Shape sensing of Timoshenko beam subjected to complex multi-node loads using isogeometric analysis

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.

Automated summary

An effective computational method utilizing fewer strain sensors to reconstruct the Timoshenko beam under complex loads is proposed, combining iFEM as the basic framework and IGA as an improved strategy. The method simplifies kinematic equations, establishes relationships between rotation deformation and surface measured strains, and determines geometric variables through constitutive equations and boundary conditions. Experimental results demonstrate higher accuracy than iFEM under complex loads.