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

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.