基于演化算法的带频率约束的桁架结构形状和尺寸优化

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振动与冲击 ›› 2010, Vol. 29 ›› Issue (12) : 13-17.

论文

基于演化算法的带频率约束的桁架结构形状和尺寸优化

薛运虎1; 韦凌云1; 赵玫2; 郝仰梅1; 唐天兵3

作者信息 +

Truss Optimization on Shape and Sizing with Frequency Constraints Based on Evolutionary Algorithm

Xue Yunhu1; Wei Lingyun1; Zhao Mei2 Hao Yangmei1; Tang Tianbing3

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文章历史 +

摘要

具有频率约束的桁架结构形状和尺寸优化设计是一个难度大的非线性动力优化问题。形状和尺寸变量的耦合通常导致收敛困难，而频率约束则使得动力灵敏度分析困难，传统的优化准则法和数学规划法难于求解。本文将单纯形算法、子空间变维技术、均匀变异有机融入郭涛算法，提出一个混合演化算法，避开繁琐的动力灵敏度分析，简单、有效地求解这类桁架形状和尺寸优化问题。典型的桁架算例验证了算法的有效性和可靠性。

Abstract

Truss optimization on shape and sizing with frequency constraints are highly nonlinear dynamic optimization problems. Coupling of two different types of design variables, nodal coordinates and cross-sectional areas, often lead to divergence while multiple frequency constraints often cause difficult dynamic sensitivity analysis. Mathematical programming and optimal criteria methods, which need complex dynamic sensitivity and are easily trapped into the local optima, are difficult to solve the problems. A modified evolutionary algorithm was proposed to solve the truss shape and sizing optimization simply and effectively. The proposed algorithm organically combined the Nelder–Mead’s simplex method, multiple-parent crossover and variant subspace technique. Several typical truss optimization examples are employed to demonstrate the validity, availability and reliability of the proposed algorithm for solving shape and sizing optimization of trusses with multiple frequency constraints.

导出引用

薛运虎;韦凌云;赵玫;郝仰梅;唐天兵. 基于演化算法的带频率约束的桁架结构形状和尺寸优化[J]. 振动与冲击, 2010, 29(12): 13-17

Xue Yunhu;Wei Lingyun;Zhao Mei Hao Yangmei;Tang Tianbing. Truss Optimization on Shape and Sizing with Frequency Constraints Based on Evolutionary Algorithm[J]. Journal of Vibration and Shock, 2010, 29(12): 13-17