汕头大学学报（自然科学版）

本文是对2016年全国大学生数学建模竞赛A题的解答,通过建立单点系泊系统二维静力学模型和三维静力学模型,求解出不同风速,水流力,水深和锚链规格情况下系泊系统的钢桶和各节钢管的倾斜角度,锚链形状,浮标的吃水深度和游动区域.在问题一中,对系泊系统中各部件作受力分析,建立单点系泊系统二维静力学模型,使用迭代法得到各节锚链坐标,画出锚链形状.问题二中,使用问题一中模型,分析可得风速为36 m/s时,因为重物球重量偏小,导致设备工作效果较差,所以使用二次拟合的方法得到合适的最小重物球重量.问题三中,建立单点三维系泊系统静力学模型,通过控制变量法,研究不同型号锚链的影响.

A solution is shown in this paper for the Problem A of Contemporary Undergraduate Mathematical Contest in Modeling in 2016. Two-dimension static model and three-dimension static model of Single Point Mooring System(SPMS)are built to work out the inclined angle of steel barrel and each steel pipe, the shape of the anchor chain, the draft and the walking range of buoy in SPMS under scenarios with different wind speeds, water current forces and the types of anchor chain rings. For first problem, force analysis of each component has been done and two-dimension static model of SPMS is built. By applying recursive algorithm, coordinates of each segment of anchor chain rings are obtained and the shape of anchor chain is plotted. For the second problem, by using the model of the first problem, it is found that, when the wind speed is 36 m/s, the weight of stable ball is not large enough, and will result in an unstable mooring system. To obtain the appropriate weight, quadratic fitting is performed. As for the third problem, by using control variable method, a three-dimension static model of SPMS is built to study how different types of anchor chain rings affect findings in the previous two problems.