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Elastoplastic analysis of solid structures using penalty-based couple stress finite element method within framework of Cosserat continuum

基于Cosserat 连续体框架罚函数偶应力有限元法的固体结构弹塑性分析

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Abstract

To obviate the complexities of the straight forward couple stress finite element method, the penalty-based couple stress finite element method (named PcouFEM) within the framework of the Cosserat continuum is utilized to obtain the approximate solution by relaxing the C1 continuity. To examine the performance of the PcouFEM, three well-known numerical examples are investigated. For the analysis on stress concentration around the circular hole of the planestrain specimen, it was found that as long as the penalty factor Gc is not less than 5 times the shear modulus of the classical continuum G (i. e., Gc⩾5G), the stress concentration factors calculated by the PcouFEM with the reduced integration scheme agree well with the analytical solutions. For the strain localization analysis in the uniaxial compression test, it was observed that by applying the PcouFEM, the pathologically mesh-dependent problem associated with the conventional FEM can be alleviated or even removed, and based on numerical simulations, it is recommended to define 5G⩽Gc⩽10G from the perspective of numerical accuracy. For the soil slope subjected to an eccentric load through the rigid strip footing, it was found that the mesh-dependent problem of the shear band simulation can be largely alleviated by applying the PcouFEM.

摘要

为了降低直接偶应力有限元方法的复杂度,在Cosserat 连续体框架下通过对C1连续性进行松弛来获得其近似解,建立基于罚函数的偶应力有限元方法(简称PcouFEM),并通过三个数值算例对PcouFEM 的性能进行了研究. 对于平面应变条件下的圆孔应力集中问题,研究发现当罚因子不小于经典连续体剪切模量的5 倍时(即Gc& ge; 5G),基于缩减积分PcouFEM 计算获得的应力集中因子与解析解基本吻合; 对于单轴压缩试验应变局部化分析,通过应用PcouFEM 可以减弱甚至消除与常规FEM 相关的网格依赖性问题,且从数值精度的角度建议取值为5G& le; Gc& le; 10G; 对于通过刚性条形基础承受偏心载荷的土质边坡,研究发现土坡剪切带模拟中的网格依赖问题同样可以通过应用PcouFEM 得到较大缓解.

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Authors and Affiliations

  1. School of Civil and Transportation Engineering, Beijing University of Civil Engineering and Architecture, Beijing, 100044, China

    Dong-yong Wang  (王冬勇), Sheng-bin Jiang  (姜升彬), Ji-lin Qi  (齐吉琳) & Li-yun Peng  (彭丽云)

  2. Key Laboratory of Urban Underground Engineering of Ministry of Education, Beijing Jiaotong University, Beijing, 100044, China

    Xi Chen  (陈曦)

Authors
  1. Dong-yong Wang  (王冬勇)
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  2. Xi Chen  (陈曦)
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  3. Sheng-bin Jiang  (姜升彬)
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  5. Li-yun Peng  (彭丽云)
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Correspondence to Ji-lin Qi  (齐吉琳).

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Foundation item

Project(2021YFF0306302) supported by the National Key R& D Program of China; Projects(42002277, 41972279, 42172299) supported by the National Natural Science Foundation of China; Projects(2020M680321, 2021T140046) supported by the China Postdoctoral Science Foundation; Projects(2020-zz-081, 2021-zz-116) supported by the Beijing Postdoctoral Research Foundation, China; Project(X21074) supported by the Fundamental Research Funds for Beijing University of Civil Engineering and Architecture, China

Contributors

WANG Dong-yong performed some analyses and wrote the first draft; CHEN Xi gave some revision suggestions on the first draft; JIANG Sheng-bin performed some analyses and provided some numerical results; QI Ji-lin provided the concept and edited the manuscript; PENG Li-yun edited the final revised draft.

Conflict of interest

WANG Dong-yong, CHEN Xi, JIANG Sheng-bin, QI Ji-lin and PENG Li-yun declare that they have no conflict of interest.

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Wang, Dy., Chen, X., Jiang, Sb. et al. Elastoplastic analysis of solid structures using penalty-based couple stress finite element method within framework of Cosserat continuum. J. Cent. South Univ. 29, 1320–1331 (2022). https://doi.org/10.1007/s11771-022-4997-6

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