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

TL;DR

This paper introduces a sub-structuring model reduction method for thin-walled structures with friction joints, effectively capturing nonlinear behaviors and improving computational efficiency in structural analysis.

Contribution

It presents a novel division of the system into regions to isolate nonlinear effects and employs an advanced reduction basis with interface and nonlinear modeling techniques.

Findings

Reduced boundary stiffness limits geometric hardening.

Frictional dissipation increases with tangential loading.

Method validated against finite element analysis.

Abstract

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: The extent of geometric hardening is limited by the reduced boundary stiffness when more sliding occurs in the clamping. On the other hand, the frictional dissipation is increased by the tangential loading induced by membrane stretching.