Abstract The theory of archgrids of minimal weight has been formulated in the late 1970s and recently reconsidered by means of duality theory in the calculus of variations. In the current study, we follow this approach by putting forward an efficient computational scheme. Trial functions for both primal and dual problems are decomposed in two function bases: trigonometric (Fourier) and polynomial (Legendre). Our focus is on structures composed of arches forming a rectangular grid, i.e. running in two mutually perpendicular directions and spanning a given rectangular domain. In the course of discussion, we show that the numerical algorithm is quickly convergent, CPU time efficient, and robust. In particular, it provides clear-cut solutions in which optimal parts of a structure are sharply distinguished from the non-optimal, hence redundant, ones.

中文翻译：

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跨越矩形域的最佳拱形网格

摘要 最小权重拱形网格理论是在 1970 年代后期提出的，最近通过变分计算中的对偶理论重新考虑。在当前的研究中，我们通过提出一种有效的计算方案来遵循这种方法。原始和对偶问题的试验函数分解为两个函数基：三角函数 (Fourier) 和多项式 (Legendre)。我们的重点是由拱形组成的结构，形成一个矩形网格，即在两个相互垂直的方向上运行并跨越给定的矩形域。在讨论过程中，我们表明该数值算法收敛速度快、CPU 时间高效且鲁棒。特别是，它提供了清晰的解决方案，其中结构的最佳部分与非最佳的，因此冗余的部分有明显的区别。