Sensivity analysis of flexible multibody systems

In this work a general formulation for the computation of the first order analytical sensitivities based on the direct method is presented. The direct method for sensitivity calculation is obtained by differentiating the equations that define the response of the flexible system with respect to the design variables. The design variables used here are the ply orientations of the laminated. The analytical sensitivities are compared with the numerical results obtained by using the finite differences method. For the beam composite material elements, the section properties and their sensitivities are found using an asymptotic procedure that involves a two-dimensional 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 sensitivities of the flexible multibody system are solved and the accelerations and velocities and sensitivities of accelerations and velocities are integrated. Through the application of the methodology to a single flexible multibody systems the difficulties and benefices of the procedure are discussed.