A deformation measurement method for discontinuous Timoshenko beams

Based on the frame of the traditional inverse finite element method (iFEM) with global continuity, an enhanced IGA-iFEM method for handling the real-time shape sensing of beam structures with multiple stiffeners is proposed in this study. This method compensates for the defect of existing iFEM in engineering applications which segmental monitors displacement and strain in discontinuous structures. The number of strain sensors required in classical iFEM would greatly increase due to the changes in material properties. In this study, discrete real-time experimental strains were collected and processed by the enhanced iFEM algorithm, and finally, full-field displacement and strain monitoring were carried out for discontinuous structures. To this end, the distribution theory and sign function are used to reconstruct the neutral axial strain field, and the corresponding constitutive formulations are given. Meanwhile considering the abrupt change of strain field at the stiffener, the IGA analysis is used as a shape function to describe the integral beam element. Furthermore, the univariate equation is used to simplify the equation of motion of the Timoshenko beam. Finally, an experimental platform for UAV wing is built to verify the effectiveness of the above method on discontinuous beam deformation reconstruction. Overall, compared with the existing iFEM, the significant advantage of this method is that the number of sensors is greatly reduced under the premise of ensuring accuracy and greatly expanding the engineering application field of iFEM.