Inverse beam-shell elements for full-field displacement reconstruction of stiffened panel structures

To obtain the displacement field of stiffened panel structures is very important for the online monitoring of aircraft or aerospace vehicles, etc. New inverse beam-shell elements are proposed in this study for the full-field displacement reconstruction of stiffened panels via strain measured by shell parts and rib parts simultaneously. The shell and rib parts in the stiffened panel are modeled by inverse shell and beam elements respectively constructed by Mindlin's plate theory and Timoshenko beam theory. To avoid the shear locking, a new inverse beam element with a virtual middle node is introduced. Constraints between the inverse shell and beam elements are given to guarantee the consistency of deformation and two typical inverse beam-shell elements are proposed. A sub-area division scheme is introduced which enables the proposed inverse elements for reconstructing the displacement field of 3D structures composed of multiple stiffened panels. Two numerical examples including a cantilever stiffened panel and a two-edge clamped 3D stiffened panel are given to demonstrate the effectiveness of the newly proposed inverse beam-shell element and the sub-area division scheme. An element-selection scheme for the arrangement of strain gauges is also proposed to reduce the measurement data used. Results show the new inverse beam-shell elements can reconstruct displacement fields accurately and the sub-area division scheme introduced guarantees the accuracy of the reconstructed displacement fields of 3D panels even when a relatively small number of strain gauges are used.