Shape sensing of variable cross-section beam using the inverse finite element method and isogeometric analysis

•This paper proposes a new iFEM method for reconstructing displacement field of variable cross-section beam.•Mechanical parameters are linearized, and the new constitutive equations are established.•This paper presents a new approach to approximate and instead of the original displacement field functions. The inverse finite element method (IFEM), which is used to reconstruct the displacement field from the discrete surface strain measurements, is of great significance to the management, control and driving of smart structures. However, the iFEM method based on constant cross-section beam elements proposed in previous works were no longer suitable for variable cross-section beam elements. To solve this problem, this paper proposes a new iFEM method for reconstructing the displacement field of variable cross-section beam based on isogeometric analysis. Firstly, the mechanical parameters of beam section are linearized, including section area, axial rigidity, shear rigidity, torsional rigidity and bending rigidity, and a new constitutive relations are established. Then, adhering to the constitutive equations and the small-strain hypothesis, the displacement equations of the theoretical deformation field are deduced. Nevertheless, considering that the deduced displacement equations can not be applied to the iFEM, this paper proposes a method for using isogeometric analysis instead of the original function, and the least-square method is used to establish the strain-displacement relation. Finally, to verify the validity and accuracy of the methodology, a concentrated load and a distributed load were applied to one airfoil in the experiment tests. The predicted displacements with previous iFEM and presented iFEM are compared with those experimentally measured values, respectively. The results show that the presented iFEM exhibited higher accuracy than the previous iFEM in the variable cross-section beam problem.