Simulation of a Moving, Elastic Beam Using Hamilton's Weak Principle

Abstract

Hamilton's Law is derived in weak form for slender beams with closed cross sections. The result is discretized with mixed space-time finite elements to yield a system of nonlinear, algebraic equations. An algorithm is proposed for solving these equations using unconstrained optimization techniques, obtaining steady-state and time accurate solutions for problems of structural dynamics. This technique provides accurate solutions for nonlinear static and steady-state problems including the cantilevered elastica and flatwise rotation of beams. Modal analysis of beams and rods is investigated to accurately determine fundamental frequencies of vibration, and the simulation of simple maneuvers is demonstrated.iv

Numerical modelling and field experimental validation of the axial load transfer on the drill-strings in deviated wells

“…So, a comprehensive model of axial load transfer should always take these complex factors into account. According to the Hamilton principle (Leigh and Kunz, 2007;Thompson et al, 2012), the kinetic energy, the potential energy and the work done by the non-potential forces, must satisfy the following energy conservation equation,…”