Multibody system optimization

The minimum number of floating point operations are based on very special optimizations, which are only possible for the benchmark system used, i.e. a serial chain with rigid bodies connected by revolute joints. These well-known results show that a multibody system program can be made more efficient by choosing an adequate formalism. As Fig. 1 shows, the eflficiency of a formalism depends strongly on the system it is applied to. Unfortunately, there are only a few comparisons for some formalisms on only some benchmark problems. To find an optimal formalism for a given problem, it would therefore be helpful to have a better comparison of formalisms on a wider variety of systems and to have an environment to program and modify comfortably formalisms and to apply them to a particular system. 

The linearization procedure was implemented in the AD AMBUS software, which has been developed for the dynamic analysis of flexible multibody systems. For each time step, the linearization procedure provides the instantaneous tangent matrices of mass, stiffness and damping, which are transferred into the control software. In accordance with the linearized equation, the control software calculates the gain matrices for optimal control of the system. 

ABSTRACT. Analytical evaluation of the performance of multibody mechanical systems becomes rapidly unmanageable as the complexity of the systems increase. For problems that involve intermittent motion due to an impact, prediction of the responses is even more difficult. In an impact, nonlinear contact forces of unknown nature are created, which act and disappear over a short period of time. In this paper, different contact force models are formulated, with which a continuous analysis method is developed for a simple two-particle impact. The procedure is then generalized to impact in multibody systems using the concept of effective mass. A piecewise analysis method is discussed, which is based on a canonical form of the system impulse/momentum equations. The suitability of these methods are discussed by application of these procedures to some examples. An optimization methodology is then discussed for the selection of proper parameters in a given contact force model. The use of this technique in the selection of the most suitable materials, which are impact-resistant, is also discussed. 

The methods discussed earlier are applied to the seat-occupant-restraint system of an aircraft. A description of a computer-aided analysis environment, including a multibody model of the occupant and a nonlinear finite element model of the seat, is provided, which can be used to re-construct variety of crash scenarios. These detailed models are useful in studies of the potential human injuries in a crash environment, injuries to the head, the upper spinal column, and the lumbar area, and also structural behavior of the seat. The problem of reducing head injuries to an occupant in case of a head contact with the surroundings (bulkhead, interior walls, or instrument panels), is then considered. The head impact scenario is re-constructed using a nonlinear visco-elastic type contact force model. A measure of the optimal values for the bulkhead compliance and displacement requirements is obtained in order to keep the possibility of a head injury as little as possible. This information could in turn be used in the selection of suitable materials for the bulkhead, instrument panels, or interior walls of an aircraft. The developed analysis tool also allows aircraft designers/engineers to simulate a variety of crash events in order to obtain information on mechanisms of crash protection, designs of seats and safety features, and biodynamic responses of the occupants as related to possible injuries. 

As an application of the theory discussed earlier, the crash responses of aircraft occupant/stnicture will be presented. To improve aircraft crash safety, conditions critical to occupants survival during a crash must be known. In view of the importance of this problem, studies of post-crash dynamic behavior of victims are necessary in order to reduce severe injuries. In this study, crash dynamics program SOM-LA/TA (Seat Occupant Model - Light Aircraft / Transport Aircraft) was used (13,14]. Modifications were performed in the program for reconstruction of an occupant s head impact with the interior walls or bulkhead. A viscoelastic-type contact force model of exponential form was used to represent the compliance characteristics of the bulkhead. Correlated studies of analytical simulations with impact sled test results were accomplished. A parametric study of the coefficients in the contact force model was then performed in order to obtain the correlations between the coefficients and the Head Injury Criteria. A measure of optimal values for the bulkhead compliance and displacement requirements was thus achieved in order to keep the possibility of a head injury as little as possible. This information could in turn be usm in the selection of suitable materials for the bulkhead, instrument panel, or interior walls of an aircraft. Before introducing the contact force model representing the occupant head impacting the interior walls, descriptions of impact sled test facilities, multibody dynamics and finite element models of the occupant/seat/restraint system, duplication of experiments, and measure of head injury are provided. 

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