Hendrik D. Linder | Searcharxiv

arXiv2026

Enabling topography-resolving structural dynamic contact simulation

Damping of structures and systems is often dominated by frictional dissipation in connections, the prediction of which remains a longstanding scientific challenge. Previous studies have shown that the actual topography of contact interfaces may have a strong effect, especially in the partial slip/liftoff regime. We recently proposed a multi-scale method, which couples finite element and boundary element modeling. The primary benefit of this approach is to analyze the effect of actual contact topography on the dynamics of jointed structures. While this multi-scale modeling method was initially developed for quasi-static analysis, we demonstrate herein how it can be used for time step integration and Harmonic Balance analysis. We cross-verify those fully dynamic analysis methods against each other and quasi-static results, for the S4 Beam benchmark. We compare the multi-scale method against state-of-the-art full-FE analysis, in terms of numerical damping and computational performance. Some discrepancy is found to be of physical origin. Depending on the load history, it is shown that the system settles to a slightly different equilibrium. Transient multi-scale simulations enable the prediction of this interesting phenomenon, for the first time, for a structure with bolted joints.

cs.CE↗

arXiv2025

A coupled FE-BE multi-scale method for the dynamics of jointed structures

The damping of built-up structures stems largely from the microscopic dry frictional interactions in the contact interfaces. The accurate prediction of friction damping has been an important scientific aim of the past several decades. Recent research indicates that very good agreement with vibration measurements is to be expected if the actual contact surface topography is sufficiently well known and finely resolved, and frictional-unilateral interactions are modeled in terms of the Coulomb-Signorini conditions. Resolving all relevant length scales in one finite element model leads to enormous or even prohibitive computation effort and regularization of the set-valued contact laws might be needed to ensure numerical stability. In this work, we propose a multi-scale approach: The stress and deformation field in the contact region is modeled using elastic half-space theory, implemented on a regular and fine grid of boundary elements (BE), so that the compliance matrix can be expressed in closed form. The vibration behavior of the remaining region is described using a relatively coarse finite element (FE) model, which is further reduced via component mode synthesis. The two models are coupled by enforcing compatibility and equilibrium conditions in the far field. The set-valued Coulomb-Signorini conditions are enforced robustly and efficiently using a projected over-relaxation scheme in conjunction with an appropriate active-set strategy. For the S4 beam benchmark, very good agreement with regard to the amplitude-dependent frequency and damping ratio of the first few modes is achieved, while the computation effort is reduced by several orders of magnitude compared to the full-FE reference. The proposed multi-scale method permits a very fine resolution of the contact surface topography without suffering from numerical instability.

eess.SY↗