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本文将序列二次规划应用于受到多阶固有频率与动力响应约束的结构动力优化设计,构造了一种交替执行调频步与减重步的迭代算法,可以有效地处理不可行设计。同时采用粗糙一维搜索确定步长并求出自适应的运动极限,使算法稳定收敛到最优点,旋翼和各种断面的梁结构动力优化数值实验证明了算法的有效性。应用序列二次规划求解组合结构静力优化已取得显著效果。对受到多频率约束的动力优化设计,序列二次规划也是有效的,但实践表明动力优化设计有其特殊性,需要我们对基本的序列二次规划算法加以修改,以适应频率、动应力和动变位约束非线性程度较高、初始设计往往不可行的特点。文[4]分析了数学规划法和结构优化中处理一维搜索的不同策略,指出应当引入粗糙一维搜索以保证算法的稳定收敛及数学的严谨性,本文将这一方法应用到动力优化中。
In this paper, Sequential quadratic programming is applied to structural dynamic optimization design constrained by multi-order natural frequency and dynamic response. It constructs an iterative algorithm to alternately perform FM step and weight reduction step, which can effectively deal with infeasible design. At the same time, the rough one-dimensional search is used to determine the step size and the adaptive limit of motion is obtained, so that the algorithm converges steadily to the most advantage. The numerical simulation of rotor dynamics optimization for rotor and various sections proves the effectiveness of the algorithm. The application of sequence quadratic programming to solve the static optimization of composite structures has achieved significant results. For multi-frequency constrained dynamic optimization design, sequential quadratic programming is also effective, but practice shows that dynamic optimization design has its own particularities. We need to modify the basic sequential quadratic programming algorithm to adapt to frequency, dynamic stress and dynamics. Displacement constraints have a high degree of nonlinearity and are often infeasible for initial design. [4] analyzes different strategies for processing one-dimensional search in mathematical programming and structural optimization, and points out that rough one-dimensional search should be introduced to ensure stable convergence and mathematical rigor of the algorithm. This paper applies this method to dynamic optimization. .