自适应有限元极限分析及岩土工程中的应用

Application of finite-element-based limit analysis with mesh adaptation in geotechnical engineering

为了探讨有限元法极限分析的网格自适应以及锥优化算法在Mohr-Coulomb材料极限分析中的应用,以屈服准则残余和变形为依据提出针对Mohr-Coulomb材料极限分析的有限元自适应策略。对局部网格自适应结合非结构三角形网格在数值极限分析中的表现进行了探讨。通过基于有限元的极限分析方法结合网络自适应寻找潜在滑移面,从而极大程度地提高了数值计算精度。数值算例证明了所提出极限分析网格自适应准则的有效性以及在岩土极限分析中的应用前景。

Refinement strategy based on the yield function slack and deformation is proposed for the finite-element-based limit analysis （FELA） of Mohr-Coulomb materials. Performance of the local mesh adaptation for the unstructured mesh is examined. The potential slip surface is traced by the adaptive procedure incorporated in the FELA such that the accuracy of the obtained bound solution is dramatically improved. The efficiency and the validity of the proposed strategy are well backed up by results of applications in two classical stability problems in geomechanics, namely, the determination of the bearing capacity of strip footing on weightless soil mass and the critical height of a critical cut. The time required in the computation is provided as well which suggests that the numerical limit analysis is both practical and necessary with the newly developed local mesh adaptation and the second-order cone programming. The obtained results reflect the promising future of the FELA as an alternative to the conventional approaches in the stability analysis in geotechnical engineering.