基于4次样条函数拱轴线优化设计的T-V求解法

拱桥拱轴线可以用4次样条函数表示,而基于4次样条函数的拱桥拱轴线优化设计问题是一个非线性规划问题。采用Topkis-Veinott可行方向法研究了优化求解方法,提出了新算法。通过对上承式钢筋混凝土拱桥实例求解,得到了符合设计要求的结果。计算结果表明,该拱轴线优化模型与初始拱轴线无关,不需要对初始拱轴线的选择做细致研究,只要初始拱轴线是连续曲线即可;在应用Topkis-Veinott容许方向法时,需要注意初始点的选择要求必须是可行点。由于容许方向法的每次迭代都是在可行域中进行的,方向是目标函数下降的方向,每步迭代结果都是可行设计,而且后一步迭代结果比前一步结果要好。因此,该拱轴线优化模型有较好的可靠性和实用性。

Topkis-Veinott Feasible Direction Method for Optimum Axis of Arch Bridge Based on Quartic Spline Function

The axis of an arch bridge can be represented using quartic spline functions.The optimisation of axis shape based on this representation can be formulated as a nonlinear programming problem.The Topkis-Veinott feasible direction method is applied for the solution of this optimisation and a new algorithm is proposed.A reinforced concrete arch bridge is used as an illustrative example,and the solution found by the new algorithm satisfies design requirements.The numerical results show that the final solution is insensitive to the initial arch axis,and therefore any smooth curve can be used and no detailed investigation is needed for the selection of initial arch axis.On the other hand,the initial design must be feasible for The Topkis-Veinott feasible direction method.When Topkis-Veinott feasible direction method is used,solutions for all iterations remain feasible and move in the descending direction for the objective function.With the new algorithm,all design obtained are feasible and design for one iteration is always better than that for the previous iteration.Therefore,the proposed optimisation model is both reliable and practical.