Abstract：The inverse finite element method (iFEM), employed as a shape reconstruction technique within the aerospace field, has attracted substantial attention due to its capacity for accurately reconstructing structural deformation from sparse measured strain via the adjustment of weighting coefficients. However, engineering application constraints that lead to sparse strain data acquisition, the iFEM approach, even with adjusted weights, exhibits limitations in accurately reconstructing deformations, thereby restricting its practical applicability. Consequently, a novel iFEM deformation reconstruction methodology has been developed. This method is characterized by a rigorous theoretical framework, a straightforward implementation process, and broad applicability, facilitating an exhaustive multi-solution search within the deformation space under sparse strain input. The methodology begins with the theoretical derivation of the iFEM solution error equation, accounting for sparse strain input. Upon judicious error truncation, a matrix mapping relationship is established between the iFEM-reconstructed deformation field and the true deformation field under sparse strain conditions. The incorporation of physically plausible deformation assumptions, alongside a virtual deformation field function approach, enables a multi-solution search within the reconstructed deformation space, guided by sparse data. A deformation reconstruction case has been investigated for a cantilevered aluminum alloy plate, subjected to a bending load of -10 mm, employing an extremely sparse sensor configuration. Through the application of the new methodology, thirteen deformation solutions were identified within the polynomial space. When the highest polynomial order was set to 2 or 3, the reconstructed full-field deformation exhibits a high degree of congruence with the actual conditions. Specifically, with the highest polynomial order of 2, the maximum deformation reconstructed at the end of the plate was -10.2146 mm. Compared with the value of -4.9595 mm obtained only by inverse finite element method, the reconstruction accuracy error has decreased from 50.4048% to -2.1460%. Additionally, the maximum spatial distribution reconstruction error was quantified at 2.7554%. The proposed method effectively addresses the issue of solution non-uniqueness in deformation reconstruction under sparse strain measurements, facilitates a comprehensive exploration of multiple feasible solutions, and achieves a substantial improvement in reconstruction accuracy. thereby exhibiting strong promise for practical engineering applications.
2026, Vol. 47 
