基于光滑有限元法的岩土体弹塑性分析

杨茂强; 张江辉; 王永伟; 吕加贺

doi:10.19509/j.cnki.dzkq.tb20240523

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基于光滑有限元法的岩土体弹塑性分析

更新时间：2026-11-05

- 基于光滑有限元法的岩土体弹塑性分析
- Bulletin of Geological Science and Technology Vol. 44, Issue 2, Pages: 330-339(2025)
- 作者机构：
  
  1. 中交第二航务工程局有限公司第五工程分公司
  2. 中国地质大学(武汉)工程学院
- 作者简介：
- 基金信息：
- DOI：10.19509/j.cnki.dzkq.tb20240523
  CLC： TU4
- Online First：21 March 2025，
  
  Published：2025
- 稿件说明：
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杨茂强, 张江辉, 王永伟, et al. 基于光滑有限元法的岩土体弹塑性分析[J]. Bulletin of Geological Science and Technology, 2025, 44(2): 330-339.
DOI：

杨茂强, 张江辉, 王永伟, et al. 基于光滑有限元法的岩土体弹塑性分析[J]. Bulletin of Geological Science and Technology, 2025, 44(2): 330-339. DOI： 10.19509/j.cnki.dzkq.tb20240523.

摘要

随着大型工程项目的日益增多，工程中的岩土极限问题也频繁出现，致使采用数值方法处理时，经常面对极端的模型变形问题。传统有限元法在处理极端的模型变形，特别是采用低阶单元分析时，往往会产生收敛问题、体积锁定问题以及网格严重畸变而导致的应力失准问题。寻找一种新的方法进行数值分析具有重要意义。光滑有限元法是一种有效改进传统有限元法固有缺陷，提高求解精度和收敛速度的算法。基于光滑有限元法，结合一种修正的Mohr-Coulomb屈服准则和线性搜索优化算法，建立了岩土体弹塑性计算模型。最后，针对经典的条形基础承载力模型和边坡模型进行验算，数值计算结果与参考解均吻合较好。结果表明光滑有限元法的计算精度明显优于传统有限元法，验证了本研究算法的可行性和实用性。本研究采用光滑有限元法建立的计算模型进一步提高了岩土体弹塑性问题的计算精度，降低了采用传统有限元法分析时存在的计算误差及网格畸变引起的应力失准问题。

Abstract

ObjectiveWith the increasing number of large engineering projects

geotechnical limit problems are becoming more common

often leading to extreme model deformation when numerical methods are employed. The traditional finite element method frequently encounters convergence issues

volume locking

and stress misalignment due to severe mesh distortion during the analysis of extreme model deformation

especially when low-order elements are used. Therefore

developing a new method for numerical analysis is of great importance. MethodsThe smooth finite element method is an effective approach to address the inherent defects of the traditional finite element method

enhancing both solution accuracy and convergence speed. Thus

based on the smooth finite element method combined with a modified Mohr-Coulomb yield criterion and a linear search optimization algorithm

an elastoplastic calculation model for rock and soil masses is developed in this study. ResultsThe classical bearing capacity model for the strip foundation and slope model was tested

and the numerical results align well with the reference solutions. The findings indicate that the calculation accuracy of the smooth finite element method is clearly superior to that of the traditional finite element method

confirming the feasibility and practicality of the proposed algorithm. ConclusionIn this work

the calculation model developed using the smooth finite element method significantly improves the calculation accuracy for rock and soil elastoplastic problems

while reducing the calculation error and stress misalignment caused by mesh distortion in traditional finite element methods.

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