Efficient implementation of a semi-recursive formulation for the dynamics of large size multibody systems

This article shows an efficient implementation of a dynamic semi-recursive formulation for large and complex multibody system simulations, with interesting applications in the automotive field and especially with industrial vehicles. These systems tend to have a huge amount of kinematic constraints, becoming usual the presence of redundant but compatible systems of equations. The maths involved in the solution of these problems have a high computational cost, making very challenging to achieve real-time simulations. In this article, two implementations to increase the efficiency of these computations will be shown. The difference between them is the way they consider the Jacobian matrix of the constraint equations. The first one treats this matrix as a dense one, using the BIAS functions to solve the system of equations. The second one takes into account the sparse pattern of the Jacobian matrix, introducing the sparse function MA48 from Harwell. Both methodologies have been applied on two multibody system models with different sizes. The first model is a vehicle IVECO DAILY 35C15 with 17 degrees of freedom. The second one is a semitrailer truck with 40 degrees of freedom. Taking as a reference the standard C/C++ implementation, the efficiency improvements that have been achieved using dense matrices (BIAS) have been of 15% and 50% respectively. The results in the first model have not improved significantly by using sparse matrices, but in the second one, the times with sparse matrices have been reduced 8% with respect to the BLAS ones. (C) 2012 CIMNE (Universitat Politecnica de Catalunya). Published by Elsevier Espana, S.L. All rights reserved.