Abstract

The paper presents a dedicated numerical algorithm. The algorithm is advantageous during investigations of the dynamics of a hybrid multibody / finite-elements system. We focus our attention on interactions resulting from mechanical contact. Pointwise contact connects a vertex of the multibody structure and a surface of the elastic reference body. Instead of a positive value of the relative penetration factor, constraint equations model the contact, and Lagrange multipliers model the constraint-associated reactions used in the dynamics equations. In the subsequent steps, the investigated procedure recalls a case-dedicated version of the classic coordinate-portioning algorithm. The dedicated numerical algorithm evaluates the algebraic unknown of the system, i.e., for each set of investigated accelerations, it calculates values of the Lagrange multipliers and values of the selected dependent accelerations resulting from the consistency of the constraint equations. When calculated, the algorithm eliminates them from the remaining equations. Consistently with purely numerical reasons, obtained differential equations are challenging for numerical integration. The paper presents one of the reasons. To solve the misadventure, it proposes an alternative numerically-rational model of the disturbing phenomena. The proposed solution recalls modal adjustment of the damping properties of the elastic subcomponent. We test the efficiency of the paper-proposed methodology with the use of a numerical example. We limit the tests to an example of a purely academic planar structure. Also, we restrict the tested elastic subcomponent to a case of a planar deformable beam. We model it with the use of two-node beam elements. Pin contacts, as well as frictionless pointwise slider-pin contacts, connect the elastic beam and the multibody. The paper presents the case-dedicated constraint equations and their associated Lagrange multipliers. Our initial tests investigate the main consequences of the presence of the uniform Rayleigh model of structural damping. In the subsequent numerical tests, we modify the main parameters of the structural damping. Indicated modification recalls the paper-proposed principles of the abovementioned modal adjustment. Paper-presented figures compare the obtained behaviours with those calculated previously for the Rayleigh model. Even if verified with a purely academic numerical model, the paper-proposed methodology is general.

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