Shape sensing of Timoshenko beam subjected to complex multi-node loads using isogeometric analysis. (November 2021) - Chen, Kangyu; Cao, Kaituo; Gao, Guoming; Bao, Hong
Highlights: A Novel method for shape sensing of Timoshenko beam subjected to complex load. The approach is operational, i.e., it needs only measured surface strain. The approach is interpretable, i.e., the continuity interpolation criteria determine the displacement fields basis functions. This method is superior, i.e., the number of sensors is reduced by comparing with the traditional iFEM method. Abstract: An effective computational method, which employs fewer strain sensors to reconstruct the Timoshenko beam under complex loads, is proposed. This method takes inverse Finite Element Method (iFEM) as a basic framework and isogeometric analysis (IGA) as an improved strategy. Initially, the kinematical equations of the Timoshenko beam are decreased to a single variable differential equation with rotation. Then, IGA can be used to describe the rotation, where the spline basis functions can be determined based on the continuity interpolation criteria. Next, relationships between rotation deformation and surface measured strains are established. Meanwhile, the geometric variables can be determined through the constitutive equations and boundary conditions. Finally, four different test loads were applied to a thin-walled aluminum beam, and the experimental results show that the presented reconstruction method has excellent accuracy than the iFEM under complex loads.