Structural Dynamic Reliability of Solid Rocket Motor Grains

Abstract

Analytical methods to predict the stochastic response of MDOF-system are quite limited [1]. In fact numerical procedures, such as Monte Carlo simulation (MCS) techniques are the only available methods to treat practical reliability problems. Direct Monte Carlo simulation, however, requires a substantial amount of computer time and resources. Variance reduction techniques such as importance, directional, etc, are utilized to increase the efficiency of Monte Carlo simulation for analysis of complex dynamical system. This paper proposes an efficient simulation procedure for stochastic analysis of nonlinear dynamical systems with multi-degree freedom, namely rocket solid motor grains, based on Monte Carlo simulation. A simple criterion is established for indicating the importance of each dynamical response sample. According to this criterion, Russian Roulette & Split (RRS) method is applied to deal with the selected samples. The efficiency of this algorithm is much higher than that of direct MCS while the number of response samples in the low probability regions is increased. Then, structure dynamic reliability of grains was analyzed based on Monte Carlo viscoelastic stochastic finite element method. On the basis of nearly incompressible viscoelastic deterministic finite element method, this efficient simulation procedure was applied to increase the efficiency on account of the inefficiency of direct Monte Carlo simulation. Considering the randomness of internal press when motor starts, reliability and its variational trend of the solid rocket motor grain under internal pressure was analyzed in combination with failure criterion and minimal transform.