摘要
抱杆优化设计需要耗费大量有限元分析计算时间,难以确定可行域.该文采用响应面法(response surface method,RSM)来模拟抱杆结构的真实响应,提出了改进的算术优化算法(improved arithmetic optimization algorithm,IAOA)对抱杆结构进行优化设计.将分数阶积分引入算术优化算法(arithmetic optimization algorithm,AOA),改善了算法的开发能力.采用拉丁超立方抽样,选取抱杆结构杆件截面试验样本,利用最小二乘法对样本点进行分析,构建了抱杆结构应力和位移关于杆件截面尺寸的二阶响应面代理模型.建立以抱杆质量最小化为优化目标,许用应力和位移为约束条件的优化模型,采用IAOA对其进行求解.结果表明:二阶响应面模型能够准确预测抱杆结构的响应值,IAOA的求解精度得到显著提升,代理模型可大幅降低有限元分析所需的计算代价,优化后抱杆结构质量减轻了8.2%.联合使用RSM和IAOA可有效求解大型空间杆系结构的优化设计问题.
The computation consumption of finite element analysis for structural optimization design of holding poles is large, and it is difficult to determine the feasible region. The response surface method(RSM) was used to simulate the real response of the holding pole, and an improved arithmetic optimization algorithm(IAOA) was proposed to optimize the holding pole. The fractional-order calculus was introduced into the arithmetic optimization algorithm(AOA) to improve the exploitation ability of the AOA. The Latin hypercube sampling was applied to select the test samples of each member of the holding pole, and the least square method was employed to analyze the sample points. Then, the 2nd-order response surface surrogate model for the stress and displacement of the holding pole on the cross-sectional sizes of each member was established. An optimization model was constructed with the minimum mass as the optimization objective and the allowable stress and displacement as constraints, and the IAOA was implemented to solve the model. The results show that, the 2ndorder response surface model can accurately predict the response value of the holding pole. The solution accuracy of the IAOA is significantly improved. The surrogate model can greatly decrease the calculation cost of the finite element analysis. The mass of the holding pole is reduced by 8.2% after optimization. The RSM and the IAOA can be combined to solve the optimization design problem of large spatial truss structures effectively.
作者
陶然
周焕林
孟增
杨小猛
TAO Ran;ZHOU Huanlin;MENG Zeng;YANG Xiaomeng(College of Civil Engineering,Hefei University of Technology,Hefei 230009,P.R.China)
出处
《应用数学和力学》
CSCD
北大核心
2022年第10期1113-1122,共10页
Applied Mathematics and Mechanics
基金
国家自然科学基金(11672098)。
关键词
响应面法
算术优化算法
分数阶积分
代理模型
抱杆
response surface method
arithmetic optimization algorithm
fractional-order calculus
surrogate model
holding pole
