约束优化理论和动力松弛技术在张拉整体结构找形分析中的联合应用

发布时间：2018-03-07 19:33

本文选题：张拉整体结构　切入点：找形分析　出处：《土木工程学报》2015年07期 　论文类型：期刊论文

【摘要】：在诸多具有代表性的张拉整体结构找形方法中,一个有效的思路是将其归结为约束优化问题,从而运用非线性规划的方法进行求解。文中首先证明了约束优化问题的最优性条件与张拉整体结构平衡方程的等价性。随后,在优化模型的求解问题上,利用目标函数的梯度向量即为节点不平衡力这一重要关系,在梯度法的基础上引入动力松弛思想,让非平衡形态下的质点系在不平衡力的作用下开始运动,并通过"运动阻尼"使结构收敛至平衡位形。计算实践表明,引入动力松弛技术可确保迭代点在无需步长调整的情况下稳定而迅速地逼近极小点的邻域,改善梯度法在极小点附近收敛缓慢,须逐步减小步长以提高收敛精度的不足。由于目标函数中幂指数的取值对找形的成败影响较大,文中对此进行了重点探讨,建议其合理取值为3或4。在幂指数取定的情况下,通过调整权重系数和目标杆长控制结构位形,从而获取理想的找形结果。对于存在固定节点的索杆体系,还给出边界条件的处理方法,为开发新型空间结构提供有效的工具。
[Abstract]:Among many representative form-finding methods for tensioning integral structures, an effective way is to reduce them to constrained optimization problems. In this paper, we first prove the equivalence between the optimality condition of constrained optimization problem and the equilibrium equation of tensioned whole structure. Using the important relation that the gradient vector of objective function is the unbalance force of the node, the idea of dynamic relaxation is introduced on the basis of the gradient method, so that the particle system in the non-equilibrium form starts to move under the action of the unbalanced force. And the structure converges to the equilibrium configuration by "motion damping". The calculation practice shows that the introduction of dynamic relaxation technique can ensure that the iterative point can approach the neighborhood of the minimal point stably and rapidly without step adjustment. The improvement of gradient method converges slowly near the minimum point, so it is necessary to gradually reduce the step size to improve the convergence accuracy. Because the value of power exponent in the objective function has a great influence on the success or failure of shape finding, the emphasis is put on the discussion in this paper. It is suggested that the reasonable value be 3 or 4. When the power exponent is determined, the optimal shape finding result is obtained by adjusting the weight coefficient and the target bar length to control the configuration of the structure. The method of dealing with boundary conditions is also given, which provides an effective tool for the development of new spatial structures.
【作者单位】：东南大学混凝土及预应力混凝土结构教育部重点实验室;东南大学国家预应力工程技术研究中心;
【基金】：国家自然科学基金(51278116)
【分类号】：TU399

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