A Real-Time Deformation Displacement Measurement Method for Timoshenko Beams With Multiple Singularities

For the problem of Timoshenko beams with multiple singularities in presence of discontinuities in the stiffness or curvature, the traditional inverse finite element method (iFEM) adopts the piecewise method to measure the real-time deformed displacements. However, as the number of singularity increases, the dimension of the strain–displacement matrix and the required number of strain sensors dramatically increases. In order to solve this problem, a novel deformation measurement approach is presented. Initially, distribution theory is employed to describe the rigidities of beams with multiple singularities involving axial rigidity, shear rigidity, torsional rigidity, and bending rigidity, and the corresponding constitutive formulations are presented. Then, considering displacement function presenting peak at these singularities, the isogeometric analysis approach is proposed to be used as basis functions to describe the displacement fields. Next, the strain–tensor transformation relations suitable for discontinuous beam structure are presented. Finally, a straight beam with circular cross sections is used as a case to verify the accuracy and effectiveness of the presented measurement method. The numerical results from simulation analysis and experiment tests demonstrate the superior accuracy capability and potential applicability of presented measurement approach for performing accurate shape prediction of the beam with multiple singularities.