【作者】 田四朋；

【导师】 唐国金；

【作者基本信息】 国防科学技术大学 ， 航空宇航科学与技术， 2007， 博士

【摘要】 固体火箭发动机药柱结构完整性分析及贮存寿命预估是设计、生产和使用部门非常关注的关键问题。固体推进剂具有粘弹性和近似不可压缩性,其材料性能和载荷环境参数通常不能精确给出。因此,进行含随机参数固体火箭发动机药柱结构完整性分析及贮存寿命预估研究具有重要的理论意义和应用价值。本文以固体火箭发动机药柱为对象,深入系统地研究了三维粘弹性随机有限元法,分析了多种载荷作用下结构的随机响应和可靠度,提出了基于粘弹性随机有限元法和老化试验的概率贮存寿命预估模型。主要研究内容如下:发展了不可压和近似不可压三维粘弹性增量有限元法。由Herrmann变分原理和对应原理出发得到了不可压和近似不可压粘弹性材料的积分型本构关系,然后利用增量法处理遗传积分,根据虚功原理给出了三维粘弹性有限元列式,推导过程中考虑了材料性能对温度的依赖关系。该方法可用于分析泊松比接近甚至等于0.5的粘弹性问题,为药柱的粘弹性随机有限元分析奠定了基础。研究和改进了三维粘弹性Monte Carlo随机有限元法。针对简单随机抽样计算量大的缺点,引入Latin超立方抽样技术以提高计算效率。采用该方法详细研究了药柱结构随机响应的正态性、随机参数与响应之间的函数关系以及随机参数的概率灵敏度,为发展其它形式的粘弹性随机有限元法奠定了基础。研究了三维粘弹性摄动随机有限元法。基于不可压和近似不可压三维粘弹性有限元法,采用一阶摄动技术处理随机参数,推导了三维粘弹性摄动随机有限元法的递推方程组,并给出了结构响应统计特征的求解方法,推导过程中同时考虑了固体推进剂力学性能和载荷环境的随机性。研究结果表明三维粘弹性摄动随机有限元法计算效率较高,且精度能够满足工程需要。提出了三维粘弹性谱随机有限元法。基于不可压和近似不可压三维粘弹性有限元法和正交展开理论,考虑固体推进剂泊松比的随机性,推导了三维粘弹性谱随机有限元法的扩阶方程。研究结果显示,粘弹性谱随机有限元法能够考虑参数随机性对结构响应均值的影响,其计算精度高于粘弹性一阶摄动随机有限元法。研究了三维粘弹性响应面随机有限元法,实现了具体型号固体火箭发动机药柱的随机结构分析。基于中心复合设计技术获得了输入、输出随机参数的多组试验值,由最小二乘法估计响应面函数的各项系数,结合Monte Carlo方法分析了某型固体火箭发动机药柱结构在不同发射条件下的随机响应。研究了结构可靠度算法,实现了具体型号固体火箭发动机药柱的结构可靠度分析。根据所选择的固体推进剂破坏判据,运用应力—强度干涉理论建立了药柱结构可靠度模型,针对不同类型粘弹性随机有限元法的特点,给出了相应的可靠度算法,研究了可靠指标与安全系数之间的对应关系,分析了某型号发动机药柱在不同发射条件下的结构可靠度。提出了基于粘弹性随机有限元法和固体推进剂高温加速老化试验的固体火箭发动机药柱概率贮存寿命预估模型。通过对老化试验数据进行统计分析得到了固体推进剂性能参数数字特征随贮存时间的变化规律,采用三维粘弹性响应面随机有限元法计算了药柱响应的均值和标准差,最后分析了某型固体火箭发动机药柱在不同贮存期的结构可靠度,并预估了其概率贮存寿命。本文的研究成果对含随机参数固体火箭发动机药柱的结构完整性分析及贮存寿命预估具有重要的指导作用,所提出的方法及分析结论可为固体火箭发动机设计、制造和使用部门参考。更多还原

【Abstract】 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.更多还原