Total Lagrangian FEM formulation for nonlinear dynamics of sliding connections in viscoelastic plane structures and mechanisms

In this work we extend a total Lagrangian formulation developed for dynamical nonlinear analysis of elastic plane frames to include structural energy dissipation and sliding connections (as prismatic and cylindrical joints). The joints move in a path that may present an arbitrary roughness profile along its trajectory. Their exact kinematical restraints are introduced in the total mechanical energy of the system by the method of Lagrange multipliers. The structural energy dissipation is considered by a modified Kelvin-Voigt rheological model, for which a pure numerical procedure for the strain rate approximation (finite difference) is proposed. The dynamical equilibrium equation is obtained by a variational principle and the nonlinear solution procedure is done by the Newton-Raphson method. Several examples are presented to demonstrate the efficiency of the proposed formulations.