Flexible Multibody Systems Models Using Composite Materials Components

Abstract

The use of a multibody methodology to describe the large motion of complex systems that experience structural deformations enables to represent the complete system motion, the relative kinematics between the components involved, the deformation of the structural members and the inertia coupling between the large rigid body motion and the system elastodynamics. In this work, the flexible multibody dynamics formulations of complex models are extended to include elastic components made of composite materials, which may be laminated and anisotropic. The deformation of any structural member must be elastic and linear, when described in a coordinate frame fixed to one or more material points of its domain, regardless of the complexity of its geometry. To achieve the proposed flexible multibody formulation, a finite element model for each flexible body is used. For the beam composite material elements, the sections properties are found using an asymptotic procedure that involves a two-dimensional finite element analysis of their cross-section. The equations of motion of the flexible multibody system are solved using an augmented Lagrangian formulation and the accelerations and velocities are integrated in time using a multi-step multi-order integration algorithm based on the Gear method.