Full-field displacement and strain reconstruction for beam structures based on the extended inverse finite element method

The inverse finite element method (iFEM) is a superior shape sensing methodology in the field of structural health monitoring. However, the standard iFEM for beams yields only displacements at iFEM nodes whose spatial resolution is limited by the number of strain measurements. This study presented an extended iFEM that renders high-quality full-field displacement and strain fields by interpolating the displacements and strains at all locations on the beam using elemental shape functions. A series of numerical studies were implemented to verify the extended iFEM algorithm for various sensor and mesh configurations under different boundary and loading conditions. It showed that the extended iFEM gives smoother and more accurate results using far fewer inverse elements than the standard iFEM.