A sub-structuring approach for model reduction of frictionally clamped thin-walled structures

Thin-walled structures clamped by friction joints, such as aircraft skin panels are exposed to bending–stretching coupling and frictional contact. We propose an original sub-structuring approach, where the system is divided into thin-walled and support regions, so that geometrically nonlinear behavior is relevant only in the former, and nonlinear contact behavior only in the latter. This permits to derive reduced component models, in principle, with available techniques. The Hurty-/Craig-Bampton method, combined with an interface reduction relying on an orthogonal polynomial series, is used to construct the reduction basis for each component. To model geometrically nonlinear behavior, implicit condensation is used, where an original, engineering-oriented proposition is made for the delicate scaling of the static load cases required to estimate the coefficients of the nonlinear terms. The proposed method is validated and its computational performance is assessed for the example of a plate with frictional clamping, using finite element analysis as reference. The numerical results shed light into an interesting mutual interaction: with increased amplitude, more sliding occurs in the clamping, which reduces the axial stiffness, and thus limits the extent of geometric hardening. On the other hand, the geometrically nonlinear bending–stretching deformation has an appreciable effect on the extent of frictional dissipation.