全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...
工程力学  2015 

基于单元应力级数展开的下限原理有限元法

DOI: 10.6052/j.issn.1000-4750.2014.02.0104

Keywords: 下限分析,有限元法,Taylor级数,稳定性,极限荷载

Full-Text   Cite this paper   Add to My Lib

Abstract:

基于Taylor级数,将三角形单元内的应力场在三角形单元中心点处展开,从而可以借助于中心点应力及应力场梯度来表达整个单元应力场,再利用平衡方程中应力场梯度之间的线性关系,使单元中未知量的个数从9个减少到7个。由于已经满足了平衡方程,因此得到下限问题的数学规划模型不仅减少了变量的个数,而且也减少了等式约束的个数,从而降低了模型的规模。该方法丰富了下限原理有限元法的理论,为进一步提高求解效率打下了基础。计算结果表明与经典Sloan方法得到的结果完全一致。

References

[1]  李泽, 王均星. 基于非线性规划的岩质边坡有限元塑性极限分析下限法研究[J]. 岩石力学与工程学报, 2007, 26(4): 747―752. Li Ze, Wang Junxing. Lower bound limit study on plastic limit analysis of rock slope using finite elements based on nonlinear progamming [J]. Chinese Journal of Rock Mechanics and Engineering, 2007, 26(4): 747―752. (in Chinese)
[2]  黄齐武. 基于锥形规划理论的数值极限分析下限法及其应用[D]. 上海, 同济大学, 2007. Huang Qiwu. Numerical lower bound limit analysis using second-order cone Programming and its applications [D]. Shanghai: Tongji University, 2007. (in Chinese)
[3]  Ciria H, Peraire J. Computation of upper and lower bounds in limit analysis using second-order cone programming and mesh adaptivity [C]// Albuquerque, American Society of Civil Engineers, 2004, 80.
[4]  Makrodimopoulos A, Martin C. Lower bound limit analysis of cohesive-frictional materials using second- order cone programming [J]. International Journal for Numerical Methods in Engineering, 2006, 66(4): 604―634.
[5]  张学言. 岩土塑性力学[M]. 天津: 人民交通出版社, 1993. Zhang Xueyan. Geotechnics plasticity [M]. Tianjin: People’s Communications Press, 1993. (in Chinese)
[6]  Grifiths D V, Lane P A. Slope stability analysis by finite elements. G'eotechnique [J]. 1999, 49(3): 387―403.
[7]  Yu H S, Salgado R, et al. Limit analysis versus limit equilibrium for slope stability [J]. Journal of Geotechnical and Geoenvironmental Engineering, 1998, 124(1): 1―11.
[8]  Drucker D C, Greenberg H J, Prager W. The safety factor of an elastic-plastic body in plane strain [J]. Journal of Applied Mechanics Transactions of the ASME, 1951, 18(4): 371―378.
[9]  Chen W F. Soil mechanics and theorems of limit analysis [J]. Journal of Soil Mechanics & Foundations Div, 1969, 95: 493―518.
[10]  Lysmer J. Limit analysis of plane problems in soil mechanics [J]. Journal of Soil Mechanics & Foundations Div, 1970, 96(SM4): 1311―1334.
[11]  Sloan S W. Lower bound limit analysis using finite-elements and linear-programming [J]. International Journal for Numerical and Analytical Methods in Geomechanics, 1988, 12(1): 61―77.
[12]  Lyamin A, Sloan S. Lower bound limit analysis using non-linear programming [J]. International Journal for Numerical Methods in Engineering, 2002, 55(5): 573―611.
[13]  Krabbenhoft K, Damkilde L. A general non-linear optimization algorithm for lower bound limit analysis [J]. International Journal for Numerical Methods in Engineering, 2003, 56(2): 165―184.
[14]  杨小礼. 线性与非线性破坏准则下岩土极限分析方法及其应用[D]. 长沙: 中南大学, 2002. Yang Xiaoli. Limit analysis method and its applieation to geoteehnieal engineering with linear and nonlinear failure criteria [D]. Changsha: Central South University, 2002. (in Chinese)
[15]  杨强, 程勇刚, 赵亚楠, 周维垣. 基于非线性规划的极限分析方法及其应用[J]. 工程力学, 2004, 21(2): 15―19. Yang Qiang, Cheng Yonggang, Zhao Ya’nan, Zhou Weiyuan. Limt analsis method based on nonlinear programming [J]. Engineering Mechanics, 2004, 21(2): 15―19. (in Chinese)

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133