Optimization of a complex flexible multibody systems with composite materials

Abstract

The paper presents a general optimization methodology for flexible multibody systems which is demonstrated to find optimal layouts of fiber composite structures components. The goal of the optimization process is to minimize the structural deformation and, simultaneously, to fulfill a set of multidisciplinary constraints, by finding the optimal values for the fiber orientation of composite structures. In this work, a general formulation for the computation of the first order analytical sensitivities based on the use of automatic differentiation tools is applied. A critical overview on the use of the sensitivities obtained by automatic differentiation against analytical sensitivities derived and implemented by hand is made with the purpose of identifying shortcomings and proposing solutions. The equations of motion and sensitivities of the flexible multibody system are solved simultaneously being the accelerations and velocities of the system and the sensitivities of the accelerations and of the velocities integrated in time using a multi-step multi-order integration algorithm. Then, the optimal design of the flexible multibody system is formulated to minimize the deformation energy of the system subjected to a set of technological and functional constraints. The methodologies proposed are first discussed for a simple demonstrative example and applied after to the optimization of a complex flexible multibody system, represented by a satellite antenna that is unfolded from its launching configuration to its functional state.

Sensitivity of a vehicle ride to the suspension bushing characteristics

“…The sensitivities are calculated here by using the finite difference method [10,11]. Neither the direct differentiation [12,13] nor the adjoint variable methods [14] are used because require analytical evaluations of the sensitivities. The perturbations used for the finite difference sensitivities are selected in order to avoid truncation and round off numerical errors [14].…”

Automatic Deduction Theorem of Overall Transfer Equation of Multibody System

“…From equations (6) and (7), the features of the overall transfer equation for a chain system can be clearly seen; overall transfer matrix of a chain system can be deduced automatically by successive premultiplication of transfer matrices of every element of the system along the transfer path from the one end to another end.…”

“…Then, using the computed values of the last step as the initial conditions, the entire procedure can be repeated from time +1 until the time required for complete analysis. It can be seen clearly from equations (5)- (7) that MSTMM belongs to one of strict analytical methods in principle. A dynamics model of any complex multibody system can be constructed with dynamics elements including bodies and hinges.…”

“…Lots of methods dealing with multibody system dynamics (MSD) have been studied by many authors since 1960s [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. They are widely used in many engineering fields such as aeronautics, astronautics, spacecraft, vehicle, robot, precision machinery, and biomechanics.…”

“…These matrices of elements are considered as building blocks that provide the dynamics properties of the entire system when assembling them together according to the topology of the system. Particularly, the positions of bodies and hinges are considered equivalent in transfer equations and transfer matrices, which is totally different from ordinary methods for MSD [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and results in the very low order of system matrix and very high computational speed in MSTMM.…”