Sensitivity analysis of flexible multibody systems using composite materials components

Abstract

In this paper, a general formulation for the computation of the first-order analytical sensitivities based on the direct method using automatic differentiation of flexible multibody systems is presented. The direct method for sensitivity calculation is obtained by differentiating the equations that define the response of the flexible multibody systems of composite materials with respect to the design variables, which are the ply orientations of the laminated. In order to appraise the benefits of the approach suggested and to highlight the risks of the procedure, the analytical sensitivities are compared with the numerical results obtained by using the finite difference method. For the beam composite material elements, the section properties and their sensitivities are found using an asymptotic procedure that involves a two-dimensional (2-D) finite element analysis of their cross section. The equations of the sensitivities are obtained by automatic differentiation and integrated in time simultaneously with the equations of motion of the multibody systems. The equations of motion and the sensitivities of the flexible multibody system are solved and the accelerations, velocities and the sensitivities of accelerations and velocities are integrated in time using a multi-step multi-order integration algorithm. Through the application of the methodology to two simple flexible multibody systems the difficulties and benefits of the procedure, with respect to finite difference approaches or to the direct implementation of the analytic sensitivities, are discussed. Copyright © 2008 John Wiley & Sons, Ltd.