赵州桥“实体迭代”与力学“数值迭代”

"Physical Iteration" of Zhaozhou Bridge and "Numerical Iteration" in Mechanics

  • 摘要: 今年是钱令希院士诞辰110周年,为了纪念和追思恩师的业绩,本文发掘了与赵州桥相关的故事,从中可以提炼出“实体迭代”的概念:以物理实体为载体,通过“试错—验证—修正”的循环路径,实现结构从反复“破坏”——“基本安全”——“更安全”——“最优”的过程。本文首次正规地讨论了实体迭代,它是数值迭代的前身,弥补了力学产生之前人类工程结构安全的困境,然而实体迭代具有极为昂贵的代价。当今的力学数值迭代替代了实体迭代,它是工程结构设计的必要前提,依托计算力学与结构优化方法,通过数学建模、循环求解与参数迭代,完成现代工程结构的理性设计过程。

     

    Abstract: This year marks the 110th anniversary of the birth of Academician Qian Lingxi. In commemoration of our esteemed teacher's achievements, this paper explores stories related to the Zhaozhou Bridge, from which the concept of “physical iteration" can be derived: using physical entities as the carrier, through a cyclic process of “trial-error—verification—correction," achieving structural evolution from repeated “destruction"—“basic safety"—“enhanced safety"—“optimality." This paper formally discusses physical iteration for the first time. As the precursor of numerical iteration, it addressed the challenges of human engineering structural safety before the advent of mechanics. However, physical iteration came at an extremely high cost. Today, mechanical numerical iteration has replaced physical iteration and become a necessary prerequisite for engineering structural design. Leveraging computational mechanics and structural optimization methods, through mathematical modeling, cyclic solving, and parameter iteration, it completes the rational design process of modern engineering structures.

     

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