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.