Shape Reconstruction of a Timoshenko Beam under the Geometric Nonlinearity Condition

Shape sensing, which is the real-time monitoring of deformed shapes using discrete surface strain, is a fundamental approach to ensure structural safety, reliability, and affordability. Large deformation shape sensing is obviously more important because large deformations can result in structural damage and failure. Nevertheless, there are few effective methods for the shape sensing of large deformations. Based on Timoshenko beam theory, this paper establishes a new method, called analogy stiffness upgrading (ASU), to reconstruct nonlinear deformation. In this method, the inverse finite element method (iFEM) is used to predict the initial displacement field and compute the analogy stiffness matrix. Then, the analogy stiffness matrix is upgraded by using coordinate transformation from a co-rotational procedure. Through iterative computation, the real displacement field is finally obtained when the rotation angle calculated from the input strain data is the same as the integral result from the section strain data. Numerical examples and model tests are carried out to verify the ASU method. It is evident from the results that the ASU method can predict largely deformed shapes of beam structures with superior precision.