A numerical analysis of the limit state for solids, with an adequately described structural geometry, is often a computationally demanding task, and there is a need for an effective method. The existing solid elements for Finite Element Limit Analysis (FELA) are either computationally expensive or require a stress cutoff of the yield surface for triaxial stress states. This paper presents an effective partially mixed lower bound tetrahedral constant stress solid element that converges rapidly and does not require modification of the yield surface. The element is based on a partially relaxed formulation of the lower bound theorem by providing strict equilibrium of the normal tractions on the element faces and a relaxed equilibrium of the shear/tangential tractions at the vertices. The performance of the element is shown in four examples applying either the von Mises yield criterion, or the Modified Mohr–Coulomb yield criterion with the possible inclusion of reinforcement. The examples show fast convergence and good performance even for relatively coarse meshes.

具有充分描述的结构几何形状的固体极限状态的数值分析通常是一项计算要求高的任务，需要一种有效的方法。有限元极限分析 (FELA) 的现有实体单元要么计算成本高，要么需要对三轴应力状态的屈服面进行应力截断。本文提出了一种有效的部分混合下界四面体恒应力实体单元，它可以快速收敛并且不需要修改屈服面。该单元基于下界定理的部分松弛公式，通过提供单元面上法向牵引力的严格平衡和顶点处剪切/切向牵引力的松弛平衡。单元的性能在四个示例中显示，应用 von Mises 屈服准则或修正的 Mohr-Coulomb 屈服准则（可能包含钢筋）。即使对于相对粗糙的网格，这些示例也显示出快速收敛和良好的性能。