A Unified Full-Field Deformation Measurement Method for Beam-Like Structure

Full-field displacement reconstruction, which uses a few strain sensors for obtaining real-time surface strain as the input data of the monitoring system, is a crucial technology to actuate and control smart structures. In the previous reconstruction algorithm, the displacement vectors consistent with some particular kinematic assumptions of the deformation theory should be determined in advance. However, obtaining the displacement vectors of complex structures accurately and quickly is difficult in engineering. Therefore, the attentions are mainly on seeking a unified method to avoid the reconstruction errors caused by structural misidentification. For this purpose, some particular generalized quantities are adopted to replace the traditional displacement functions, and the unified displacement field of beam-like structures is proposed based on the homogenized theory. Meanwhile, the reconstruction function is established based on the classic inverse finite-element method (iFEM). Next, the transformation relationships are determined between the generalized numerical strains and the measured strains using a tailored strain measurement scheme. Finally, several beam-like structures with different slenderness ratios are used as the test examples to verify the reliability and effectiveness of the presented full-field displacement monitoring method. The simulation and experimental results demonstrate the superior precision and stable reliability of the presented measurement method for performing shape sensing of beam-like structures.