Structural sensitivity analysis assisted by automatic differentiation

The integration of reverse-mode automatic differentiation (AD), implemented through taping-based libraries, into large-scaleparallel finite-element (FE) structural solvers for sensitivity analysis and gradient-based optimisation is investigated. Whilst AD provides accurate and efficient gradients essential for sensitivity analysis and gradient-based optimisation, its deployment in high-fidelity structural frameworks is often hindered by significant memory overhead, runtime cost, and parallel implementation complexity. This work provides a detailed assessment of AD performance, focussing on memory consumption, execution time, and sensitivity accuracy. The paper contributes the methodology and quantitative evidence required to deploy reverse-mode automatic differentiation reliably and efficiently in large-scale, MPI-parallel, geometrically nonlinear finite-element structural solvers for optimisation. A selective Jacobian recording strategy is evaluated, showing significant reductions in memory usage and runtime without compromising the quality of computed derivatives in well-converged problems. In addition, the impact of design variable (DV) registration strategies is assessed, showing that global DV mappings can be a viable alternative to more complex local implementations under practical parallel workloads. A comprehensive time breakdown highlights the relative contributions of the various AD phases, including the linear-solver computational cost. The methodology is further demonstrated on an engineering-scale gradient-based structural optimisation problem based on the NASA Common Research Model (CRM) wingbox, involving approximately one hundred design variables and KS-aggregated stress constraints, where AD-assisted gradients are employed within the optimisation loop. Two sensitivity workflows are compared on the CRM problem: an adjoint method, based on the residual formulation and tangent matrix, and a reverse-mode AD approach, applied to the fixed-point solver. The accuracy of the resulting sensitivities is assessed in the presence of a non-fully-consistent tangent matrix, showing that full reverse-mode AD yields more reliable gradients than adjoint formulations relying on approximate tangents. Overall, the results provide practical, implementation-oriented guidance for deploying reverse-mode AD in large-scale structural optimisation and identify key implementation choices that control memory footprint, runtime overhead, and gradient reliability in parallel FE solvers.