Identification of young’s modulus for a cantilever beam subjected to a follower force using geometrically nonlinear beam models

Abstract A core task of industrial digital twins is the identification of parameters from measured process data. Inspired by such an industrial application, we consider a cantilever beam with Hookean material behavior subjected to a transverse follower force and focus on the inverse problem of determining Young’s modulus from known (measured) bending force and bending angle. Within the framework of Reissner’s beam theory, accounting for shear deformation, moderate strains, and large displacements, the relationship between applied force, bending angle and Young’s modulus is formulated. The inverse problem is discussed for the shear rigid Kirchhoff and the shear deformable Reissner formulation, including their corresponding theories for small displacements. While for the Kirchhoff case an analytical inverse solution is possible, the Reissner formulation requires numerical solution methods. The proposed identification strategies are verified through finite element simulations and a parameter study is conducted to quantify the accuracy across a broad range of geometric configurations. The comparison between the Reissner model, the Kirchhoff model and their linearizations highlights the influence of shear and geometric assumptions on the achievable identification accuracy. The outcome of this work is a verified solution framework for the identification of the Young’s modulus together with a clear characterization of the several variants of beam theory.