Inverse Finite Element Method for Structural Health Monitoring

The inverse finite element method (iFEM) is a computational approach that reconstructs the full‐field displacement and strain state of a structure from measured surface strains. By minimising a weighted least‐squares functional, iFEM iteratively adjusts nodal displacements until analytical strains match the input data. This enables real‐time shape sensing and damage detection in diverse engineering systems, from aerospace wings to civil infrastructure. A key advantage of iFEM is its independence from external loading and precise material properties, relying solely on geometric definitions and in situ sensor readings. Recent advances have extended the method to fracture mechanics, incorporating specialised inverse elements to capture stress singularities at crack tips, and to curved shell structures through isogeometric formulations that employ smooth basis functions. Optimal sensor placement strategies, often based on eigenvalue or variational analyses, further enhance accuracy while reducing hardware requirements. The global impact of iFEM is evident in its capacity to monitor structural integrity under extreme or unpredictable conditions, improving operational safety, extending service life and enabling predictive maintenance across multiple sectors.

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Technical terms

Inverse finite element method (iFEM): A computational technique that reconstructs displacements and strains from measured surface strains by minimising a least‐squares functional.

Shape sensing: The process of determining a structure’s deformation field in real time using strain measurements and computational models.

Variational least‐squares functional: A scalar quantity defined as the weighted sum of squared differences between measured and analytical strains, minimised in iFEM.

Stress intensity factor (SIF): A parameter characterising the stress state near a crack tip, essential for fracture mechanics analyses.

Non‐uniform rational B-splines (NURBS): Smooth, parametric functions used in isogeometric analysis to represent exact geometries and basis functions for numerical methods.

References

1. Structural health monitoring of precracked structures using an in‐plane inverse crack‐tip element. International Journal of Mechanical System Dynamics (2024).
2. Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method. Sensors (2021).
3. Isogeometric iFEM Analysis of Thin Shell Structures †. Sensors (2020).