Joint nonlinearity in a stiffened aluminium wingbox panel and what it requires of a reduced basis

A shell finite-element model of a stiffened aluminium wingbox panel, a laboratory structure shared by several experimental studies, is built with its plate-to-stiffener joints at the $78$ physical fastener positions and calibrated against measured modal data, a six-parameter sensitivity update of the substructure moduli within $\pm 20\mathrm{\%}$ reproducing the first five measured modes to $1.1$–$4.3\mathrm{\%}$ with modal-assurance values of $0.88$–$1.00$. Making the fasteners nonlinear, at equal mesh, mass and damping, shows that joint nonlinearity enters the response strongly asymmetrically. Hardening is almost invisible, at most $+1\mathrm{\%}$ in frequency, whereas softening or slipping the joints moves the first three resonances by $-2.1$, $-4.9$ and $-9.2\mathrm{\%}$, and friction removes up to $80\mathrm{\%}$ of the resonant peak before it recovers. Newmark integration of all $\mathrm{18,804}$ degrees of freedom and a harmonic balance condensed exactly onto the joints and continued in arclength agree to $5.5\times {10}^{-4}$. A projection-based nonlinear model order reduction then locates the criterion that a jointed structure imposes on a reduced basis. The binding quantity is not the linear response, which eleven vectors reproduce to better than $0.01\mathrm{\%}$, but the receptance of the structure between the joints, of which $126$ global eigenvectors carry about $2\mathrm{\%}$, and without which the reduced model overpredicts the hardening shift of the fundamental by a factor of thirty and returns a value beyond the rigid-joint limit of the panel.