Structural health management systems that, by way of real-time monitoring, help mitigate accidents due to structural failures, will become integral technologies of the next-generation aerospace vehicles. Advanced sensor arrays and signal processing technologies are utilized to provide optimally distributed in-situ sensor information related to the states of strain, temperature, and aerodynamic pressure. To process the massive quantities of measured data, and to infer physically admissible structural behavior, requires robust and computationally efficient physics-based algorithms.
The inverse Finite Element Method (iFEM) is a computational tool that integrates sensor strain data across the entire structural domain, and produces a continuous displacement field of the discretized structure, i.e., the algorithm solves an inverse problem. The method’s mathematical foundation is a weighted least-squares variational principle that relies on the discretization of structural geometry by any type of structural element including beam, frame, plate, shell, and solid. Displacement boundary conditions and in-situ strain measurements are used as prescribed input quantities imposed on a model. The discretized model results in a system of linear algebraic equations that has a nonsingular square matrix that depends on the strain-sensor positions. For a given model and fixed strain-sensor locations, the matrix is decomposed (inverted) only once. The right-hand-side vector is a function of the strain values that change as the structure deforms under loading. Thus, the computational algorithm involves multiplication of a matrix that stays unchanged. The right-handside vector is recomputed in real time and hence reflects changes in strain-sensor readings during deformation.
The algorithm is capable of producing reliable and accurate displacement predictions of the discretized structure. The reconstructed displacements are then used to compute strains, stresses, and failure criteria, thus providing the requisite information for an onboard structural-integrity analysis tool.
The methodology explicitly enforces all strain compatibility relations, and does not use elastic or inertial material properties to reconstruct full-field displacements. It is therefore applicable to both static and dynamic applications. An example problem of a cantilevered plate was examined, for which experimental measurements were obtained in a structures laboratory. Direct and inverse FEM solutions were obtained to validate the high-accuracy predictions of deformations afforded through the iFEM modeling. The methodology is seen as an essential technology for providing real-time displacement feedback to the actuation and control systems of the next generation of aerospace vehicles, as well as for applications in airframe structural health-monitoring information systems.