A numerical tool for the design of assembled structures under dynamic loads

•The aim of this work is to compute the stiffness and damping properties of jointed structures.•The proposed quasi-static FEM circumvents high CPU cost due to non-linear dynamics.•It relies on the use of normal modes as BC for the localized contact problem of the joints.•The use of Masing rules to model joints behavior is discussed.•It is investigated on a lap-joint benchmark and compared with a non-linear dynamic analysis.

Mechanical joints in assembled structures cause energy dissipation due to micro-slip in contact and softening effects that play an important role in the dynamic behavior of such structures. The contact non-linearity is governed by micro and meso-scale parameters (geometry, roughness, local pressure, etc.) and as a result cannot be included in a macro-size model of a whole structure because of the computational cost. The present paper investigates the idea of using the normal modes of the linearized structure as boundary conditions on a detailed model reduced to the joints only. Since contact non-linearities alter mode shapes, they are corrected as vibrational energy increases. The method relies on a corrected quasi-static formulation associated with the Masing hypothesis. These assumptions circumvent considerable numerical expense due to the non-linear dynamics. The formulation of the method is detailed and investigated on a lap-joint benchmark.