Load Reconstruction for Nonlinear Structural Dynamics

  • Aamodt Resell, Anders (NTNU)
  • Hopperstad, Odd Sture (NTNU)
  • Aune, Vegard (NTNU)

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Load reconstruction is an inverse problem where unknown external forces acting on a structure are inferred from measured kinematic responses. This capability is valuable when direct measurement of spatio-temporal pressure distributions is impractical, such as during impact events or fluid-structure interaction involving flexible structures. Direct measurement is challenging because it requires dense sensor networks with high spatial resolution, which are often infeasible due to cost, accessibility, and the risk of altering the structures’s behavior. Full-field displacement measurement techniques, such as digital image correlation (DIC), have made load reconstruction increasingly feasible. While ex- tensively studied for linear problems and mildly nonlinear problems that can be linearized about a known state [1], load reconstruction in the presence of significant material and geometric nonlinearities remains largely unexplored. This work presents a computational framework for load reconstruction in nonlinear struc- tural dynamics using the finite element method. The inverse problem is formulated as a regularized optimization problem, minimizing the discrepancy between measured and simulated displacements. An iterative minimization approach is used, where gradient evaluation is performed efficiently using the adjoint state method, enabling application to large-scale nonlinear problems [2]. The framework accommodates geometric nonlinearity and inelastic material behavior. The forward problem is solved using implicit time integration, and the corresponding adjoint equations are derived for consistent gradient computation [3]. Appropriate load parametrization and regularization techniques are employed to address ill-posedness. The capability of the framework to reconstruct spatially and temporally varying surface loads from noisy displacement data is demonstrated on metal plate structures.