Two-node curved inverse finite element formulations based on exact strain-displacement solution

The inverse finite element method (iFEM) is an efficient algorithm developed for real-time monitoring of structures equipped by a network of strain sensors. The inverse element for modeling curved beams was previously developed using an approximate solution based on independently interpolated displacement components. In this study, a new formulation is proposed by the development of a least-squares variational principle using the kinematic framework of the curved beam theory. The library of existing iFEM-based elements is expanded by introducing three different inverse curved elements named iCB3, iCB4 and iCB5 respectively. This new formulation has been developed considering the exact solution of the curved beam theory that corresponds to the membrane-bending coupling and the explicit statement of the rigid-body motions. The three inverse elements, which require three, four and five measurement points respectively, extend the practical utility of iFEM for shape sensing analysis of curved structures according to the minimum available quantity of strain sensors. The effectiveness and higher accuracy of the iCB/iFEM methodology compared to other solutions present in literature are demonstrated considering numerical studies on curved beams under static transverse force and distributed loading conditions. For these problems, the effect of strain measurements error, number of sensors and discretization refinement on the solution accuracy is evaluated.