Design problems in structural engineering are often modeled as differential equations. These problems are posed as initial or boundary value problems with several possible variations in structural designs. In this paper, we have derived a mathematical model that represents different structures of beam-columns by varying axial load with or without internal forces including bending rigidity. We have also developed a novel solver, the LeNN-NM algorithm, which consists of weighted Legendre polynomials, and a single path following optimizer, the Nelder–Mead (NM) algorithm. To evaluate the performance of our solver, we have considered three design problems representing beam-columns. The values of performance indicators, MAD, TIC, NSE, and ENSE, are calculated for a hundred simulations. The outcome of our statistical analysis points to the superiority of the LeNN-NM algorithm. Graphical illustrations are presented to further elaborate on our claims.

中文翻译：

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通过使用新的软计算技术通过改变内力和弯曲刚度来改变轴力来分析梁柱设计

结构工程中的设计问题通常被建模为微分方程。这些问题被认为是具有结构设计中几种可能变化的初始值或边值问题。在本文中，我们推导了一个数学模型，该模型通过改变有无内力（包括弯曲刚度）的轴向载荷来表示梁柱的不同结构。我们还开发了一种新颖的求解器LeNN-NM算法，它由加权的Legendre多项式组成，并采用了一条遵循优化器的单路径Nelder-Mead（NM）算法。为了评估求解器的性能，我们考虑了代表梁柱的三个设计问题。针对一百次仿真计算了性能指标MAD，TIC，NSE和ENSE的值。我们的统计分析结果指出了LeNN-NM算法的优越性。呈现图形图示以进一步详细说明我们的权利要求。