This work presents a shape sensing method capable of handling some geometrical complexities commonly observed in aerospace structures. The method presented is based on the one-dimensional inverse Finite Element Method (1D-iFEM), which is capable of accurately reconstructing structural displacements of beam structures using surface strain measurements. The effects of cross-sectional variation in shear strains due to transverse or torsional loads for any general beam profile is accounted for in this 1D-iFEM formulation. The introduction of these effects allows the use of iFEM for the shape sensing of solid or thin-walled prismatic beams with any general beam profile. The performance of the new method is demonstrated through some example problems of prismatic beams under various static loading scenarios.

这项工作提出了一种形状感应方法，该方法能够处理在航空航天结构中通常观察到的某些几何复杂性。提出的方法基于一维逆有限元方法（1D-iFEM），该方法能够使用表面应变测量准确地重建梁结构的结构位移。在此一维-iFEM公式中，考虑到了任何普通梁截面的横向或扭转载荷引起的剪切应变截面变化的影响。这些效果的引入允许将iFEM用于具有任何常规光束轮廓的实心或薄壁棱镜光束的形状感测。通过在各种静态载荷情况下棱镜梁的一些示例问题证明了该新方法的性能。