Abstract A lower bound (LB) axisymmetric limit analysis formulation is presented for Mohr-Coulomb materials using finite elements and semidefinite programming (SDP). The details of the application of SDP to the axisymmetric LB finite element method for Mohr-Coulomb materials are described in this paper. Through the use of the SDP, the axisymmetric Mohr-Coulomb yield criterion can be directly applied in its native form in terms of principal stresses without any smoothing of the parent yield surface, and no assumption needs to be made about σ θ . A node-stress-based adaptive mesh algorithm is also introduced into the proposed method to obtain an accurate high-accuracy LB solution. The proposed method is then applied to estimate the collapse load of circular footings and the stability of an unlined vertical circular excavation. The results are also compared with those reported in the literature; the results obtained from the proposed method are accurate and can provide failure patterns with greater clarity.

中文翻译：

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使用半定规划法对 Mohr-Coulomb 材料进行轴对称自适应下限分析

摘要 使用有限元和半定规划(SDP) 提出了Mohr-Coulomb 材料的下界(LB) 轴对称极限分析公式。本文详细介绍了 SDP 在 Mohr-Coulomb 材料的轴对称 LB 有限元方法中的应用。通过使用 SDP，轴对称 Mohr-Coulomb 屈服准则可以直接应用于主应力方面的原始形式，无需对母体屈服面进行任何平滑处理，并且无需对 σ θ 进行任何假设。该方法还引入了基于节点应力的自适应网格算法，以获得准确的高精度 LB 解。然后将所提出的方法应用于估计圆形基础的倒塌荷载和无衬砌垂直圆形开挖的稳定性。结果也与文献报道的结果进行了比较；从所提出的方法中获得的结果是准确的，并且可以更清晰地提供故障模式。