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Abstract
An efficient multibody dynamics formulation is developed for simulating the forward dynamics of mechanical systems. Systems can be composed of rigid and flexible bodies interconnected by revolute, prismatic, free, and fixed joints. The topology can be open or closed loop. Forces can be applied to the system by displacement and velocity dependent force producing elements and externally applied forces. No restrictions are placed on the form of damping describing flexible substructures.
The approach is based on Kane's equation without multipliers. The resulting formulation generates 2 ndof + m first order ordinary differential equations directly where ndof is the number of system degrees of freedom and m is the number of loop closure velocity constraint equations. The equations are integrated in the time domain to propagate the solution.
Flexible bodies are discretized using a finite element approach. The mass and stiffness matrices for six degree of freedom planar beam elements are developed including mass coupling terms, rotary inertia, centripetal and coriolis forces, and geometric stiffening terms.
The formulation is implemented in a general purpose multibody dynamics computer program scFLXDYN. Extensive validation of the formulation and corresponding computer program is performed against analytically derived equations, alternative approximate solutions, and benchmark problems selected from the literature. The current formulation is found to perform well in terms of accuracy and solution efficiency.
