Development of contact formulations applied to geometrical nonlinear dynamical analysis of three-dimensional structures and mechanisms with connections

Abstract

The development and computational implementation of a finite element formulation for the simulation of three-dimensional structures and mechanisms with the introduction of sliding connections by means of Lagrange multipliers is proposed in this project. Local models will be considered for the analysis of the sliding that occur in spherical, rotational, prismatic, cylindrical and plane joints in solid, shell and 3D frame finite elements. Particular attention will be given to the study of contact and impact between the surfaces modelled by solid and shell elements, as well as between frame elements and surfaces without pre-defined trajectories, as guided connections between frame and shell elements were already accomplished during the doctorate of the candidate. Aspects such as path roughness and frictional dissipation in the connections will also be considered. Those connections have several applications in structures and mechanisms present in civil, aerospace and mechanical industries, for instance, drawbridges, tensegrities, contact between vehicle and bridge or soil pavements, train/rail contact, seismic protection devices, satellite antennas, robotic arms and cranes, etc. The positional finite element method formulation, in a total Lagrangian environment, will be used; this formulation has been developed in the research group where this project is inserted for over fifteen years. The Saint-Venant-Kirchhoff constitutive model will be employed for the materials. The system dynamical equilibrium is found by the Principle of Stationary Total Energy and the nonlinear system solution will be done by the Newton-Raphson method with the Newmark and generalized-alpha time integrators.