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

TL;DR

The paper addresses the challenge of predicting dynamics in frictionally clamped thin-walled structures where bending–stretching nonlinearity and frictional contact interact. It proposes a sub-structuring ROM that partitions the system into a thin-walled region (geometric nonlinearity) and a support region (nonlinear contact), using Hurty–Craig–Bampton CMS with interface reduction and implicit condensation to model geometry nonlinearities within the thin-walled part. A novel engineering-oriented load-scaling scheme for the implicit condensation regression is introduced to robustly estimate nonlinear coefficients while avoiding buckling and excessive higher-order terms. Validation on a friction-clamped plate demonstrates accurate amplitude-dependent modal properties, effective damping modeling, and substantial computational speedups, while highlighting the modularity and practical applicability of the approach along with its limitations and avenues for enhancement.

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.

Figures (14)

• Figure 1: Proposed sub-structuring approach: (left) division into thin-walled and support regions; (right) definition of coupling forces.
• Figure 2: Illustration of an orthogonal polynomial series on a rectangular interface. First row corresponds to degree-zero, second and third row to degree-one polynomial terms.
• Figure 3: Overview of the proposed method.
• Figure 4: Benchmark problem consisting of a panel with frictional clamping: (a) finite element model; (b) division of symmetric half of system into thin-walled (blue) and support (red) region; (c) normalized initial contact pressure distribution $\chi(x,y)$; (d) deflection shape of lowest-frequency bending mode of underlying linear system
• Figure 5: Reduced basis: Panel interface (constraint) modes. The modes were normalized, respectively, so that the maximum displacement is equal among all modes, and indicated by red color, while green corresponds to zero displacement.