This contribution is addressing the ultimate limit state design of massive three‐dimensional reinforced concrete structures based on a finite‐element implementation of yield design theory. The strength properties of plain concrete are modeled either by means of a tension cutoff Mohr Coulomb or a Rankine condition, while the contribution of the reinforcing bars is taken into account by means of a homogenization method. This homogenization method can either represent regions of uniformly distributed steel rebars smeared into the concrete domain, but it can also be extended to model single rebars diluted into a larger region, thereby simplifying mesh generation and mesh size requirements in this region. The present paper is mainly focused on the implementation of the upper bound kinematic approach formulated as a convex minimization problem. The retained strength condition for the plain concrete and homogenized reinforced regions are both amenable to a formulation involving positive semidefinite constraints. The resulting semidefinite programming problems can, therefore, be solved using state‐of‐the‐art dedicated solvers. The whole computational procedure is applied to some illustrative examples, where the implementation of both static and kinematic methods produces a relatively accurate bracketing of the exact failure load for this kind of structures.

中文翻译：

---

三维钢筋混凝土结构极限承载力的数值上限

这项贡献是基于屈服设计理论的有限元实现，解决了大型三维钢筋混凝土结构的极限状态设计。普通混凝土的强度特性可通过截断莫尔库仑（Mohr Coulomb）或兰金条件进行建模，而钢筋的贡献可通过均质化方法加以考虑。这种均质方法既可以表示涂抹在混凝土区域中的均匀分布的钢筋区域，也可以扩展为对稀释到较大区域的单个钢筋进行建模，从而简化了该区域中网格的生成和网格尺寸要求。本文主要集中在上限运动学方法的实现上，该方法被构造为凸极小化问题。普通混凝土和均质钢筋区域的保留强度条件均适用于涉及正半确定约束的公式。因此，可以使用最新的专用求解器解决由此产生的半定程序问题。整个计算过程应用于一些说明性示例，其中静态方法和运动学方法的实现都产生了针对此类结构的准确破坏载荷的相对准确的包围。