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An effective form-finding method for form-fixed spatial network structures is presented in this paper. The adaptive formfinding method is introduced along with the example of designing an ellipsoidal network dome with bar length variations being as small as possible. A typical spherical geodesic network is selected as an initial state, having bar lengths in a limit group number. Next, this network is transformed into the ellipsoidal shape as desired by applying compressions on bars according to the bar length variations caused by transformation. Afterwards, the dynamic relaxation method is employed to explicitly integrate the node positions by applying residual forces. During the form-finding process, the boundary condition of constraining nodes on the ellipsoid surface is innovatively considered as reactions on the normal direction of the surface at node positions, which are balanced with the components of the nodal forces in a reverse direction induced by compressions on bars. The node positions are also corrected according to the fixed-form condition in each explicit iteration step. In the serial results of time history, the optimal solution is found from a time history of states by properly choosing convergence criteria, and the presented form-finding procedure is proved to be applicable for form-fixed problems.

This paper investigates the application and reliability of using high-order mode shape derivatives especially, the fourth derivative in damage detection of plate-like structures. Numerical analyses have been carried out for low-and high-order mode shapes of simply supported and cantilever steel plate models. Six scenarios of damages are studied for plate models to represent different damage characteristics. The influence of artificial noise on the damage identification using changes in fourth derivative of mode shapes has been investigated. Based on the numerical studies, it is shown that the fourth derivative of mode shape is promising in detecting and locating structural damage in plate-like structures since it is localized at the damage locations even for a small amount of damage using only one of the mode shapes. Both low-and high-order mode shapes give successful results. Also, damage indices of the fourth derivatives give smoother localization and consequently better damage identification than those of curvature of mode shapes. Furthermore, using high-order modes (which can be measured by advanced sensors) does not improve the results of damage identification using the fourth derivative. Unfortunately, damage detection using changes in fourth derivative of mode shapes is sensitive to measurement noise.

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