NEW FORMULATION FOR FLEXIBLE BEAMS UNDERGOING LARGE OVERALL PLANE MOTION

A new flexible body dynamic formulation, called the augmented imbedded geometric constraint approach, for beam structures undergoing large overall motion is developed. It is restricted to small elastic deformations of the beam about the large overall motion. The formulation outlined herein pertains to two-dimensional motion and deformation of a single beam when the overall motion is prescribed as a function of time. The formulation can be easily extended to beam assemblies undergoing arbitrary motion in three dimensional space. Elastic deformation is characterized by the superposition of a number of assumed global shape functions. The motion of the system is governed by a set of differential and algebraic equations. The algebraic constraints arise from enforcement of the boundary conditions. The new approach improves upon two existing approaches by allowing the solution of two disparate classes of elasto-dynamics problems with a single formulation, demonstrated by simulations for several verification problems. The problems are ones in which the lateral deformation of the beam is dominated by either bending or membrane behavior. Because the new formulation is problem independent, it is applicable to beam problems where the dominant stiffness effects are not known beforehand.