Sliding connections for geometrical nonlinear dynamical analysis of three-dimensional structures and mechanisms

Abstract

This project proposes the development and computational implementation of a finite element formulation to model three-dimensional structures and mechanisms with sliding connections introduced by Lagrange multipliers. Sliding connections known as prismatic, cylindrical and plane joints will be considered in shell and three-dimensional frame finite elements in addition to rotational and spherical joints. Especial attention will be given to the connections between shell elements where a trajectory restriction path, or paths, will be created to allow motion for the sliding structure. Aspects such as surface roughness and energy dissipation by dry friction will be considered in the joints. Those connections presents numerous applications in structures and mechanisms of the aerospace, mechanical and civil industries. The finite element method formulation and implementation will be performed in a Total Lagrangian environment using positions as nodal parameters. This approach has been developed by the advisor of this project for more than ten years and it has proven to be a simple and efficient alternative for geometrical nonlinear dynamical analysis of structures. The Saint-Venant-Kirchhoff constitutive model, which relates the Green-Lagrange objective strain measure to the second Piola-Kirchhoff stress tensor, will be adopted. The system dynamical equilibrium is obtained by the Principle of Stationary Total Energy and the solution of the resulting nonlinear system is done by the Newton-Raphson method. The time integration to be used employs the Newmark method, which has adapted well to the Total Lagrangian formulation developed in the research group wherein this work belongs. Several examples will be presented to validate the formulation and the developed code.