Abstract We propose a new adaptive NURBS upper-bound limit analysis approach for the assessment of general three-dimensional curved masonry structures, based on different meta-heuristic mesh adaptation schemes. The method, which can easily be integrated within CAD modeling environments, allows to establish the actual failure mechanism and load bearing capacity of a masonry structure by iteratively adjusting a tentative pattern of yield lines, defined upon a suitable initial mesh of NURBS rigid elements, by means of a suitable meta-heuristic algorithm which searches for the minimum collapse load multiplier, thus enforcing the upper-bound theorem of limit analysis. In particular, we investigate and discuss the efficiency of several meta-heuristic algorithms in delivering the optimal solution: a specifically devised Prey Predator Algorithm (PPA) is compared with the Particle Swarm Optimization (PSO) Algorithm, the Firefly Algorithm (FA) and a suitable Genetic Algorithm (GA). Four masonry vaults have been chosen as case studies. In particular, the modified PPA proves to be the most efficient mesh-adjustment scheme for the proposed adaptive NURBS-based limit analysis procedure.

中文翻译：

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曲面三维砌体结构 NURBS 上限分析的高效元启发式网格自适应策略

摘要 基于不同的元启发式网格自适应方案，我们提出了一种新的自适应 NURBS 上限分析方法，用于评估一般三维曲面砌体结构。该方法可以很容易地集成到 CAD 建模环境中，允许通过迭代调整屈服线的暂定模式来建立砌体结构的实际失效机制和承载能力，屈服线的暂定模式定义在 NURBS 刚性单元的合适初始网格上，通过一种合适的元启发式算法，该算法搜索最小坍塌载荷乘数，从而执行极限分析的上限定理。特别是，我们调查并讨论了几种元启发式算法在提供最佳解决方案方面的效率：将专门设计的 Prey Predator 算法 (PPA) 与粒子群优化 (PSO) 算法、萤火虫算法 (FA) 和合适的遗传算法 (GA) 进行比较。四个砖石拱顶被选为案例研究。特别是，改进的 PPA 被证明是所提议的基于 NURBS 的自适应极限分析程序的最有效的网格调整方案。