3D Viscoelastic Stochastic Finite Element Analysis And Probabilistic Storage Life Prediction Of Solid Rocket Motor Grain

Structural integrity analysis and storage life prediction of grain is a critical problem for the designers, manufacturers and users of Solid Rocket Motor (SRM).As solid propellant is a kind of viscoelastic and nearly incompressible material, its property parameters and load/environment parameters can't be given accurately in general. Therefore, it is of important value both on theory and application to research structural integrity analysis and storage life prediction of SRM grain with random parameters. Taking SRM grain as the object, a deep investigation is conducted about 3D viscoelastic Stochastic Finite Element Method (SFEM) systematically, random response and structural reliability of grain under different loads are analyzed, and a probabilistic storage life prediction model based on viscoelastic SFEM and aging test is proposed in this dissertation. The main work and achievements are summarized as follows:Incompressible and nearly incompressible 3D viscoelastic incremental Finite Element Method (FEM) is developed. Based on Herrmann variational prinple and correspondence principle, integral constitutive relation of incompressible and nearly incompressible viscoelastic material is derived, incremental arithmetic is applied to solve the hereditary integral and 3D viscoelastic finite element formulations are obtained in terms of the principle of virtual work. During the derivation, the dependence relation between material properties and temperature is considered. This method is suitable for viscoelastic problems whose Poisson's ratio is close even equal to 0.5 and it provides the basis for viscoelastic stochastic finite element analysis of grain.3D Viscoelastic Monte Carlo SFEM (VMCSFEM) is researched and developed. Latin Hypercube Sampling (LHS) technique is introduced to enhance computing efficiency because of the deficiency of simple random sampling. Normality of response, functional relations between parameters and response, and probabilistic sensitivity of random parameters are all investigated in detail based on VMCSFEM. This research provides the basis for developing other viscoelastic SFEMs.3D Viscoelastic Perturbation SFEM (VPSFEM) is researched. Based on incompressible and nearly incompressible viscoelastic FEM, first order perturbation technique is applied to deal with random parameters. Recursive formulations of 3D VPSFEM are derived and the solution method for evaluating statistical characters of structural response is also presented. The randomicity of solid propellant mechanical properties and load/environment parameters is taken into account in the derivation process. The results show that 3D VPSFEM is efficient, and its accuracy can meet practical engineering requirements. 3D Viscoelastic Spectral SFEM (VSSFEM) is proposed. Considering the randomicity of solid propellant Poisson's ratio, 3D viscoelastic spectral stochastic finite element formulations are derived based on incompressible and nearly incompressible viscoelastic FEM and orthogonal expansion theory. The results show that VSSFEM can consider the influence of random parameter on structural response mean value, so its accuracy is higher than viscoelastic first order perturbation SFEM.3D Viscoelastic Response Surface SFEM (VRSSFEM) is researched and stochastic structural analysis of a practical SRM grain is achieved. Multiple experimental points of input-output parameters are obtained by central composite design technique. The coefficients of the response surface function are acquired by the least square method. Under different ignition conditions, stochastic response analysis of a certain SRM grain is completed based on the response surface function and Monte Carlo method.Structural reliability arithmetics are investigated and structural reliability of a practical SRM grain is analyzed. Stress-strength interference theory is applied to establish structural reliability model of SRM grain based on the selected failure criterion of solid propellant, and corresponding reliability analysis arithmetics are presented in account with different viscoelastic SFEMs. The relation between reliability index and safety factor is investigated, and structural reliability of a certain SRM grain under different ignition conditions is evaluated.A probabilistic storage life prediction model of SRM grain is proposed based on viscoelastic SFEM and temperature accelerated aging test of solid propellant. Variation tendency along with storage time of digital characteristics of solid propellant property parameters is obtained by statistical analysis of aging test data, and the mean value and standard deviation of grain response is calculated by 3D VRSSFEM. Structural reliability of a certain SRM grain at different storage time is analyzed and probabilistic storage life of this grain is predicted.The achievements obtained in this dissertation provide an important guidance to the structural integrity analysis and storage life prediction of SRM grain with random parameters. The methods and conclusions would be available for the designers, manufacturers and users of SRM.