Solid Rocket Motor Grain The Viscoelastic Uncertainty Structure Analysis

Solid Rocket Motor (SRM) grain is casted integrally from solid propellants. It is one of the important structural components and also provides fuels for SRM. The reliability of SRM grain should be paid great attention. However, solid propellant is viscoelastic and nearly-incompressible, and the material parameters and load process can't be given accurately in general. So it has important value both on theory and practical application to perform uncertain structural analysis for SRM grain. The main purpose of this paper is to establish viscoelastic stochastic finite element method and non-probabilistic method for uncertain structural analysis of SRM grain. Several reliability models are analyzed and structural response of SRM grain with random parameters under different loads is investigated. The main work and achievements are summarized as follows:Based on Herrmann variational principle and the nearly-incompressible viscoelastic constitutive relation, a new type of viscoelastic incremental finite element method is presented. In this method, incremental arithmetic is applied to solving the hereditary integrals. It needs less memory space, has simple parameter matrix, and calculates stiffness matrix only once. The method is suitable for structural analysis of SRM grain, and furthermore, provides the basis for viscoelastic uncertain analysis.A new type of viscoelastic stochastic finite element method is established using first-order perturbation theory based on local averaging method of random field and Karhunen-Loeve expansion theory of random process. The amount of computations is greatly reduced by transforming correlated random variables to a set of uncorrelated random variables. The relations of different random response variables are analyzed and Monte Carlo simulations for viscoelastic stochastic structures are investigated. The application of stochastic perturbation method to viscoelastic problems doesn't result in the emergence of undesirable secular terms although the viscoelastic constitutive relation is time-dependent.The stochastic principle of virtual work is formulated for viscoelastic structural analysis. The innovated principle has solid theoretical basis and allows incorporation of different kinds of random factors. By using vector random field model and second-order perturbation method, viscoelastic stochastic finite element formulation is developed, which can take the correlation of random parameters into account and is suitable for stochastic structural analysis with larger variance of the uncertainties.The stochastic equation of virtual work based on Total Lagrangian method is developed to analyze the influences of vicoelasticity, large deformation and randomness simultaneously. The nonlinear equilibrium equations of viscoelasticstochastic FEM are derived. The full Newton-Raphson method is used to get the numerical solutions. This developed method is suitable for SRM grain with low modulus and large deformation.Convex models are defined to describe the uncertainties of parameters in SRM grain. Perturbation method is used to predict the variability of structural response. By comparing with stochastic structural analysis, relations between the two methods have been found. The response surface method is used to obtain the second order estimates of the calculated results bound.By means of viscoelastic stochastic finite element method, the instantaneous reliability, the first passage reliability and fuzzy reliability of SRM grain are investigated. The influences of uncertain parameters on SRM grain structures are studied. Viscoelastic stochastic FEM can not only calculate reliability index, but also determine the accuracy requirement for parametric testing according to given reliability.In conclusion, viscoelastic uncertain structural analysis methods have been successfully established for SRM grain. Some developments have been gained both in methods and applications. The research in this paper lays a foundation for further investigation of practical SRM grain structures.