As NASA moves towards developing technologies needed to implement its new Exploration program, studies conducted for Apollo in the 1960s to understand the rollover stability of capsules landing are being revisited. Although rigid body kinematics analyses of the rollover behavior of capsules on impact provided critical insight to the Apollo problem, extensive ground test programs were also used. For the new Orion spacecraft, airbag designs have improved sufficiently for NASA to consider their use to mitigate landing loads to ensure crew safety and to enable reusability of the capsule.

Simple kinematics models provide only limited understanding of the behavior of these airbag systems, and more sophisticated tools must be used. In particular, NASA and its contractors are using the LS-Dyna nonlinear simulation code for impact response predictions of the full Orion vehicle with airbags by leveraging the extensive airbag prediction work previously done by the automotive industry. However, even in today’s computational environment, these analyses are still high-dimensional, time-consuming, and computationally intensive. To alleviate the computational burden, a new approach uses deterministic sampling techniques and an adaptive response surface method to not only use existing LS-Dyna solutions, but also to interpolate from LS-Dyna solutions to predict the stability boundaries for a capsule fitted with airbags.

Two aspects of this approach are relatively unique: the use of adaptive response surface techniques, and the use of deterministic sampling to create multiple parameter values for statistical analyses. The Moving Least Squares (MLS) adaptive response surface technique is used to predict time responses outside the parameter set computed using LS-Dyna. The Halton-leaped deterministic sampling approach is used to efficiently sample the parameter space and to parallelize the computations to take advantage of multiple computers. An added benefit of using Halton-leaped parameter sampling is that if additional LS-Dyna runs are needed to improve accuracy, the method easily creates new parameter samples without the risk of duplicating existing solutions.

For this study, the MLS technique provides predictions better than 10 percent for most of the cases studied at a fraction of the computational cost of new LS-Dyna runs. Using the MLS surrogate model, predictions of the stability boundaries showing the interaction of parameters like horizontal and vertical velocity, pitch angles, and friction can all be studied independently of LS-Dyna after a core set of solutions is computed. In the case studied, 90° rollover of the capsule is most likely to occur for horizontal velocities from 460 in./s to 490 in./s (≈11.7 to 12.5 m/s), and friction coefficients from 0.6 to 1.

The computational procedure developed allows for the stability analysis of complex nonlinear systems using commercially available nonlinear codes. Results from these computationally intensive codes are collected and used externally to the program to make predictions about non-existent solutions. This ability reduces the computational time significantly and allows users to obtain estimates at a fraction of the maxon product range time otherwise required. In fact, for problems where the computational time is measured in days, this approach can provide estimates otherwise unattainable within reasonable time constraints.

This work was done by Lucas Horta and Mercedes Reaves of Langley Research Center. LAR-17628-1