A spectral viscosity method for correcting the long-term behavior of POD models
Journal of Computational Physics
Uncertainty quantification of limit-cycle oscillations
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Optimum design of composite plate wings for aeroelastic characteristics using lamination parameters
Computers and Structures
Spectral element method in time for rapidly actuated systems
Journal of Computational Physics
Minimal Repetition Dynamic Checkpointing Algorithm for Unsteady Adjoint Calculation
SIAM Journal on Scientific Computing
Finite Elements in Analysis and Design
Adjoint sensitivities of time-periodic nonlinear structural dynamics via model reduction
Computers and Structures
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Gradient-based optimization, via the adjoint method, is needed to realistically enable the reliability-based design of a nonlinear unsteady aeroelastic system with many random and/or deterministic design variables. The adjoint derivatives of a time-marched system entail a cumbersome reverse-time integration, and so a time-periodic spectral element scheme is used here to efficiently capture the gradients of the limit cycle oscillations. Further reductions in the computational cost of the monolithic-time adjoint vector are obtained with proper orthogonal decomposition, which projects the large system onto a reduced basis. Design reliability is computed with the first order reliability method, which provides an estimate of the failure probability without resorting to sampling-based approaches (infeasible for large systems). Analytical gradients are needed to obtain the most probable point (in the random variable space), as well as the reliability design derivatives. These computational strategies are utilized to locate the optimal thickness distribution of a cantilevered wing operating beyond its flutter point in supersonic flow (via piston theory). Specifically, the wing mass is minimized under both deterministic and non-deterministic limit cycle oscillation amplitude constraints, with both structural and flow uncertainties considered in the latter.