This paper re-considers a recent analysis on the so-called Couplet–Heyman problem of least-thickness circular masonry arch structural form optimization and provides complementary and novel information and perspectives, specifically in terms of the optimization problem, and its implications in the general understanding of the Mechanics (statics) of masonry arches. First, typical underlying solutions are independently re-derived, by a static upper/lower horizontal thrust and a kinematic work balance, stationary approaches, based on a complete analytical treatment; then, illustrated and commented. Subsequently, a separate numerical validation treatment is developed, by the deployment of an original recursive solution strategy, the adoption of a discontinuous deformation analysis simulation tool and the operation of a new self-implemented Complementarity Problem/Mathematical Programming formulation, with a full matching of the achieved results, on all the arch characteristics in the critical condition of minimum thickness.

中文翻译：

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最小厚度圆形砌体拱优化的静态上/下推力和运动学工作平衡平稳性

本文重新考虑了最近对最小厚度圆形砌体拱结构形式优化的所谓 Couplet-Heyman 问题的分析，并提供了补充和新颖的信息和观点，特别是在优化问题方面，及其在一般情况下的影响。了解砌体拱门的力学（静力学）。首先，基于完整的分析处理，通过静态上/下水平推力和运动学工作平衡、静止方法独立重新导出典型的基础解决方案；然后，插图和评论。随后，通过部署原始递归解决方案策略，开发了单独的数值验证处理，