the external loads are applied on the models as distributed and nodal loads, respectively. The effect of initial stress and configuration on deformation of practically designed prism tensegrity under self-weight is investigated. Geometrical nonlinear analysis was carried out on nine different regular and irregular examples with different base polygon, number of layer and configuration under four different sets of initial member force and four different member cross sections. From the results of analysis, effects of number of side of the base polygon, number of layers, configuration, initial member force and member cross section of prism tensegrity on maximum joint displacement, member deflection, tensile and compression stress of members are obtained.