本文将扩展多尺度有限元法应用于非平稳随机振动时域显式法中,实现了对非均质结构非平稳随机响应的快速精确计算。首先,论文阐述了扩展多尺度有限元法基本原理。其次,探讨了时域显式法在非平稳随机响应分析中的优势。时域显式法基于动力响应显式表达式直接在时域进行随机振动分析,较传统反应谱法,具有良好的计算精度和计算效率。最后,根据两算法的特性和优势提出统一的多尺度算法框架,使其适用于非均质结构非平稳随机响应分析的快速求解。数值算例验证了该算法的高效性和精确性。
Abstract
A fast computation is implemented for non-stationary random response analysis of heterogeneous material structures by applying extended multiscale finite element method (EMsFEM) into time-domain explicit method(TDEM). Firstly, the fundamental principle of EMsFEM is illustrated. Then, the advantages of TDEM in non-stationary random response analysis are discussed. Based on the explicit expressions of dynamic responses, the random response analysis is performed directly in time domain, and TDEM has a good accuracy and efficiency which is compared with response spectrum method. Finally, according to the characteristics and advantages of the two algorithms, a unified multiscale framework is proposed, which is applicable for non-stationary random response analysis of heterogeneous material structures. Numerical examples show that the proposed method has high efficiency and accuracy.
关键词
非均质结构
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非平稳随机振动;展多尺度有限元法 /
基函数; 时域显式法
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Key words
heterogeneous material structures /
non-stationary random response analysis /
extended multiscale finite element method /
base function /
time-domain explicit method
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参考文献
[1] J. H. Lin, W. S. Zhang, J. J. Li. Structural responses to arbitrarily coherent stationary random excitations[J]. Computers & structures, 1994, 50: 629-633.
[2] J. H. Lin, J. J. Li, W. S. Zhang, et al. Random seismic responses of multi-support structures in evolutionary inhomogeneous random fields[J]. Earthquake Engineering & Structural Dynamics, 1997, 26: 135-145.
[3]苏成, 徐瑞. 非平稳激励下结构随机振动时域分析法[J]. 工程力学, 2010, 12:77-83. (SU Cheng, XU Rui. Random vibration analysis of structures subjected to non-stationary excitations by time domain method[J]. Engineering Mechanics, 2010,12:77-83. (in Chinese))
[4]苏成, 徐瑞, 刘小璐, 廖旭钊. 大跨度空间结构抗震分析的非平稳随机振动时域显式法[J]. 建筑结构学报, 2011, 11:169-176. (SU Cheng, XU Rui, LIU Xiaolu, LIAO Xuzhao. Non-stationary seismic analysis of large-span spatial structures by time-domain explicit method[J]. Journal of Building Structures, 2011,11:169-176. (in Chinese))
[5] I Babuska, G Caloz, E Osborn. Special finite element methods for a class of second order elliptic problems with rough coefficients[J]. SIAM J. Numer. Anal. 1994, 31(4): 945-981.
[6] H. W. Zhang, Z. D. Fu, J. K. Wu. Coupling multiscale finite element method for consolidation analysis of heterogeneous saturated porous media[J]. Advances in water resources, 2009, 32(2): 268-279.
[7 H. W. Zhang, M. K. Lu, Y. G. Zheng, S. Zhang. General coupling extended multiscale FEM for elasto-plastic consolidation analysis of heterogeneous saturated porous media[J].International Journal for Numerical and Analytical Methods in Geomechanics, 2014(online)
[8] 张洪武, 吴敬凯, 刘辉, 付振东. 扩展的多尺度有限元法基本原理[J]. 计算机辅助工程, 2010, 19(2): 3-9. (ZHANG Hongwu, WU Jingkai, LIU Hui, FU Zhendong. Basic theory of extended multiscale finite element method[J]. Computer Aided Engineering, 2010, 19(2): 3-9. (in Chinese))
[9] 张洪武, 吴敬凯, 付振东. 周期性点阵桁架材料力学性能分析的一种新的多尺度计算方法[J]. 固体力学学报, 2011, 32(2): 109-118. (ZHANG Hongwu, WU Jingkai, FU Zhendong. A new multiscale computational method for mechanical analysis of periodic truss materials[J]. Chinese Journal of Solid Mechanics, 2011, 32(2): 109-118. (in Chinese))
[10] S. Zhang, D. S. Yang, H. W. Zhang, Y. G. Zheng. Coupling extended multiscale finite element method for thermoelastic analysis of heterogeneous multiphase materials[J]. Computers and Structures, 2013, 121: 32-49.
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脚注
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