轮印载荷下多跨梁最危险工况分析与优化

Worst-case analysis and optimization of multi-span beams under multiple patch loading

多种轮印载荷工况作用于船舶多跨梁结构时,找到最危险工况并进行结构优化设计,对于船舶结构的安全校核与降低结构重量有重要意义。提出一种将遗传算法与有限元方法相结合,以多跨梁上轮印载荷的布置位置为设计变量,载荷间的间距大小为约束条件,每一跨的最大弯矩和最大剪力为目标函数,求解任意多跨梁上有多种轮印载荷作用时最危险工况的方法,并根据最危险工况分析的结果调整支座位置,降低多跨梁最大弯矩,并进一步进行构件尺寸的优化设计。计算结果表明:基于提出的多跨梁优化设计方法,能找到每一跨应力满足强度要求的剖面积最小的构件尺寸,且构件尺寸的变化对最危险工况时的最大弯矩与轮印载荷位置几乎没有影响。调整支座位置的优化方案,与支座初始位置方案相比,最危险工况时的最大弯矩降低22.64%,重量降低10.55%,因此支座位置的调整,能有效降低最危险工况时的最大弯矩,从而达到降低多跨梁重量的目的。

The worst-case analysis and optimization design of multi-span beams under multiple patch loading conditions are of vital significance for both ship safety checking and structural weight reducing. In this paper, a method combining the genetic algorithm and finite element analysis is proposed. Specifically, it incorporates the location of the patch loading as a design variable, takes the distance between two patch loadings as the constraint condition, and adopts the maximum bending moment and maximum shear force of each span as the objective function. The method can obtain the worst-case of each span when the multi-span beam is under multiple patch loading conditions. Additionally, this method can be used to adjust the position of support to reduce the maximum bending moment and to optimize the scantling based on the result of worst-case analysis. Numerical results show that a multi-span beam, after the optimization, displays minimal cross-sectional area in each span that satisfies the constraints. Meanwhile, the change of scantling shows little influence on the maximum bending moment and the worst position of patch loading;support position adjustment can reduce the maximum bending moment, thus reducing the structure weight. In an actual project, the support position adjustment reduces 22.64%of the maximum bending moment and 10.55%of the structural weight.