COROTATIONAL FINITE-ELEMENT ANALYSIS OF PLANAR FLEXIBLE MULTIBODY SYSTEMS

A computer-oriented method for the formulation and the solution of nonlinear constrained differential equations of motion is developed. The method is applicable to flexible multibody systems with large displacements and rotations. A corotational finite element formulation is derived for the dynamic analysis of a planar flexible multibody system. An inertial frame is used to define the nodal coordinates, velocities, accelerations, displacements, and rotations. The equations of motion are defined in terms of that inertial frame, while strains are measured in the corotational coordinate system of the element. This elemental coordinate system rotates and translates with each element but does not deform with it. The equations of motion are derived using Lagrange's equations. The numerical solution is obtained by employing an incremental-iterative method based on the Newmark direct integration algorithm and the Newton-Raphson method. The applicability and the accuracy of the method are demonstrated by studying some nonlinear flexible mechanical systems.