固体火箭发动机粘弹性药柱的动态可靠度分析
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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。
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.
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。
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.
引文
[1] 陈汝训, 固体火箭发动机设计与研究, 北京: 宇航出版社, 1991.
[2] 谭三五,王秉勋, 固体火箭发动机结构可靠性数字仿真的基本问题, 推进技术,1993,4: 47~54.
[3] 王铮, 固体火箭发动机使用寿命的预估和“延寿”, 推进技术,1999,22(1): 23~28.
[4] 胡昌寿, 可靠性工程-设计、试验、分析、管理, 北京: 宇航出版社, 1998.
[5] Collins J.D.,Thompson W.T., The eigenvalue problem for structural systems with uncertain parameters, AIAA. J.,1969,7(4): 642~648.
[6] Chen P.C.,Soroka W.W., Impulse response of a dynamic system with statistical properties, Journal of Sound and Vibration,1973,31(3): 309~314.
[7] 李杰, 随机结构系统-分析与建模, 北京: 科学出版社, 1996.
[8] 郝志明, 随机结构有限元法及可靠性研究, 北京: 中国工程物理研究院博士学位论文, 2001.
[9] Hien T.D.,Kleiber M., Stochastic finite element modeling in linear transient heat transfer, Comput. Methods Appl. Mech. Engrg.,1997,144: 111~124.
[10] Liu W.K.,Belytschko T.,Mani A., Random field finite elements, Int. J. Numer. Meths. Engrg.,1986,23(10): 1831~1845.
[11] Liu W.K.,Belytschko T.,Mani A., Probabilistic finite elements for nonlinear structural dynamics, Comput. Methods Appl. Mech. Engrg.,1986,56(1): 61~81.
[12] Liu W.K.,Besterfield G.,Belytschko T., Transient probabilistic systems, Comput. Methods Appl. Mech. Engrg.,1988,67(1): 27~54.
[13] Hien T.D.,Kleiber M., Stochastic structural design sensitivity of static response, Comput. Struct.,1991,38(5-6): 659~667.
[14] 张海联, 固体火箭发动机药柱的粘弹性不确定结构分析, 长沙: 国防科学技术大学博士学位论文, 2002.
[15] Liu P.L.,Kiureghian A.D., Finite element reliability of geometrically nonlinear uncertain structures, J. Engrg. Mech.,1991,117(8): 1806~1825.
[16] Ryu R.S. et al., Structural design sensitivity analysis of nonlinear response, Comput. Struct.,1985,21(2): 245-255.
[17] Haldar A.,Zhou Y., Reliability of geometrically nonlinear pr frams, J. Engrg. Mech.,1992,118(10): 2148~2155.
[18] Chang C.,Yang H.T.Y., Reliability of uncertain flexible laminated skewed plated under random compressions, AIAA J.,1992,30(2): 464~472.
[19] Engelasted S.P.,Reddy J.N., Probability nonlinear finite element analysis of composite structures, AIAA J.,1993,31(2): 362~369.
[20] 刘宁,卓家寿, 三维弹塑性随机有限元迭代计算方法研究, 河海大学学报,1996,24(1): 1~8.
[21] 刘宁,卓家寿, 基于三维弹塑性随机有限元的可靠度计算, 水利学报,1996,9: 53~62.
[22] 赵雷,陈虬, 不确定性结构非线性动力分析的增量随机有限元法, 工程力学增刊,1996: 353~357.
[23] Pradlwarter H.J.,Schueller G.I.,Schenk C.A., A computational procedure to estimate the stochastic dynamic response of large non-linear fe-models, Comput. Methods Appl. Mech. Engrg.,2003,192(7-8): 777~801.
[24] 赵雷,陈虬, 随机有限元动力分析方法的研究进展, 力学进展,1999,29(1): 9~18.
[25] Jenesn H.,Iwan W.D., Response variability in structural dynamics, Earthquake Engineering and Structural Dynamics,1991,20: 949~959.
[26] Lawrence M.A., Basic random variables in finite analysis, Int. J. Numer. Meths. Engrg.,1987,24: 1849~1863.
[27] Kiureghian A.D.,Ke J.B., The stochastic finite element method in structural reliability, Probabilistic Engineering Mechanics,1988,3(2): 83~91.
[28] Zeldin B.A.,Spanos P.D., On random field discretization in stochastic finite elements, J. Appl. Mech.,1998,65(2): 320~327.
[29] 秦权, 随机有限元及其进展 i.随机场的离散和反应矩的计算, 工程力学,1994,11(4): 1~10.
[30] Vanmarcke E., Stochastic finite elements and experimental measurements, Probabilistic Engineering Mechanics,1994,9(1-2): 103~114.
[31] 朱位秋,任永坚, 随机场的局部平均与随机有限元, 航空学报,1986,7(6): 604~612.
[32] 朱位秋,任永坚, 基于随机场局部平均的随机有限元法, 固体力学学报,1988,4: 285~292.
[33] 朱位秋,吴伟强, 基于随机场局部平均的随机有限元法在实特征值问题中的应用, 航空学报,1989,10(2): 20~26.
[34] Zhu W.Q.,Ren Y.J.,Wu W.Q., Stochastic fem based on local averages of random vector fields, J. Engrg. Mech.,1992,118(3): 496~511.
[35] Deodatis G., Bounds on response variability of stochastic finite element systems, J. Engrg. Mech.,1990,116(3): 565~585.
[36] Ghanem R.G.,Spanos P.D., Polynomial chaos in stochastic finite elements, J. Appl. Mech.,1990,57: 197~202.
[37] Ghanem R.G.,Spanos P.D., Stochastic finite elements: A spectral approach, New York: Springer-Verlag, 1991.
[38] Ghanem R.G.,Kruger R.M., Numerical solution of spetral stochastic finite element systems, Comput. Methods Appl. Mech. Engrg.,1996,129: 289~303.
[39] Jensen H.,Iwan W.D., Response of systems with uncertain parameters to stochastic excitation, J. Engrg. Mech.,1992,118(5): 1012~1025.
[40] Iwan W.D.,Jensen H., On the dynamic response of continuous systems including model uncertainty, J. Appl. Mech.,1993,60(2): 484~490.
[41] 李杰, 随机结构分析的扩阶系统方法(i)扩阶系统方程, 地震工程与工程振动,1995,15(3): 111~118.
[42] 李杰, 随机结构分析的扩阶系统方法(ii)结构动力分析, 地震工程与工程振动,1995,15(4): 27~35.
[43] 李杰, 随机结构动力分析的扩阶系统方法, 工程力学,1996,13(1): 93~102.
[44] 李杰, 线性随机结构在随机激励下动力响应分析, 力学学报,2002,34(3): 416~423.
[45] 李杰,魏星, 随机结构动力分析的递归聚缩算法, 固体力学学报,1996,17(3):263~267.
[46] Shinozuka M.,Astill J., Random eigenvalue problems in structural mechanics, AIAA J.,1972,10(4): 456~462.
[47] Shinozuka M., Probabilistic modeling of concrete structures, J. Engrg. Mech.,1972,8: 1433~1451.
[48] Shinozuka M.,Deodatis G., Response variability of stochastic finite element systems, J. Engrg. Mech.,1988,114(3): 499~519.
[49] Yamazaki F.,Shinozuka M.,Dasgupta G., Neumann expansion for finite element analysis, J. Engrg. Mech.,1988,114(8): 1335~1354.
[50] 刘宁,吕泰仁, 随机有限元及其工程应用, 力学进展,1995,25(1): 114~126.
[51] Chakraborty S.,Dey S.S., Stochastic finite element simulation of random structure on uncertain foundation under random loading, Int. J. Mech. Sci.,1996,38(11): 1209~1218.
[52] Chakraborty S.,Dey S.S., A stochastic finite element dynamic analysis of structures with uncertain parameters, Int. J. Mech. Sci.,1998,40(11): 1071~1087.
[53] 陈顺祥,郝志明, 纽曼随机有限元分析复合材料回旋结构的可靠性及其优化设计, 强度与环境,1998,4: 49~54.
[54] 郝志明,张铎,姜晋庆,陈儒,陈顺祥, 结构可靠性的纽曼展开蒙特卡罗随机有限元分析, 固体力学学报,1999,20(4): 320~324.
[55] Papadrakakis M.,Kotsopulos A., Parallel solution methods for stochastic finite element analysis using monte carlo simulation, Comput. Methods Appl. Mech. Engrg.,1999,168: 305~320.
[56] Johnson E.A.,Proppe C.,Spencer Jr B.F.,Bergman L.A.,Szekely G.S.,Schueller G.I., Parallel processing in computational stochastic dynamics, Probabilistic Engineering Mechanics,2003,18(1): 37~60.
[57] Liu W.K.,Ong J.S.,Uras R.A., Finite element stabilization matrices-a unification approach, Comput. Meths. Appl. Mech. Engrg.,1985,53: 13~46.
[58] Liu W.K.,Besterfield G.H.,Belytschko T., Variational approach to probabilistic finite elements, J. Eng. Mech.,1988,114(12): 2115~2133.
[59] Hien T.,Kleiber M., Finite element analysis based on stochastic hamilton variational principle, Comput. Struct.,1990,37(6): 893~902.
[60] 张汝清 , 高行山 , 随机变量的变分原理及有限元法 , 应用数学和力学,1992,13(5): 383~388.
[61] 张汝清,高行山, 有限变形弹性理论随机变量变分原理及有限元法, 应用数学和力学,1994,15(10): 855~862.
[62] 刘宁,刘光廷, 大体积混凝土结构温度场的随机有限元方法, 清华大学学报,1996,36(1): 41~47.
[63] Ren Y.J.,Elishakoff I., Finite element method for stochastic beams based on variational principle, J. Appl. Mech.,1997,64: 664~669.
[64] 赵雷,陈虬, 结构动力分析的随机变分原理及随机有限元法, 计算力学学报,1998,15(3): 263~274.
[65] 杨绿峰,高兑现,李桂青, 随机结构在随机激励下的二阶摄动随机势能泛函及其应用, 应用力学学报,1999,16(4): 35~39.
[66] Mckay M.D.,Beckman R.J.,Conover W.J., A comparison of three methods for selecting values of input variables in the analysis of output from a computercode, Technometrics,1979,2: 239~245.
[67] 周渊, 关于蒙特卡罗模拟抽样方法的研究, 强度与环境,1997,3: 14~18.
[68] 朱位秋, 随机振动, 北京: 科学出版社, 1998.
[69] 庄表中,梁以德,张佑启, 结构随机振动, 北京: 国防工业出版社, 1995.
[70] 欧进萍,王光远, 结构随机振动, 北京: 高等教育出版社, 1998.
[71] Schueller G.I.,Pradlwarter H.J.,Schenk C.A., Non-stationary response of large linear fe models under stochastic loading, Comput. Struct.,2003,81: 937~947.
[72] Kiureghian A.D.,Neuenhofer A., Response spectrum method for multi-support seismic excitations, Earthquake Engineering and Structural Dynamics,1992,21(8): 713~740.
[73] Zavoni E.H.,Venmark E.H., Seismic random vibration analysis of multi-support structural systems, J. Engrg. Mech.,1994,120(5): 1107~1128.
[74] Lin J.H.,Zhong W.X.,Zhang W.S.,Sun D.K., High efficiency computation of the variances of structural of evolutionary random responses, Shock and Vibration,2000,7(4): 209~216.
[75] Oksendal B., Stochastic differential equations,4th ed., Berlin: Springer-Verlag, 1995.
[76] 林家浩, 随机地震响应的确定性算法, 地震工程与工程振动,1985,5(1): 89~93.
[77] Lin J.H.,Zhang W.S.,Williams F.W., Pseudo-excitation algorithm for nonstationary random seismic response, Engineering structures,1994,16: 270~276.
[78] Lin J.H.,Zhang W.S.,Li J.J., Structural response to arbitrarily coherent stationary random excitations, Comput. Struct.,1994,44(3): 683~687.
[79] 林家浩,沈为平,宋华茂,孙东科, 结构非平稳随机响应的混合型精细时程积分, 振动工程学报,1995,8(2): 127~135.
[80] Lin J.H.,Sun D.K.,Sun Y.,Williams F.W., Structural response to non-uniformly modulated evolutionary random seismic excitations, Communications in numerical methods in engineering,1997,13: 605~616.
[81] 林家浩,张亚辉,孙东科,孙勇, 受非均匀调制演变随机激励结构响应快速精确计算, 计算力学学报,1997,14(1): 2~8.
[82] 钟万勰, 应用力学对偶体系, 北京: 科学出版社, 2002.
[83] Caughey T.K.,Ma F., The exact steady-state solution of a class of non-linear stochastic systems, Int. J. Non-Linear Mechanics,1982,17(3): 137~142.
[84] 朱位秋, 非线性随机动力学与控制, 北京: 科学出版社, 2003.
[85] 赵雷,陈虬, 分析非线性系统随机响应的一种等效非线性化方法, 应用数学与力学,1997,18(6): 513~521.
[86] 缪炳祺,许礼深,胡夏夏, 非线性系统非平稳随机响应矩计算的 newmark 递推算法, 振动工程学报,1997,10(2): 242~246.
[87] 张明 , 非线性随机振动等效线性化的一种推广 , 西南交通大学学报,1998,33(1): 77~81.
[88] Shinozuka M., Monte carlo solution of structural dynamics, Int. J. Comput. and Struct.,1972,2: 855~874.
[89] Shinozuka M.,Jan C.M., Digital simulation of random process and its applications, Journal of Sound and Vibration,1972,25: 111~128.
[90] Shinozuka M., Monte carlo solution of nonlinear vibrations, AIAA J.,1972,10(1): 37~40.
[91] Tsurui A.,Ishikawa H., Application of the fokker-planck equation to a stochastic fatigue crack growth model, Structural Safety,1986,4(1): 15~30.
[92] Tanaka H.,Tsurui A., Reliability degradation of structural components in the process of fatigue crack propagationunder stationary random loading, Eng. Fract. Mech.,1987,27: 501~516.
[93] Papadimitriou C.,katafygiotis L.S.,Beck J.L., Approximate analysis of response variability of uncertain linear systems, Probabilistic Engineering Mechanics,1995,10(4): 251~264.
[94] Zhao L.,Chen Q., Neumann dynamic stochastic finite element method of vibration for structures with stochastic parameters to random excitation, Comput. Struct.,2000,77(6): 651~657.
[95] 王元战,周晶,周锡, 随机过程激励下随机结构系统可靠度分析的一种方法, 固体力学学报,1998,19(2): 106~111.
[96] 林家浩,易平, 线性随机结构的平稳随机响应, 计算力学学报,2001,18(4): 402~408.
[97] 易平,林家浩,赵岩, 线性随机结构的非平稳随机响应变异性分析, 固体力学学报,2002,23(1): 93~97.
[98] 李杰, 复合随机振动分析的扩阶系统方法, 力学学报,1996,28(1): 66~75.
[99] 戴君,陈建军,马洪波, 随机参数结构在随机载荷激励下的动力响应分析, 力学学报,2002,19(3): 64~68.
[100] 何水清,王善, 结构可靠性分析与设计, 北京: 国防工业出版社, 1993.
[101] Rackwitz R.,Fiessler B., Structural reliability under combined random load sequences, Comput. Struct.,1978,9: 489~494.
[102] Chen X.,Lind N.C., Fast probability integration by three parameter normal tail approximation, Structural Safety,1983,1(4): 269~276.
[103] Wu Y.T., Computational methods for efficient structural reliability and reliability sensitivity analysis, AIAA J.,1994,32(8): 1717~1723.
[104] 董聪, 现代结构系统可靠性理论与应用, 北京: 科学出版社, 2000.
[105] Karamchandani A.,Cornell C.A., Sensitivity estimation within first and second order reliability methods, Structural Safety,1992,11(2): 95~107.
[106] 董聪,夏人伟, 现代结构系统可靠性评估理论研究进展, 力学进展,1995,25(4): 537~548.
[107] 张炳根,赵玉芝, 科学与工程中的随机微分方程, 北京: 海洋出版社, 1980.
[108] 李桂青,曹宏,李秋胜, 结构动力可靠性理论及其应用, 北京: 地震出版社, 1993.
[109] Veneziano D.,Grigorio M.,Conell C.A., Vector-process models for system reliability, J. Engrg. Mech.,1977,103(3): 441~460.
[110] Ditlevsen O., Gaussian oucrossings from safe convex polyhedrons, J. Engrg. Mech. Div.,1983,109(1): 127~148.
[111] Ang A.H.,Chaker A.A.,Abdelnour J., Analysis of activity network under uncertainty, J. Engrg. Mech. Div.,1975,101(4): 373~387.
[112] Moses F., System reliability development in structural engineering, Structural Safety,1982,1(1): 3~13.
[113] Melchers R.E.,Tang L.K., Dominant failure models in stochastic structural systems, Structural Safety,1982,1(1).
[114] Feng Y.S., Enumerating significant fail mode of structural system by using criterion methods, Comput. Struct.,1988,50(5): 1153~1157.
[115] Feng Y.S.,Moses F.A., Method of structural optimization based on structural system reliability, J. Struct. Mech.,1986,14(4): 437~453.
[116] 董聪, 结构系统可靠性理论:进展与回顾, 工程力学,2001,18(4): 79~88.
[117] Cornell C.A., Bounds on the reliability of structural systems, J. Struct. Div.,1967,93: 171~200.
[118] Ditlevsen O., Narrow reliability bounds for structural system, J. Struct. Mech.,1979,7(4): 453~472.
[119] Vanmarcke E.H., Matrix formulation of reliability analysis and reliability-based design, Comput. Struct.,1973,3: 757~770.
[120] Hohenbichler M.,Rackwitz R., First order concepts in system reliability, Structural Safety,1983,1(3): 177~188.
[121] Der K.A.,Ke J., Stochastic finite element method in structural reliability, Probabilistic Engineering Mechanics,1988,3(2): 83-91.
[122] Kiureghian A.D.,Zhang Y., Space-variant finite element reliability analysis, Comput. Methods Appl. Mech. Engrg.,1999,168(1-4): 173~183.
[123] Madsen H.O.,Tvedt L., Methods for time-dependent reliability and sensitivity analysis, J. Engrg. Mech.,1990,116(10): 2118~2135.
[124] Mahadevan S.,Mehta S., Dynamic reliability of large frames, Comput. Struct.,1993,47(1): 57~67.
[125] 管昌生,高兑现,李桂青, 抗震结构时变动力可靠度分析的随机过程法, 应用力学学报,1997,14(1): 70~76.
[126] 刘宁,刘光廷, 混凝土结构温度徐变应力的首次超越可靠度, 固体力学学报,1998,19(1): 38~44.
[127] Kahn H., Application of monte carlo, AECU-3259,1954.
[128] Bucher C.G., Adaptive sampling - an iterative fast monte carlo procedure, Structural Safety,1988,5(2): 119~126.
[129] Mori Y.,Ellingwood B., Time-dependent system reliability analysis by adaptive importance sampling, Structural Safety,1993,12(1): 59~73.
[130] Ziha K., Descriptive sampling in structural safety, Structural Safety,1995,17: 33~41.
[131] 吕震宙,岳珠峰, 结构可靠度计算中的描述抽样法, 力学与实践,1998,20: 52~54.
[132] Qi E.,Cui W., Latin hypercube sampling in ultimate strength reliability of ship hull girder, Journal of Ship Mechanics,2002,3: 52~60.
[133] Melchers R.E., Importance sampling in structural systems, Structural Safety,1989,6(1): 3~10.
[134] Melchers R.E., Search-based importance sampling, Structural Safety,1990,9(2): 117~128.
[135] Ibrahim Y., Observations on applications of importance sampling in structural reliability analysis, Structural Safety,1991,9(4): 269~281.
[136] Maes M.A.,Breitung S.,Dupuis D.J., Asymptotic importance sampling, Structural Safety,1993,12(3): 167~186.
[137] Engelund S.,Rackwitz R., A benchmark study on importance sampling techniques in structural reliability, Structural Safety,1993,12(4): 255~276.
[138] 李亚东, 重要抽样模拟及其在结构可靠度计算中的应用, 西南交通大学学报,1992,4: 105~110.
[139] 丁克勤,柳春图, 重要抽样法在管点疲劳可靠性分析中的应用, 力学学报,1996,28(3): 359~362.
[140] 李强,冯元生, 结构可靠性问题的改进分层抽样法, 航空学报,1995,16(5): 513~520.
[141] 沙风焕, 压力容器接管断裂失效概率计算, 石油化工设备,1999,28(3): 35~37.
[142] Wu Y.T.,Millwater H.R.,Cruse T.A., Advanced probabilistic structural analysis methods for implicit performance functions, AIAA J.,1990,28(9): 1663~1669.
[143] 吴斌,欧进萍,张纪刚,吕大刚, 结构动力可靠度的重要抽样法, 计算力学学报,2001,18(4): 478~482.
[144] Harnpornchai N.,Pradlwarter H.J.,Schueller G.I., Stochastic analysis of dynamical systems by phase-space-controlled monte carlo simulation, Comput. Methods Appl. Mech. Engrg.,1999,168: 273~283.
[145] Schueller G.I.,Pradlwarter H.J.,Bucher C.G., Efficient computational procedures for reliability estimations of mdof-systems, International Journal of Non-Linear Mechanics,1991,26(6): 961~974.
[146] Pradlwarter H.J.,Schueller G.I.,Melnikov P.G., Reliability of mdof systems, Probabilistic Engineering Mechanics,1994,9(4): 235~243.
[147] Pradlwarter H.J.,Schueller G.I., On advanced monte carlo simulation procedures stochastic structural dynamics, Int. J. Non-Linear Mechanics,1997,32(4): 735~744.
[148] Proppe C.,Pradlwarter H.J.,Schueller G.I., Equivalent linearization and monte carlo simulation in stochastic dynamics, Probabilistic Engineering Mechanics,2003,18(1): 1~15.
[149] 裴鹿成, 蒙特卡罗方法及其在粒子输运问题中的应用, 北京: 科学出版社, 1980.
[150] 张书俊,任钧国, 非线性随机动态响应的高效模拟方法, 国防科技大学学报,2006,28(1): 117~120.
[151] 董聪, 结构可靠性理论与模拟算法, 强度与环境,1997,4: 51~61.
[152] Faravelli L., A response surface method approach for reliability analysis, J. Engrg. Mech.,1989,115(12): 2763~2781.
[153] Schueller G.I.,Bucher C.G.,Bourgund U., On efficient computational schemes to calculate structural failure probabilities, Probabilistic Engineering Mechanics,1989,4(1): 10~18.
[154] Bucher C.G.,Bourgund U., A fast and efficient response surface approach for structural reliability problems, Structural Safety,1990,12(7): 57~66.
[155] 董聪, 多层前向网络的全局最优化问题, 大自然探索,1996,15(4): 27~31.
[156] 杨成永,张弥,白小亮, 用于结构可靠度分析的多响应面法, 北方交通大学学报,2001,25(1): 1~4.
[157] 刘英卫, 序列响应面法及其在飞机结构可靠性分析中的应用, 洪都科技,1994,1: 1~6.
[158] 张书俊,任钧国, 具有随机初始条件的结构动力可靠性分析, 工程与科学中的计算力学, 2003: 362~366.
[159] 安伟光, 结构系统可靠性和基于可靠性的优化设计, 北京: 国防工业出版社, 1997.
[160] 张书俊,任钧国, 基于可靠性的结构动力特性优化设计, 湖南省力学学会年会, 2001.
[161] 张书俊, 基于频率可靠性约束的随机结构优化设计, 长沙: 国防科技大学硕士学位论文, 2002.
[162] 田四朋,任钧国,张书俊, 稳态随机过程激励下基于首次超越破坏的结构优化设计, 国防科技大学学报,2002,24(5): 5~9.
[163] 杨挺青, 粘弹性力学, 武汉: 华中理工大学出版社, 1990.
[164] 杨挺青,罗文波,危银涛等, 粘弹性理论与应用, 北京: 科学出版社, 2004.
[165] 王元有, 推进剂药柱在内压载荷下的应力、应变的粘弹性分析, 兵工学报,1983,3: 20~33.
[166] 唐国金,周建平, 自由装填药柱的结构完整性分析, 固体火箭技术,1994,2: 13~19.
[167] Janovsky V.,Shaw S.,Warby M.K.,Whiteman J.R., Numerical methods for treating problems of viscoelastic isotropic solid deformation, Journal of Computational and Applied Mathematics,1995,63: 91~107.
[168] Zocher M.A.,Groves S.E.,Allen D.H., A three-dimensional finite element formulation for thermoviscoelastic orthotropic media, Int. J. Numer. Meths. Engrg.,1997,40(12): 2267~2288.
[169] 邢耀国,马银民,董可海, 用长期贮存定期检测法预测药柱使用寿命, 推进技术,1999,20(5): 39~43.
[170] 刘中兵,利凤祥,李越森,胡春波, 轴向过载下固体推进剂药柱变形研究, 推进技术,2004,25(2): 162~164.
[171] Herrmann L.R., Elasticity equations for incompressible and nearly incompressible materials by variational theorem, AIAA J.,1965,3(10): 1896~1900.
[172] 王元有,王新华,胡亚非, 不可压缩粘弹性有限元法及其对推进剂药柱应力分析的应用, 航空动力学报,1993,8(4): 313~317.
[173] 张海联,周建平, 固体推进剂药柱的近似不可压缩粘弹性增量有限元, 固体火箭技术,2001,24(2): 36~40.
[174] Swanson S.R.,Christenson L.W., A constitutive formulation for high elongation propellants, J. Spacecraft,1983,20(6): 559~566.
[175] 沈亚鹏,陈宜亨,彭亚非, 以 kirchhoff 应力张量-green 应变张量表示本构关系的粘弹性大变形平面问题的有限元法, 固体力学学报,1987,4: 310~319.
[176] 王本华,刘晓,张戈, 固体药柱的大变形分析, 推进技术,1993,5: 25~30.
[177] Negaard Gordon, Non-linear finite element analysis of viscoelastic materials, ADA361168,1998.
[178] 强洪夫,汪亮, 固体火箭发动机药柱大变形数值分析, 宇航学报,2000,21: 77~83.
[179] 赵国荣,张淳源, 一个考虑损伤的非线性粘弹性本构关系, 湘潭大学自然科学学报,2001,23(3): 28~33.
[180] 吴淇泰,徐博侯,王泉, 粘弹性结构动力响应的一个计算方法, 计算结构力学及其应用,1989,6(4): 21~27.
[181] 王本华,张戈,黄涵,刘校, 粘弹性结构动力响应的有限元分析, 强度与环境,1993,3: 49~52.
[182] 李卓 , 徐秉业 , 蒲建军 , 固体推进剂杆状药柱的动态响应 , 宇航学报,2001,22(2): 51~55.
[183] Chyuan Shiang-Woei, Dynamic analysis of solid propellant grains subjected to ignition pressurization loading, Journal of Sound and Vibration,2003,268(3): 465~483.
[184] Cozzarelli F.A.,Huang W.N., Effect of random material parameters on nonlinear steady creep solutions, Int. J. Solids Structures,1971,7: 1477~1494.
[185] 张强, 含随机参数结构的动态响应研究, 北京: 中国农业大学博士学位论文, 2001.
[186] 刘建新,张强,焦群英, 含随机参数粘弹性结构的有限元法分析, 地震工程与工程振动,2003,23(6): 70~73.
[187] 张海联,周建平, 粘弹性随机有限元, 固体力学学报,2002,23(4): 387~395.
[188] 张海联,周建平, 粘弹性随机分析的虚功原理及随机有限元, 计算力学学报,2003,20(2): 133~139.
[189] 张海联,周建平, 固体推进剂药柱泊松比随机粘弹性有限元分析, 推进技术,2001,22(3): 245~249.
[190] 张海联,周建平, 固体推进剂药柱松弛模量随机粘弹性有限元分析, 推进技术,2001,22(4): 332~336.
[191] 张海联,周建平, 固体火箭发动机药柱随机结构分析及其相关函数研究, 固体火箭技术,2001,24(4): 25~28.
[192] 张海联,周建平, 基于粘弹性随机有限元的固体推进剂药柱可靠性分析, 固体火箭技术,2003,26(3): 21~24.
[193] 张海联,周建平, 固体推进剂药柱结构分析的非概率模型凸集合理论模型, 国防科技大学学报,2002,24(2): 1~5.
[194] Heller R.A.,Singh M.P., Thermal storage life of soild-propellant moters, J. Spacecraft,1982,20(2): 144~149.
[195] 刘兵吉, 随机载荷下药柱强度累积损伤可靠性计算, 推进技术,1993,3: 42~46.
[196] Amaniampong G.,Ariaratnam S.T., Reliability of linear viscoelastic systems excited by gaussian process, J. Engrg. Mech.,1998,124(3): 245~251.
[197] 侯军旗,吴连元, 非线性滞迟系统的随机振动分析, 上海力学,1997,18(4): 332~337.
[198] 韩强,张午梅,杨桂通, 非线性粘弹性梁在随机载荷作用下的混沌运动, 力学与实践,1998,20(6): 21~24.
[199] 张天舒,方同, 弹性-粘弹性复合结构系统的随机响应分析, 工程力学,2001,18(5): 71~76.
[200] 冉志,张天舒,方同, 弹性-粘弹性复合结构随机响应的各阶谱矩的计算方法, 振动工程学报,2003,16(3): 364~367.
[201] 桂洪斌,赵德有,金咸定, 基于材料参数随机性的粘弹性结构振动特性分析, 振动与冲击,2002,21(4): 66~68.
[202] 王铮, 药柱结构完整性的可靠性分析, 固体火箭技术,2001,24(1): 16~18.
[203] 刘兵吉, 固体推进剂贮存可靠寿命的 monte carlo 仿真计算, 推进技术,1992,2: 68~71.
[204] Philpot T.A.,Fridley K.J.,Rosowsky D.V., Structural reliability analysis method for viscoelastic members, Comput. Struct.,1994,53(3): 591~599.
[205] 张世英,姜洪开,陈家照, 固体推进剂药柱强度可靠性蒙特卡罗法数字仿真, 固体火箭技术,2001,24(4): 29~32.
[206] 张书俊,任钧国,田四朋, 固体火箭发动机粘弹性药柱结构可靠性分析, 固体火箭技术,2006,29(3): 183~185.
[207] 张书俊,任钧国,吴志桥, 固体推进剂药柱的近似不可压缩粘弹性随机有限元, 强度与环境,2006,33(2): 33~38.
[208] 张书俊,任钧国,吴志桥, 固体火箭发动机药柱点火过程结构可靠性的响应面算法, 固体火箭技术,2006.
[209] Christensen R.M., Theory of viscoelasticity: An introduction(second edition), New York: Academic Press, 1982.
[210] 胡亚非,王元有,王新华, 不可压缩和近乎不可压缩粘弹性问题的有限单元法, 计算结构力学及其应用,1992,9(4): 381~386.
[211] 宋天霞,邹时智,杨文兵, 非线性结构有限元计算, 武汉: 华中理工大学出版社, 1995.
[212] 吴长春, 非协调数值分析与杂交元法, 北京: 科学出版社, 1997.
[213] 胡广书, 数字信号处理-理论、算法与实现, 北京: 清华大学出版社, 2003.
[214] 王宏禹, 非平稳随机信号分析与处理, 北京: 国防工业出版社, 1999.
[215] 于雷,郑云龙, 逐步回归响应面法, 大连理工大学学报,1999,39(6): 792~796.
[216] 董聪,刘西拉, 非线性结构系统可靠性理论及其模拟算法, 土木工程学报,1998,31(1): 33~43.
[217] 丁士晟, 多元分析方法及其应用, 长春: 吉林人民出版社, 1981.
[218] 马宏伟,吴斌, 弹性动力学及其数值解法, 北京: 中国建材工业出版社, 2000.
[219] Whiteman J.R., Robust adaptive finite element schemes for nonlinear viscoelastic solid deformation: An investigative study, ADA335531,1997.
[220] Whiteman J.R., Robust adaptive finite element schemes for nonlinear viscoelastic solid deformation: An investigative study, ADA341249,1998.
[221] Simon Shaw,Whiteman J.R., Robust adaptive finite element schemes for viscoelastic solid deformation an investigative study, ADA359215,1998.
[222] Bathe K.L., 工程分析中的有限元法, 北京: 机械工业出版社, 1992.
[223] Rice S.O., Mathematical analysis of random noise, Bell system Technical Journal,1944,23: 282~332.
[224] 王铮,胡永强, 固体火箭发动机, 北京: 宇航出版社, 1993.
[225] 贝达特 J.S.,皮尔索 A.G., 随机数据分析方法, 北京: 国防工业出版社, 1980.
[2] 谭三五,王秉勋, 固体火箭发动机结构可靠性数字仿真的基本问题, 推进技术,1993,4: 47~54.
[3] 王铮, 固体火箭发动机使用寿命的预估和“延寿”, 推进技术,1999,22(1): 23~28.
[4] 胡昌寿, 可靠性工程-设计、试验、分析、管理, 北京: 宇航出版社, 1998.
[5] Collins J.D.,Thompson W.T., The eigenvalue problem for structural systems with uncertain parameters, AIAA. J.,1969,7(4): 642~648.
[6] Chen P.C.,Soroka W.W., Impulse response of a dynamic system with statistical properties, Journal of Sound and Vibration,1973,31(3): 309~314.
[7] 李杰, 随机结构系统-分析与建模, 北京: 科学出版社, 1996.
[8] 郝志明, 随机结构有限元法及可靠性研究, 北京: 中国工程物理研究院博士学位论文, 2001.
[9] Hien T.D.,Kleiber M., Stochastic finite element modeling in linear transient heat transfer, Comput. Methods Appl. Mech. Engrg.,1997,144: 111~124.
[10] Liu W.K.,Belytschko T.,Mani A., Random field finite elements, Int. J. Numer. Meths. Engrg.,1986,23(10): 1831~1845.
[11] Liu W.K.,Belytschko T.,Mani A., Probabilistic finite elements for nonlinear structural dynamics, Comput. Methods Appl. Mech. Engrg.,1986,56(1): 61~81.
[12] Liu W.K.,Besterfield G.,Belytschko T., Transient probabilistic systems, Comput. Methods Appl. Mech. Engrg.,1988,67(1): 27~54.
[13] Hien T.D.,Kleiber M., Stochastic structural design sensitivity of static response, Comput. Struct.,1991,38(5-6): 659~667.
[14] 张海联, 固体火箭发动机药柱的粘弹性不确定结构分析, 长沙: 国防科学技术大学博士学位论文, 2002.
[15] Liu P.L.,Kiureghian A.D., Finite element reliability of geometrically nonlinear uncertain structures, J. Engrg. Mech.,1991,117(8): 1806~1825.
[16] Ryu R.S. et al., Structural design sensitivity analysis of nonlinear response, Comput. Struct.,1985,21(2): 245-255.
[17] Haldar A.,Zhou Y., Reliability of geometrically nonlinear pr frams, J. Engrg. Mech.,1992,118(10): 2148~2155.
[18] Chang C.,Yang H.T.Y., Reliability of uncertain flexible laminated skewed plated under random compressions, AIAA J.,1992,30(2): 464~472.
[19] Engelasted S.P.,Reddy J.N., Probability nonlinear finite element analysis of composite structures, AIAA J.,1993,31(2): 362~369.
[20] 刘宁,卓家寿, 三维弹塑性随机有限元迭代计算方法研究, 河海大学学报,1996,24(1): 1~8.
[21] 刘宁,卓家寿, 基于三维弹塑性随机有限元的可靠度计算, 水利学报,1996,9: 53~62.
[22] 赵雷,陈虬, 不确定性结构非线性动力分析的增量随机有限元法, 工程力学增刊,1996: 353~357.
[23] Pradlwarter H.J.,Schueller G.I.,Schenk C.A., A computational procedure to estimate the stochastic dynamic response of large non-linear fe-models, Comput. Methods Appl. Mech. Engrg.,2003,192(7-8): 777~801.
[24] 赵雷,陈虬, 随机有限元动力分析方法的研究进展, 力学进展,1999,29(1): 9~18.
[25] Jenesn H.,Iwan W.D., Response variability in structural dynamics, Earthquake Engineering and Structural Dynamics,1991,20: 949~959.
[26] Lawrence M.A., Basic random variables in finite analysis, Int. J. Numer. Meths. Engrg.,1987,24: 1849~1863.
[27] Kiureghian A.D.,Ke J.B., The stochastic finite element method in structural reliability, Probabilistic Engineering Mechanics,1988,3(2): 83~91.
[28] Zeldin B.A.,Spanos P.D., On random field discretization in stochastic finite elements, J. Appl. Mech.,1998,65(2): 320~327.
[29] 秦权, 随机有限元及其进展 i.随机场的离散和反应矩的计算, 工程力学,1994,11(4): 1~10.
[30] Vanmarcke E., Stochastic finite elements and experimental measurements, Probabilistic Engineering Mechanics,1994,9(1-2): 103~114.
[31] 朱位秋,任永坚, 随机场的局部平均与随机有限元, 航空学报,1986,7(6): 604~612.
[32] 朱位秋,任永坚, 基于随机场局部平均的随机有限元法, 固体力学学报,1988,4: 285~292.
[33] 朱位秋,吴伟强, 基于随机场局部平均的随机有限元法在实特征值问题中的应用, 航空学报,1989,10(2): 20~26.
[34] Zhu W.Q.,Ren Y.J.,Wu W.Q., Stochastic fem based on local averages of random vector fields, J. Engrg. Mech.,1992,118(3): 496~511.
[35] Deodatis G., Bounds on response variability of stochastic finite element systems, J. Engrg. Mech.,1990,116(3): 565~585.
[36] Ghanem R.G.,Spanos P.D., Polynomial chaos in stochastic finite elements, J. Appl. Mech.,1990,57: 197~202.
[37] Ghanem R.G.,Spanos P.D., Stochastic finite elements: A spectral approach, New York: Springer-Verlag, 1991.
[38] Ghanem R.G.,Kruger R.M., Numerical solution of spetral stochastic finite element systems, Comput. Methods Appl. Mech. Engrg.,1996,129: 289~303.
[39] Jensen H.,Iwan W.D., Response of systems with uncertain parameters to stochastic excitation, J. Engrg. Mech.,1992,118(5): 1012~1025.
[40] Iwan W.D.,Jensen H., On the dynamic response of continuous systems including model uncertainty, J. Appl. Mech.,1993,60(2): 484~490.
[41] 李杰, 随机结构分析的扩阶系统方法(i)扩阶系统方程, 地震工程与工程振动,1995,15(3): 111~118.
[42] 李杰, 随机结构分析的扩阶系统方法(ii)结构动力分析, 地震工程与工程振动,1995,15(4): 27~35.
[43] 李杰, 随机结构动力分析的扩阶系统方法, 工程力学,1996,13(1): 93~102.
[44] 李杰, 线性随机结构在随机激励下动力响应分析, 力学学报,2002,34(3): 416~423.
[45] 李杰,魏星, 随机结构动力分析的递归聚缩算法, 固体力学学报,1996,17(3):263~267.
[46] Shinozuka M.,Astill J., Random eigenvalue problems in structural mechanics, AIAA J.,1972,10(4): 456~462.
[47] Shinozuka M., Probabilistic modeling of concrete structures, J. Engrg. Mech.,1972,8: 1433~1451.
[48] Shinozuka M.,Deodatis G., Response variability of stochastic finite element systems, J. Engrg. Mech.,1988,114(3): 499~519.
[49] Yamazaki F.,Shinozuka M.,Dasgupta G., Neumann expansion for finite element analysis, J. Engrg. Mech.,1988,114(8): 1335~1354.
[50] 刘宁,吕泰仁, 随机有限元及其工程应用, 力学进展,1995,25(1): 114~126.
[51] Chakraborty S.,Dey S.S., Stochastic finite element simulation of random structure on uncertain foundation under random loading, Int. J. Mech. Sci.,1996,38(11): 1209~1218.
[52] Chakraborty S.,Dey S.S., A stochastic finite element dynamic analysis of structures with uncertain parameters, Int. J. Mech. Sci.,1998,40(11): 1071~1087.
[53] 陈顺祥,郝志明, 纽曼随机有限元分析复合材料回旋结构的可靠性及其优化设计, 强度与环境,1998,4: 49~54.
[54] 郝志明,张铎,姜晋庆,陈儒,陈顺祥, 结构可靠性的纽曼展开蒙特卡罗随机有限元分析, 固体力学学报,1999,20(4): 320~324.
[55] Papadrakakis M.,Kotsopulos A., Parallel solution methods for stochastic finite element analysis using monte carlo simulation, Comput. Methods Appl. Mech. Engrg.,1999,168: 305~320.
[56] Johnson E.A.,Proppe C.,Spencer Jr B.F.,Bergman L.A.,Szekely G.S.,Schueller G.I., Parallel processing in computational stochastic dynamics, Probabilistic Engineering Mechanics,2003,18(1): 37~60.
[57] Liu W.K.,Ong J.S.,Uras R.A., Finite element stabilization matrices-a unification approach, Comput. Meths. Appl. Mech. Engrg.,1985,53: 13~46.
[58] Liu W.K.,Besterfield G.H.,Belytschko T., Variational approach to probabilistic finite elements, J. Eng. Mech.,1988,114(12): 2115~2133.
[59] Hien T.,Kleiber M., Finite element analysis based on stochastic hamilton variational principle, Comput. Struct.,1990,37(6): 893~902.
[60] 张汝清 , 高行山 , 随机变量的变分原理及有限元法 , 应用数学和力学,1992,13(5): 383~388.
[61] 张汝清,高行山, 有限变形弹性理论随机变量变分原理及有限元法, 应用数学和力学,1994,15(10): 855~862.
[62] 刘宁,刘光廷, 大体积混凝土结构温度场的随机有限元方法, 清华大学学报,1996,36(1): 41~47.
[63] Ren Y.J.,Elishakoff I., Finite element method for stochastic beams based on variational principle, J. Appl. Mech.,1997,64: 664~669.
[64] 赵雷,陈虬, 结构动力分析的随机变分原理及随机有限元法, 计算力学学报,1998,15(3): 263~274.
[65] 杨绿峰,高兑现,李桂青, 随机结构在随机激励下的二阶摄动随机势能泛函及其应用, 应用力学学报,1999,16(4): 35~39.
[66] Mckay M.D.,Beckman R.J.,Conover W.J., A comparison of three methods for selecting values of input variables in the analysis of output from a computercode, Technometrics,1979,2: 239~245.
[67] 周渊, 关于蒙特卡罗模拟抽样方法的研究, 强度与环境,1997,3: 14~18.
[68] 朱位秋, 随机振动, 北京: 科学出版社, 1998.
[69] 庄表中,梁以德,张佑启, 结构随机振动, 北京: 国防工业出版社, 1995.
[70] 欧进萍,王光远, 结构随机振动, 北京: 高等教育出版社, 1998.
[71] Schueller G.I.,Pradlwarter H.J.,Schenk C.A., Non-stationary response of large linear fe models under stochastic loading, Comput. Struct.,2003,81: 937~947.
[72] Kiureghian A.D.,Neuenhofer A., Response spectrum method for multi-support seismic excitations, Earthquake Engineering and Structural Dynamics,1992,21(8): 713~740.
[73] Zavoni E.H.,Venmark E.H., Seismic random vibration analysis of multi-support structural systems, J. Engrg. Mech.,1994,120(5): 1107~1128.
[74] Lin J.H.,Zhong W.X.,Zhang W.S.,Sun D.K., High efficiency computation of the variances of structural of evolutionary random responses, Shock and Vibration,2000,7(4): 209~216.
[75] Oksendal B., Stochastic differential equations,4th ed., Berlin: Springer-Verlag, 1995.
[76] 林家浩, 随机地震响应的确定性算法, 地震工程与工程振动,1985,5(1): 89~93.
[77] Lin J.H.,Zhang W.S.,Williams F.W., Pseudo-excitation algorithm for nonstationary random seismic response, Engineering structures,1994,16: 270~276.
[78] Lin J.H.,Zhang W.S.,Li J.J., Structural response to arbitrarily coherent stationary random excitations, Comput. Struct.,1994,44(3): 683~687.
[79] 林家浩,沈为平,宋华茂,孙东科, 结构非平稳随机响应的混合型精细时程积分, 振动工程学报,1995,8(2): 127~135.
[80] Lin J.H.,Sun D.K.,Sun Y.,Williams F.W., Structural response to non-uniformly modulated evolutionary random seismic excitations, Communications in numerical methods in engineering,1997,13: 605~616.
[81] 林家浩,张亚辉,孙东科,孙勇, 受非均匀调制演变随机激励结构响应快速精确计算, 计算力学学报,1997,14(1): 2~8.
[82] 钟万勰, 应用力学对偶体系, 北京: 科学出版社, 2002.
[83] Caughey T.K.,Ma F., The exact steady-state solution of a class of non-linear stochastic systems, Int. J. Non-Linear Mechanics,1982,17(3): 137~142.
[84] 朱位秋, 非线性随机动力学与控制, 北京: 科学出版社, 2003.
[85] 赵雷,陈虬, 分析非线性系统随机响应的一种等效非线性化方法, 应用数学与力学,1997,18(6): 513~521.
[86] 缪炳祺,许礼深,胡夏夏, 非线性系统非平稳随机响应矩计算的 newmark 递推算法, 振动工程学报,1997,10(2): 242~246.
[87] 张明 , 非线性随机振动等效线性化的一种推广 , 西南交通大学学报,1998,33(1): 77~81.
[88] Shinozuka M., Monte carlo solution of structural dynamics, Int. J. Comput. and Struct.,1972,2: 855~874.
[89] Shinozuka M.,Jan C.M., Digital simulation of random process and its applications, Journal of Sound and Vibration,1972,25: 111~128.
[90] Shinozuka M., Monte carlo solution of nonlinear vibrations, AIAA J.,1972,10(1): 37~40.
[91] Tsurui A.,Ishikawa H., Application of the fokker-planck equation to a stochastic fatigue crack growth model, Structural Safety,1986,4(1): 15~30.
[92] Tanaka H.,Tsurui A., Reliability degradation of structural components in the process of fatigue crack propagationunder stationary random loading, Eng. Fract. Mech.,1987,27: 501~516.
[93] Papadimitriou C.,katafygiotis L.S.,Beck J.L., Approximate analysis of response variability of uncertain linear systems, Probabilistic Engineering Mechanics,1995,10(4): 251~264.
[94] Zhao L.,Chen Q., Neumann dynamic stochastic finite element method of vibration for structures with stochastic parameters to random excitation, Comput. Struct.,2000,77(6): 651~657.
[95] 王元战,周晶,周锡, 随机过程激励下随机结构系统可靠度分析的一种方法, 固体力学学报,1998,19(2): 106~111.
[96] 林家浩,易平, 线性随机结构的平稳随机响应, 计算力学学报,2001,18(4): 402~408.
[97] 易平,林家浩,赵岩, 线性随机结构的非平稳随机响应变异性分析, 固体力学学报,2002,23(1): 93~97.
[98] 李杰, 复合随机振动分析的扩阶系统方法, 力学学报,1996,28(1): 66~75.
[99] 戴君,陈建军,马洪波, 随机参数结构在随机载荷激励下的动力响应分析, 力学学报,2002,19(3): 64~68.
[100] 何水清,王善, 结构可靠性分析与设计, 北京: 国防工业出版社, 1993.
[101] Rackwitz R.,Fiessler B., Structural reliability under combined random load sequences, Comput. Struct.,1978,9: 489~494.
[102] Chen X.,Lind N.C., Fast probability integration by three parameter normal tail approximation, Structural Safety,1983,1(4): 269~276.
[103] Wu Y.T., Computational methods for efficient structural reliability and reliability sensitivity analysis, AIAA J.,1994,32(8): 1717~1723.
[104] 董聪, 现代结构系统可靠性理论与应用, 北京: 科学出版社, 2000.
[105] Karamchandani A.,Cornell C.A., Sensitivity estimation within first and second order reliability methods, Structural Safety,1992,11(2): 95~107.
[106] 董聪,夏人伟, 现代结构系统可靠性评估理论研究进展, 力学进展,1995,25(4): 537~548.
[107] 张炳根,赵玉芝, 科学与工程中的随机微分方程, 北京: 海洋出版社, 1980.
[108] 李桂青,曹宏,李秋胜, 结构动力可靠性理论及其应用, 北京: 地震出版社, 1993.
[109] Veneziano D.,Grigorio M.,Conell C.A., Vector-process models for system reliability, J. Engrg. Mech.,1977,103(3): 441~460.
[110] Ditlevsen O., Gaussian oucrossings from safe convex polyhedrons, J. Engrg. Mech. Div.,1983,109(1): 127~148.
[111] Ang A.H.,Chaker A.A.,Abdelnour J., Analysis of activity network under uncertainty, J. Engrg. Mech. Div.,1975,101(4): 373~387.
[112] Moses F., System reliability development in structural engineering, Structural Safety,1982,1(1): 3~13.
[113] Melchers R.E.,Tang L.K., Dominant failure models in stochastic structural systems, Structural Safety,1982,1(1).
[114] Feng Y.S., Enumerating significant fail mode of structural system by using criterion methods, Comput. Struct.,1988,50(5): 1153~1157.
[115] Feng Y.S.,Moses F.A., Method of structural optimization based on structural system reliability, J. Struct. Mech.,1986,14(4): 437~453.
[116] 董聪, 结构系统可靠性理论:进展与回顾, 工程力学,2001,18(4): 79~88.
[117] Cornell C.A., Bounds on the reliability of structural systems, J. Struct. Div.,1967,93: 171~200.
[118] Ditlevsen O., Narrow reliability bounds for structural system, J. Struct. Mech.,1979,7(4): 453~472.
[119] Vanmarcke E.H., Matrix formulation of reliability analysis and reliability-based design, Comput. Struct.,1973,3: 757~770.
[120] Hohenbichler M.,Rackwitz R., First order concepts in system reliability, Structural Safety,1983,1(3): 177~188.
[121] Der K.A.,Ke J., Stochastic finite element method in structural reliability, Probabilistic Engineering Mechanics,1988,3(2): 83-91.
[122] Kiureghian A.D.,Zhang Y., Space-variant finite element reliability analysis, Comput. Methods Appl. Mech. Engrg.,1999,168(1-4): 173~183.
[123] Madsen H.O.,Tvedt L., Methods for time-dependent reliability and sensitivity analysis, J. Engrg. Mech.,1990,116(10): 2118~2135.
[124] Mahadevan S.,Mehta S., Dynamic reliability of large frames, Comput. Struct.,1993,47(1): 57~67.
[125] 管昌生,高兑现,李桂青, 抗震结构时变动力可靠度分析的随机过程法, 应用力学学报,1997,14(1): 70~76.
[126] 刘宁,刘光廷, 混凝土结构温度徐变应力的首次超越可靠度, 固体力学学报,1998,19(1): 38~44.
[127] Kahn H., Application of monte carlo, AECU-3259,1954.
[128] Bucher C.G., Adaptive sampling - an iterative fast monte carlo procedure, Structural Safety,1988,5(2): 119~126.
[129] Mori Y.,Ellingwood B., Time-dependent system reliability analysis by adaptive importance sampling, Structural Safety,1993,12(1): 59~73.
[130] Ziha K., Descriptive sampling in structural safety, Structural Safety,1995,17: 33~41.
[131] 吕震宙,岳珠峰, 结构可靠度计算中的描述抽样法, 力学与实践,1998,20: 52~54.
[132] Qi E.,Cui W., Latin hypercube sampling in ultimate strength reliability of ship hull girder, Journal of Ship Mechanics,2002,3: 52~60.
[133] Melchers R.E., Importance sampling in structural systems, Structural Safety,1989,6(1): 3~10.
[134] Melchers R.E., Search-based importance sampling, Structural Safety,1990,9(2): 117~128.
[135] Ibrahim Y., Observations on applications of importance sampling in structural reliability analysis, Structural Safety,1991,9(4): 269~281.
[136] Maes M.A.,Breitung S.,Dupuis D.J., Asymptotic importance sampling, Structural Safety,1993,12(3): 167~186.
[137] Engelund S.,Rackwitz R., A benchmark study on importance sampling techniques in structural reliability, Structural Safety,1993,12(4): 255~276.
[138] 李亚东, 重要抽样模拟及其在结构可靠度计算中的应用, 西南交通大学学报,1992,4: 105~110.
[139] 丁克勤,柳春图, 重要抽样法在管点疲劳可靠性分析中的应用, 力学学报,1996,28(3): 359~362.
[140] 李强,冯元生, 结构可靠性问题的改进分层抽样法, 航空学报,1995,16(5): 513~520.
[141] 沙风焕, 压力容器接管断裂失效概率计算, 石油化工设备,1999,28(3): 35~37.
[142] Wu Y.T.,Millwater H.R.,Cruse T.A., Advanced probabilistic structural analysis methods for implicit performance functions, AIAA J.,1990,28(9): 1663~1669.
[143] 吴斌,欧进萍,张纪刚,吕大刚, 结构动力可靠度的重要抽样法, 计算力学学报,2001,18(4): 478~482.
[144] Harnpornchai N.,Pradlwarter H.J.,Schueller G.I., Stochastic analysis of dynamical systems by phase-space-controlled monte carlo simulation, Comput. Methods Appl. Mech. Engrg.,1999,168: 273~283.
[145] Schueller G.I.,Pradlwarter H.J.,Bucher C.G., Efficient computational procedures for reliability estimations of mdof-systems, International Journal of Non-Linear Mechanics,1991,26(6): 961~974.
[146] Pradlwarter H.J.,Schueller G.I.,Melnikov P.G., Reliability of mdof systems, Probabilistic Engineering Mechanics,1994,9(4): 235~243.
[147] Pradlwarter H.J.,Schueller G.I., On advanced monte carlo simulation procedures stochastic structural dynamics, Int. J. Non-Linear Mechanics,1997,32(4): 735~744.
[148] Proppe C.,Pradlwarter H.J.,Schueller G.I., Equivalent linearization and monte carlo simulation in stochastic dynamics, Probabilistic Engineering Mechanics,2003,18(1): 1~15.
[149] 裴鹿成, 蒙特卡罗方法及其在粒子输运问题中的应用, 北京: 科学出版社, 1980.
[150] 张书俊,任钧国, 非线性随机动态响应的高效模拟方法, 国防科技大学学报,2006,28(1): 117~120.
[151] 董聪, 结构可靠性理论与模拟算法, 强度与环境,1997,4: 51~61.
[152] Faravelli L., A response surface method approach for reliability analysis, J. Engrg. Mech.,1989,115(12): 2763~2781.
[153] Schueller G.I.,Bucher C.G.,Bourgund U., On efficient computational schemes to calculate structural failure probabilities, Probabilistic Engineering Mechanics,1989,4(1): 10~18.
[154] Bucher C.G.,Bourgund U., A fast and efficient response surface approach for structural reliability problems, Structural Safety,1990,12(7): 57~66.
[155] 董聪, 多层前向网络的全局最优化问题, 大自然探索,1996,15(4): 27~31.
[156] 杨成永,张弥,白小亮, 用于结构可靠度分析的多响应面法, 北方交通大学学报,2001,25(1): 1~4.
[157] 刘英卫, 序列响应面法及其在飞机结构可靠性分析中的应用, 洪都科技,1994,1: 1~6.
[158] 张书俊,任钧国, 具有随机初始条件的结构动力可靠性分析, 工程与科学中的计算力学, 2003: 362~366.
[159] 安伟光, 结构系统可靠性和基于可靠性的优化设计, 北京: 国防工业出版社, 1997.
[160] 张书俊,任钧国, 基于可靠性的结构动力特性优化设计, 湖南省力学学会年会, 2001.
[161] 张书俊, 基于频率可靠性约束的随机结构优化设计, 长沙: 国防科技大学硕士学位论文, 2002.
[162] 田四朋,任钧国,张书俊, 稳态随机过程激励下基于首次超越破坏的结构优化设计, 国防科技大学学报,2002,24(5): 5~9.
[163] 杨挺青, 粘弹性力学, 武汉: 华中理工大学出版社, 1990.
[164] 杨挺青,罗文波,危银涛等, 粘弹性理论与应用, 北京: 科学出版社, 2004.
[165] 王元有, 推进剂药柱在内压载荷下的应力、应变的粘弹性分析, 兵工学报,1983,3: 20~33.
[166] 唐国金,周建平, 自由装填药柱的结构完整性分析, 固体火箭技术,1994,2: 13~19.
[167] Janovsky V.,Shaw S.,Warby M.K.,Whiteman J.R., Numerical methods for treating problems of viscoelastic isotropic solid deformation, Journal of Computational and Applied Mathematics,1995,63: 91~107.
[168] Zocher M.A.,Groves S.E.,Allen D.H., A three-dimensional finite element formulation for thermoviscoelastic orthotropic media, Int. J. Numer. Meths. Engrg.,1997,40(12): 2267~2288.
[169] 邢耀国,马银民,董可海, 用长期贮存定期检测法预测药柱使用寿命, 推进技术,1999,20(5): 39~43.
[170] 刘中兵,利凤祥,李越森,胡春波, 轴向过载下固体推进剂药柱变形研究, 推进技术,2004,25(2): 162~164.
[171] Herrmann L.R., Elasticity equations for incompressible and nearly incompressible materials by variational theorem, AIAA J.,1965,3(10): 1896~1900.
[172] 王元有,王新华,胡亚非, 不可压缩粘弹性有限元法及其对推进剂药柱应力分析的应用, 航空动力学报,1993,8(4): 313~317.
[173] 张海联,周建平, 固体推进剂药柱的近似不可压缩粘弹性增量有限元, 固体火箭技术,2001,24(2): 36~40.
[174] Swanson S.R.,Christenson L.W., A constitutive formulation for high elongation propellants, J. Spacecraft,1983,20(6): 559~566.
[175] 沈亚鹏,陈宜亨,彭亚非, 以 kirchhoff 应力张量-green 应变张量表示本构关系的粘弹性大变形平面问题的有限元法, 固体力学学报,1987,4: 310~319.
[176] 王本华,刘晓,张戈, 固体药柱的大变形分析, 推进技术,1993,5: 25~30.
[177] Negaard Gordon, Non-linear finite element analysis of viscoelastic materials, ADA361168,1998.
[178] 强洪夫,汪亮, 固体火箭发动机药柱大变形数值分析, 宇航学报,2000,21: 77~83.
[179] 赵国荣,张淳源, 一个考虑损伤的非线性粘弹性本构关系, 湘潭大学自然科学学报,2001,23(3): 28~33.
[180] 吴淇泰,徐博侯,王泉, 粘弹性结构动力响应的一个计算方法, 计算结构力学及其应用,1989,6(4): 21~27.
[181] 王本华,张戈,黄涵,刘校, 粘弹性结构动力响应的有限元分析, 强度与环境,1993,3: 49~52.
[182] 李卓 , 徐秉业 , 蒲建军 , 固体推进剂杆状药柱的动态响应 , 宇航学报,2001,22(2): 51~55.
[183] Chyuan Shiang-Woei, Dynamic analysis of solid propellant grains subjected to ignition pressurization loading, Journal of Sound and Vibration,2003,268(3): 465~483.
[184] Cozzarelli F.A.,Huang W.N., Effect of random material parameters on nonlinear steady creep solutions, Int. J. Solids Structures,1971,7: 1477~1494.
[185] 张强, 含随机参数结构的动态响应研究, 北京: 中国农业大学博士学位论文, 2001.
[186] 刘建新,张强,焦群英, 含随机参数粘弹性结构的有限元法分析, 地震工程与工程振动,2003,23(6): 70~73.
[187] 张海联,周建平, 粘弹性随机有限元, 固体力学学报,2002,23(4): 387~395.
[188] 张海联,周建平, 粘弹性随机分析的虚功原理及随机有限元, 计算力学学报,2003,20(2): 133~139.
[189] 张海联,周建平, 固体推进剂药柱泊松比随机粘弹性有限元分析, 推进技术,2001,22(3): 245~249.
[190] 张海联,周建平, 固体推进剂药柱松弛模量随机粘弹性有限元分析, 推进技术,2001,22(4): 332~336.
[191] 张海联,周建平, 固体火箭发动机药柱随机结构分析及其相关函数研究, 固体火箭技术,2001,24(4): 25~28.
[192] 张海联,周建平, 基于粘弹性随机有限元的固体推进剂药柱可靠性分析, 固体火箭技术,2003,26(3): 21~24.
[193] 张海联,周建平, 固体推进剂药柱结构分析的非概率模型凸集合理论模型, 国防科技大学学报,2002,24(2): 1~5.
[194] Heller R.A.,Singh M.P., Thermal storage life of soild-propellant moters, J. Spacecraft,1982,20(2): 144~149.
[195] 刘兵吉, 随机载荷下药柱强度累积损伤可靠性计算, 推进技术,1993,3: 42~46.
[196] Amaniampong G.,Ariaratnam S.T., Reliability of linear viscoelastic systems excited by gaussian process, J. Engrg. Mech.,1998,124(3): 245~251.
[197] 侯军旗,吴连元, 非线性滞迟系统的随机振动分析, 上海力学,1997,18(4): 332~337.
[198] 韩强,张午梅,杨桂通, 非线性粘弹性梁在随机载荷作用下的混沌运动, 力学与实践,1998,20(6): 21~24.
[199] 张天舒,方同, 弹性-粘弹性复合结构系统的随机响应分析, 工程力学,2001,18(5): 71~76.
[200] 冉志,张天舒,方同, 弹性-粘弹性复合结构随机响应的各阶谱矩的计算方法, 振动工程学报,2003,16(3): 364~367.
[201] 桂洪斌,赵德有,金咸定, 基于材料参数随机性的粘弹性结构振动特性分析, 振动与冲击,2002,21(4): 66~68.
[202] 王铮, 药柱结构完整性的可靠性分析, 固体火箭技术,2001,24(1): 16~18.
[203] 刘兵吉, 固体推进剂贮存可靠寿命的 monte carlo 仿真计算, 推进技术,1992,2: 68~71.
[204] Philpot T.A.,Fridley K.J.,Rosowsky D.V., Structural reliability analysis method for viscoelastic members, Comput. Struct.,1994,53(3): 591~599.
[205] 张世英,姜洪开,陈家照, 固体推进剂药柱强度可靠性蒙特卡罗法数字仿真, 固体火箭技术,2001,24(4): 29~32.
[206] 张书俊,任钧国,田四朋, 固体火箭发动机粘弹性药柱结构可靠性分析, 固体火箭技术,2006,29(3): 183~185.
[207] 张书俊,任钧国,吴志桥, 固体推进剂药柱的近似不可压缩粘弹性随机有限元, 强度与环境,2006,33(2): 33~38.
[208] 张书俊,任钧国,吴志桥, 固体火箭发动机药柱点火过程结构可靠性的响应面算法, 固体火箭技术,2006.
[209] Christensen R.M., Theory of viscoelasticity: An introduction(second edition), New York: Academic Press, 1982.
[210] 胡亚非,王元有,王新华, 不可压缩和近乎不可压缩粘弹性问题的有限单元法, 计算结构力学及其应用,1992,9(4): 381~386.
[211] 宋天霞,邹时智,杨文兵, 非线性结构有限元计算, 武汉: 华中理工大学出版社, 1995.
[212] 吴长春, 非协调数值分析与杂交元法, 北京: 科学出版社, 1997.
[213] 胡广书, 数字信号处理-理论、算法与实现, 北京: 清华大学出版社, 2003.
[214] 王宏禹, 非平稳随机信号分析与处理, 北京: 国防工业出版社, 1999.
[215] 于雷,郑云龙, 逐步回归响应面法, 大连理工大学学报,1999,39(6): 792~796.
[216] 董聪,刘西拉, 非线性结构系统可靠性理论及其模拟算法, 土木工程学报,1998,31(1): 33~43.
[217] 丁士晟, 多元分析方法及其应用, 长春: 吉林人民出版社, 1981.
[218] 马宏伟,吴斌, 弹性动力学及其数值解法, 北京: 中国建材工业出版社, 2000.
[219] Whiteman J.R., Robust adaptive finite element schemes for nonlinear viscoelastic solid deformation: An investigative study, ADA335531,1997.
[220] Whiteman J.R., Robust adaptive finite element schemes for nonlinear viscoelastic solid deformation: An investigative study, ADA341249,1998.
[221] Simon Shaw,Whiteman J.R., Robust adaptive finite element schemes for viscoelastic solid deformation an investigative study, ADA359215,1998.
[222] Bathe K.L., 工程分析中的有限元法, 北京: 机械工业出版社, 1992.
[223] Rice S.O., Mathematical analysis of random noise, Bell system Technical Journal,1944,23: 282~332.
[224] 王铮,胡永强, 固体火箭发动机, 北京: 宇航出版社, 1993.
[225] 贝达特 J.S.,皮尔索 A.G., 随机数据分析方法, 北京: 国防工业出版社, 1980.
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