This paper proposes a stiffness method based structural analysis algorithm for geometrically non-linear structures. In this study, the applied load on the joints has been discretized to a sequence of a few loadings applied. Each loading step produces incremental external nodal displacements, which are added to the corresponding coordinates to get a new geometrical shape of the structure. This process is iteratively repeated until the sum of the loading of all iterations matches the total initial applied loading. The size of the increments affects the technique’s accuracy, subsequently affecting the number of iterations. The configuration of non-linear geometrical structures is vital in the work; a slight change of the coordinates makes a considerable variation of nodal displacements. In this paper, three pin-jointed assemblies and a cantilever beam have been examined using the proposed technique; significantly reasonable outcomes emerged, compared to the non-linear approaches, such as Dynamic Relaxation Method (DRM) and Non-linear approach by Kwan. In a numerical sense, the dissimilarity between the results of the conventional Stiffness Matrix (SM) method and the non-linear method is about 228%, while the maximum discrepancy between the proposed approach and the non-linear methods is just above 15%.
Cable arch stayed bridges are one type of tensile structures, and there are increasingly such structures constructed. Their performance relies on how they are designed. This type of structures can suffer big deflections under load, in this situation the displacements may need to be reduced. Sometimes, it may be necessary to control internal force of a specific cable so the cable force remains within the desired limit. More study need to be done to develop the techniques that are available for such adjustments. This paper deals with theoretical and experimental adjusting of two physical models, and the linear and nonlinear geometrical behavior of cable (arch) stayed bridges. It was concluded that the techniques of adjustment were practical and efficient to reduce, eliminate shape distortion, and control internal bar force of both structures. For structures that behave linearly, it is easier to get the target (displacement or force), but for non-linear structures one iteration of adjustments was not enough to get the displacement target. Through the techniques of the internal bar force adjustment, the amount of force can be reduced even to the zero, e.g. in case of replacing damaged members.
Shape adjustment and stress control can be considered as one of the effective parameters in prestressed cable structures since such structures are widely constructed nowadays due to their characteristics. The assembly errors and applied loads hugely affect the cables’ nodal positions and stress due to their delicacy. The former could disturb the shape, which affects the appearance and the function of the structure. In contrast, the latter may increase the stress in some cables above the upper limit or induce slack in some others. Accordingly, a technique has been proposed that combined fmincon optimization that relies on four different algorithms with a controlling approach based on the force method. The presented method aims to minimize the total amount of actuation and miniaturize the number of actuators. The targets of previously confirmed techniques can be obtained with less actuation and fewer actuators by using the current technique. Based on the verified examples, the advantage of the current approach over the quoted methods is up to 55% and 37% in terms of the number of actuators and the total amount of actuation, respectively.
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