| The object of the present work is to re-examine and appropriately modify the geometrically exact beam theory, originally developed by Simo, and develop a finite element formulation to describe the static and dynamic behavior of flexible electrical equipment cables. The nonlinear equations of motion of a beam undergoing large displacements and rotations are derived from the 3D theory of continuum mechanics by use of the virtual power equation. A linear viscoelastic constitutive equation and an additional mass proportional damping mechanism are used to account for energy dissipation. The weak form of the equations of motion is linearized and discretized, in time and space, leading to the definition of a tangent operator and a system of equations solvable by means of an iterative scheme of the Newton type. Particular attention is focused on issues related to how large rotations are handled and how the configuration update process is performed. Numerical examples are presented, and energy balance calculations demonstrate the accuracy of the computed solutions. The beam model is then applied to describe the static and dynamic behavior of an electrical conductor tested at the SEESL at the University at Buffalo. Preliminary results of the simulation of free and forced vibration tests are presented. Next an approach is presented for the dynamic analysis of tensegrity structures in the small displacement regime. Such analyses are characterized by cables in the structure switching between taut and slack states. The approach is based on casting the computation in each time increment as a complementarity problem. Numerical examples are presented to illustrate the approach. Despite the non-smooth nature of cables switching between taut and slack states, the computed solutions exhibit remarkable long-term energy balance. Furthermore, by exploiting some features of the tensegrity model, significant computational efficiency can be gained in the solution of the complementarity problem in each time increment. |
