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本文在给定结构拓扑和结构几何形状的条件下用序列二次规划的优化方法,研究了杆系钻机底座的结构优化设计。文中给出了底座结构优化设计的数学模型,其目标函数为底座结构的质量,所考虑的约束有尺寸上、下限约束、应力约束、刚度约束、位移约束以及局部稳定约束。文中对设计空间进行了转换,利用曲线拟合得出了单元截面各种参数的关系,使底座结构优化设计的数学模型大大简性。为了提高计算效率,本文采用序列二次规划法避免了灵敏度分析中的复杂计算。还利用Kuhn-Tucker条件,给出了优化算法的增量形式。文中推导了相应的计算公式,给出了计算步骤,并编制了相应的计算机程序。为了验证文中的理论及程序,计算了一个工程实例,该底座有176个节点,265个单元,受三种何载工况作用。优化设计迭代八次收敛,结构质量减少12.6％。这些表明文中所用的理论和方法对杆系钻机底座进行结构优化设计是可行的。
In this paper, given the structural topology and structural geometry under the conditions of sequence quadratic programming optimization method, the study of the rod rig base structural optimization design. In this paper, the mathematical model of the optimal design of the base structure is given. The objective function is the mass of the base structure. The upper and lower bound constraints, the stress constraints, the stiffness constraints, the displacement constraints and the local stability constraints are considered. In this paper, the design space is converted, and the relationship between various parameters of the cell cross section is obtained through curve fitting, so that the mathematical model of the optimal design of the base structure is greatly simplified. In order to improve the computational efficiency, this paper uses the sequential quadratic programming method to avoid the complex calculations in sensitivity analysis. Kuhn-Tucker conditions are also used to give an incremental version of the optimization algorithm. In this paper, the corresponding calculation formulas are deduced, the calculation steps are given, and the corresponding computer programs are compiled. In order to verify the theory and procedure in this paper, an engineering example was calculated. The base has 176 nodes and 265 units, which are affected by three load conditions. The optimization design iterated eight times and the quality of the structure decreased by 12.6%. These show that the theory and method used in this paper is feasible for structural optimization design of the rod rig base.