【作者】 张书俊；

【导师】 任钧国；

【作者基本信息】 国防科学技术大学 ， 力学， 2006， 博士

【摘要】 采用数值模拟方法,系统地研究固体火箭发动机药柱结构的动态可靠度问题。基于通过改进的Monte Carlo模拟方法,分析了材料参数、载荷随机性对药柱结构分析的影响,并结合多种动态可靠度分析模型,探索了提高粘弹性药柱动态可靠度计算效率的途径,为固体火箭发动机药柱结构分析和设计提供了新的思路和依据。本文的主要研究内容如下:从Herrmann变分原理出发,发展了一种粘弹性增量有限元法,适用于所有泊松比下粘弹性问题的分析计算。针对三维药柱情况,为了进一步提高精度和效率,引入了一种高精度六面体有限元。该方法所需要的存储空间较少,精度和效率较高,为下一步的随机有限元分析奠定了基础。研究了随机过程和随机场的Monte Carlo模拟方法。通过随机场的离散化,实现了随机场向离散随机变量集合的转化,通过相关结构分解转换为独立的随机变量。探讨了三角级数合成方法模拟高斯平稳随机过程,着重研究了提高模拟效率的FFT方法。在AR和MA系统的基础上,研究了具有严格数学基础的ARMA模拟方法,为随机过程激励的模拟提供有力的工具。考虑泊松比、松弛模量等药柱材料参数的随机性,采用拉丁超立方体抽样技术来提高、改善抽样效率,考察参数随机性对药柱结构响应的影响。通过少量设计样本,基于二次多项式函数的响应面法构造有限元模型,进一步提高了计算效率,而且精度较高,能够应用于实际的工程。基于Hamilton变分原理,推导出了一种粘弹性结构动力响应的增量有限元法,适用于任意泊松比,为不可压缩或近似不可压缩粘弹性结构分析提供了更加精确和有意义的方法。考虑激励的随机性,基于Monte Carlo模拟方法,采用俄罗斯轮盘赌与分裂方法来处理响应样本,建立了结构系统动态响应样本重要性的判别准则,增加了样本在低失效概率区域出现的几率,大大提高了模拟效率。该方法能够直接用来分析非线性粘弹性结构的动态响应,能够提供更为精确的结果。基于Herrmann变分原理,采用Total Lagrangian方法,推导出了一种大变形粘弹性增量有限元法,能够处理任意泊松比的情况。结合改进的Monte Carlo模拟方法,分析药柱的准静态响应或动态响应的大变形问题,可以直接利用现有的确定性有限元分析程序,通用性强,非常适用于复杂药柱结构的随机响应问题。针对含随机参数的药柱结构,采用拉丁超立方体抽样方法和响应面法,在较少抽样样本的情况下,得到了系统响应在各个时刻的时域信息。结合药柱的失效判据,研究了系统的瞬态可靠度和动态可靠度。采用改进的Monte Carlo抽样方法模拟随机过程激励,只需要较少的抽样次数,就得到了较为精确的可靠度信息。总之,本文成功地将随机模拟方法应用于分析药柱随机结构和随机激励的可靠度问题,在方法和应用上取得了一定进展,为工程实际提供了切实有效的解决途径。更多还原

【Abstract】 Structure dynamic reliability of Solid Rocket Motor (SRM) grain is analyzed based on Monte Carlo viscoelastic stochastic finite element method. Advance technique is applied to increase the efficiency on account of the inefficiency of direct Monte Carlo simulation (MCS). Considering the randomness of grain material and exterior load, structure dynamic reliability is analyzed in combination with several reliability models, thus provides new ideas and reference for structural analysis and design of SRM grain. The main work and achievements of this paper are summarized as follows:Based on Herrmann variational principle, a new type of viscoelastic incremental finite element method is presented. It is suitable for nearly-incompressible viscoelastic grain. At the same time a hexahedron generalized conforming element with high accuracy are adopted in order to gain high precision for 3D grain. This method is accurate and effective, and needs less memory space, then provides the basis for viscoealstic stochastic analysis.Monte Carlo simulation method is used to simulate random field and stochastic process. Random field is translated to discrete random variables set, and then these correlated variables are converted into independent ones respectively through correlation structures factorization. Trigonometric series is used to simulate Gaussian stationary stochastic processes, and effective FFT method is adopted in particular. Based on AR and MA system, ARMA model with rigorous mathematic foundation offers the basis for simulating random excitation.Considering the randomness of Poisson ratio and relaxation modulus, Latin Hypercube Sampling technique is applied to increase the efficiency, then the relations of the random parameters and stochastic response is analyzed. On the basis of a series of numerical experiments with a few design points, response surface methodology based on second-order polynomial is comparative accurate and more effective, thus suitable for engineering application.Aiming at nearly incompressible effect and the deficiency of quasi-static analysis, a new type of incremental finite element method on the basis of Hamilton variational theorem is developed for dynamic response analysis of viscoelasticity structure. Considering the randomness of excitation, an efficient simulation procedure based on Monte Carlo simulation is presented. A simple criterion is established for indicating the importance of each dynamical response sample. According to this criterion, Russian Roulette&Split 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. This method can be directly used for stochastic analysis of nonlinear dynamical systems to gain more accurate result. Based on Herrmann variational principle and Total Lagrangian method, a new type of viscoelastic incremental finite element method with large deformation is presented. It is also suitable for nearly-incompressible viscoelastic grain. In combination with improved Monte Carlo simulation method, it is suitable for stochastic response of complex grain with large deformation.Considering the randomness of SRM grain material parameters, Latin Hypercube Sampling and response surface methodology need fewer samples to gain adequacy stochastic response information. Dynamic reliability and its variational trend of the SRM grain are analyzed in combination with failure criterion. Random load is simulated by improved Monte Carlo simulation method, and reliability is quite accurate with less effort.In conclusion, efficient simulation procedures have been successfully applied to analyzed structure reliability of SRM grain with stochastic parameters or under random excitation. Some developments have been gained both in methods and applications. The research in this paper offers an effective and universal approach for engineering application.更多还原