Efficient <i>C</i> ¹-Continuous Deformation Measurement of Thin-Plate Structures via Strain-Based Method and Variational Principle

Inverse finite element method (iFEM) has become a valuable technique for structural health monitoring in engineering applications due to its capability for real-time structural deformation measurement. However, the existing iFEM framework lacks <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>-continuity, meaning it does not ensure the continuity of both the displacement field and its first derivative (slope) between elements. This limitation leads to reduced convergence and accuracy, particularly in thin-plate structures. To address this limitation, the displacement field is formulated using state-of-motion factors based on the biharmonic partial differential equation and the strain-based method in this paper. Subsequently, the transformation relationship between nodal degrees of freedom (DOF) and state-of-motion factors is employed to express the calculated strain field. The system equation is then established by minimizing the error between the measured and calculated strain. By solving this equation, the DOF of discrete nodes can be determined, allowing for the deformation field measurement. Finally, the developed approach’s key advantages, including resistance to element distortion, high convergence, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i><sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>-continuity, are evaluated through a series of numerical and experimental tests.