基于乘子-Newton优化算法确定钢箱梁斜拉桥的合理成桥状态

Reasonable Completed State for Cable-stayed Bridge with Steel Box Girder Based on Newton Method

针对钢箱梁斜拉桥成桥状态的优化问题,以钢箱梁斜拉桥主梁和桥塔的弯曲能量之和为目标函数,以主梁和桥塔位移、应力、斜拉索索力及其均匀性等为约束条件,建立钢箱梁斜拉桥成桥状态优化的二次规划数学模型,并采用乘子-Newton优化算法进行求解;结合该方法和有限元方法对国内某座大跨径独塔钢箱梁斜拉桥的成桥状态进行了优化,并与无约束最小弯曲能量法及刚性支承连续梁法的优化结果进行了对比。研究结果表明:该方法优化所得结构位移、内力、应力及索力与其余两种方法优化结果的最大相对误差分别为21mm、127.29%(16 194kN·m)、154.21%(4.58MPa)以及22.51%(346kN);该方法所得成桥状态下,主梁线形平顺,内力及上下缘应力分布均匀,桥塔塔顶向边跨有一定的预偏,且为全截面受压状态,斜拉索索力随斜拉索长度的增长均匀递增,过渡墩与辅助墩的支承反力均为正值,具备一定的压力储备;该方法简便、有效、实用性强,可避免采用传统方法时,人为调索的随意性,可方便地获得钢箱梁斜拉桥的合理成桥状态。

In order to optimize the completed state for cable-stayed bridge with steel box girder,aquadratic programming model was established,in which sum of bending energy of girder and pylon was taken as objective function,and displacements of girder and pylon,normal stresses of girder and pylon,cable forces and their distributional uniformity were taken as constraint conditions.Multiplier-Newton method was employed to solve the quadratic program.Combined with this algorithm and finite element method,optimization analysis of reasonable completed state for a large span cablestayed bridge with steel box girder and single pylon was conducted,and analysis results were compared with which obtained from unrestraint minimum bending energy method and continuous rigid support beam method.The experimental results show that the maximum relative errors of displacement,internal force,normal stress and cable force of structure gained from the method proposed in this paper among the other two methods are 21 mm,217.29%（16 194kN·m）,154.21%（4.58 MPa）,and 22.51%（346kN）,respectively.Under the condition of completion state obtain through this method,the shape of steel box girder is smooth,distribution of top and bottom fiber normal stress is uniform,top of the pylon has a certain amount of pre-deviation to side span,and the whole cross section is under a state of compression,cable forces grows uniformly with the growth of cable length,and reactions of side pier and auxiliary pier are all positive,which suggests that they have certain amount of pressure reservation.The method proposed in the paper is simple,effective,and practical.It can avoid the arbitrariness of cable force adjustment when using the traditional method,and can easily obtain the reasonable completed state for cable-stayed bridge with steel box girder.