Gain in computational efficiency by vectorization in the dynamic simulation of multi-body systems

Abstract

This paper presents a new technique developed for increasing the computational efficiency of the dynamic simulation of multi-body systems, providing the computer code with the speed of execution, which is an order of magnitude ahead of the procedure outlined in S. K. Ider and F. M. L. Amirouche [ J. appl. Mech. 56, (2) (1989)]. This technique is useful with the finite element based algorithm for the solution of dynamical equations of motion for the constrained and unconstrained systems with flexible/rigid interconnected bodies. The implementation of the technique has totally eliminated the costly multiplications of large Boolean matrices, where intensive cpu utilization was required. The overall expensive computer time has been drastically reduced, particularly for the three-dimensional systems involving large degrees of freedom, as a result of their intricate geometry. The algorithmic procedure has been presented in a matrix form and is based on the recursive formulation using Kane's equation, strain energy, mode synthesis, finite element approach, a stable and efficient method for reducing the number of equations subsequent to the constraints resulting from closed loops and/or prescribed motions. Further enhancement in the speed of execution has been achieved by subjecting the developed code to vectorization on the vector-processing machine. A study of simple robot with flexible links has been presented comparing the execution times on the scalar machine ( IBM-3081) and the vector-processor ( IBM-3090) with and without vector options. Performance figures has been plotted demonstrating the large gains achieved by the technique developed.