Abstract This paper explores a pathway for increasing efficiency in numerical 3D limit analysis through r-h adaptivity, wherein nodal positions (r) and element lengths (h) are successively refined. The approach uses an iterative, nested optimization procedure involving three components: (1) determination of velocities for a fixed mesh of rigid, translational elements (blocks) using second-order cone programming; (2) adaptation of nodal positions using non-linear optimization (r adaptivity); and (3) subdivision of elements based on the magnitude of the velocity jumps (h adaptivity). Examples show that the method can compute reasonably accurate limit loads at relatively low computational cost.

中文翻译：

---

一种用于 3D 极限分析的 rh 自适应运动学方法

摘要 本文探索了一种通过 rh 自适应性提高数值 3D 极限分析效率的途径，其中节点位置 (r) 和单元长度 (h) 连续细化。该方法使用涉及三个组件的迭代嵌套优化程序：(1) 使用二阶锥规划确定刚性、平移元素（块）的固定网格的速度；(2) 使用非线性优化（r自适应）对节点位置进行自适应；(3) 根据速度跳跃的幅度（h 自适应性）对元素进行细分。示例表明，该方法可以以相对较低的计算成本计算相当准确的极限载荷。