非均质地层网格加密与稀疏并举的高阶单元自适应上限有限元研究

doi:10.13722/j.cnki.jrme.2023.0428

Abstract
Figure/Table
References (0)
Related Citation (15)

Download: PDF (2458 KB) HTML (1 KB)
Export: BibTeX | EndNote (RIS)

Abstract In geotechnical engineering，upper bound finite element method with adaptive mesh refinement often evaluates the plastic failure area in a posterior manner，which may cause an excessive refinement in the buffer zone between rigid and plastic zones and lead to a high computational cost. Meanwhile，the initial mesh for the adaptive upper bound finite element method should not be too sparse to avoid the large error caused by the over-rigidity of model，as it can induce subsequent adaptive refinement to deviate from the correct direction. In this study，with a combination of six-node triangular elements and a second-order cone programming model，an upper bound finite element method with simultaneous adaptive mesh refining and coarsening algorithm is proposed. This method can automatically determine both active elements and inactive elements using plastic power dissipation-based estimators. For each adaptive step，those active elements are automatically refined and those inactive ones are thus coarsened，which can achieve the purpose of reducing the total number of elements and improving computational accuracy. The proposed method is then extended to the stability analysis in non-homogeneous soils，and numerical implementation of the proposed method is discussed. Two examples including tunnel face stability and failure of active trapdoors in non-homogeneous soils are analyzed to evaluate the validity of the proposed method through a series of parameter analysis.

Key words： numerical analysis adaptive upper bound finite element method mesh refinement mesh coarsening non-homogeneous soil six-node triangular element second-order cone programming failure mode

	Service

	E-mail this article
	Add to my bookshelf
	Add to citation manager
	E-mail Alert
	RSS
	Articles by authors
	ZHENG Xiangcou
	QIN Aohan
	YANG Feng
	YANG Junsheng

Cite this article:

ZHENG Xiangcou,QIN Aohan,YANG Feng, et al. A simultaneous adaptive mesh refining and coarsening algorithm in high-order element-based upper bound finite element method in non-homogeneous soils[J]. , 2024, 43(S2): 3951-3959.

URL:

https://rockmech.whrsm.ac.cn/EN/10.13722/j.cnki.jrme.2023.0428 OR https://rockmech.whrsm.ac.cn/EN/Y2024/V43/IS2/3951

[1]	YU H S，SLOAN S W，KLEEMAN P W. A quadratic element for upper bound limit analysis[J]. Engineering Computations，1994，11(3)：195-212.
[2]	MAKRODIMOPOULOS A，MARTIN M. Upper bound limit analysis using simplex strain elements and second order-cone programming[J]. International Journal for Numerical and Analytical Methods in Geomechanics，2007，31(6)：835-865.
[3]	杨峰，阳军生，李昌友，等. 基于六节点三角形单元和线性规划模型的上限有限元研究[J]. 岩石力学与工程学报，2012，31(12)：2 556-2 563.(YANG Feng. YANG Junsheng，LI Changyou，et al. Investigation of finite element upper bound solution based on six nodal triangular elements and linear programming model[J]. Chinese Journal of Rock Mechanics and Engineering，2012，31(12)：2 556-2 563.(in Chinese))
[4]	杨峰，阳军生. 用于上限有限元的非结构网格重划加密方法研究[J]. 中南大学学报：自然科学版，2014，(10)：3 571-3 577.(YANG Feng，YANG Junsheng. Investigation of unstructured mesh regeneration and Refinement method for finite element upper bound solution[J]. Journal of Central South University：Science and Technology，2014，(10)：3 571-3 577.(in Chinese))
[5]	CIRIA H，PERAIRE J，BONET J. Mesh adaptive computation of upper and lower bounds in limit analysis[J]. International Journal for Numerical Methods in Engineering，2008，75(8)：899-944.
[6]	MARTIN C M. The use of adaptive finite-element limit analysis to reveal slip-line fields[J]. Geotechnique Letters，2011，(1)：23-29
[7]	SLOAN S W. Geotechnical stability analysis[J]. Geotechnique，2013，63(7)：531-572.
[8]	赵明华，张锐. 有限元上限分析网格自适应方法及其工程应用[J]. 岩土工程学报，2016，38(3)：537-545.(ZHAO Minghua，ZHANG Rui. Adaptive mesh refinement of upper bound finite element method and its applications in geotechnical engineering[J]. Chinese Journal of Geotechnical Engineering，2016，38(3)：537-545.(in Chinese))
[9]	阳军生，张箭，杨峰. 浅埋隧道掌子面稳定性二维自适应上限有限元分析[J]. 岩土力学，2015，36(1)：257-264.(YANG Junsheng，ZHANG Jian，YANG Feng. Stability analysis of shallow tunnel face using two-dimensional finite element upper bound solution with mesh adaptation[J]. Rock and Soil Mechanics，2015，36(1)：257-264.(in Chinese))
[10]	李大钟，郑榕明，王金安，等. 自适应有限元极限分析及岩土工程中的应用[J]. 岩土工程学报，2013，35(5)：922-929.(LI Dazhong，CHENG Yungming，WANG Jin?an，et al. Application of finite-element-based limit analysis with mesh adaptation in geotechnical engineering[J]. Chinese Journal of Geotechnical Engineering，2013，35(5)：922-929.(in Chinese))
[11]	孙锐，杨峰，阳军生，等. 基于二阶锥规划与高阶单元的自适应上限有限元研究[J]. 岩土力学，2020，41(2)：687-694.(SUN Rui，YANG Feng，YANG Junsheng，et al. Investigation of upper bound adaptive finite element method based on second-order cone programming and higher-order element[J]. Rock and Soil Mechanics，2020，41(2)：687-694.(in Chinese))
[12]	AUGARDE C E，LYAMIN A V，SLOAN S W. Stability of an undrained plane strain heading revisited[J]. Computers and Geotechnics，2003，30(5)：419-430.
[13]	HUANG M，SONG C. Upper-bound stability analysis of a plane strain heading in non-homogeneous clay[J]. Tunnelling and Underground Space Technology，2013，38：213-223.
[14]	KEAWSAWASVONG S，UKRITCHON B. Undrained stability of plane strain active trapdoors in anisotropic and non-homogeneous clays[J]. Tunnelling and Underground Space Technology，2021，107：103628.
[15]	KEAWSAWASVONG S，UKRITCHON B. Undrained stability of an active planar trapdoor in non-homogeneous clays with a linear increase of strength with depth[J]. Computers and Geotechnics，2017，81：284-293.
[16]	YANG F，HE S H，WU Y J，et al. Tunnel face stability analysis by the upper-bound finite element method with rigid translatory moving element in heterogeneous clay[J]. Rock and Soil Mechanics，2020，41(4)：1 412-1 419