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多变量单元结构共振解耦动力优化设计方法
Optimal method of resonance decoupling design for multivariable cross-sectional structure
投稿时间:2019-11-04  修订日期:2019-12-24
DOI:
中文关键词:  多变量单元  梯度函数  频率约束  优化设计  拉格朗日乘子
英文关键词:multivariate element  gradient function  frequency constraints  optimization design  Lagrange multiplier
基金项目:国家重点研发计划(2017YFE0103000);天津市交通运输科技发展计划(2018-35) ;河北省交通运输厅科技项目(TH-201916)
作者单位E-mail
黄海新 河北工业大学 hhxhebut@126.com 
李涛 河北工业大学  
程寿山 交通运输部公路科学研究所  
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中文摘要:
      针对截面多变量单元结构的动力优化问题,建立了带频率约束的结构动力优化设计模型,对隐式非线性频率约束函数进行Taylor近似展开,给出了截面多变量单元频率梯度函数显式表达式,基于kuhn-Tucker条件构建迭代算法,其中拉格朗日乘子通过建立联合方程组求解,形成了含多变量单元共振解耦优化设计方法。质量和刚度矩阵对线性和非线性单元结构均适用,并就双变量单元结构,给出了迭代求解中各参数的具体理论解析式,指出计算中应注意对被动变量的分类处理。以矩形截面单元结构为测试案例,结果表明:所给单元多变量算法具有良好的准确性;发现截面变量对频率的贡献存在主次之分,区分指标可采用梯度值;次要变量的修正因子迭代中可采用定值,且其下限应尽可能降低,利于节约成本。本文工作对多变量复杂截面的结构动力优化设计可提供理论指导,提高了结构动力优化方法的适用性。
英文摘要:
      Dynamic optimization design model for multivariable cross-sectional structures with frequency constraints is studied.Implicit nonlinear frequency constraint function is approximately obtained by Taylor’s expansion formulation,and the explicit expression of gradient function of frequency to cross-sectional design variables is given.Based on the Kuhn-Tucker condition, an iteration algorithm consisting of constraints and objective function gradient and Lagrange multipliers derived by solving a set of simultaneous equations is deduced,which constitutes the optimization method of resonance decoupling design for multivariable cross-sectional structures.The algorithm is suitable to linear and nonlinear mass and stiffness matrices,and the specific theoretical formula for the iterative parameters of bivariate cross-sectional structures is given. Attention should be paid to the classification of passive variables in the calculation. The results show that the accuracy of the algorithm is satisfied in terms of calculation of rectangular section structure.It is found that the contribution of cross-sectional variables to frequency is different, frequency gradient values can be taken as a indicator to distinguish dominant and inferior variables.The modified factors of inferior variables may be constant value in iteration solution,and its lower limit should be reduced as much as possible,which is good for cost savings.The work done here can provide theoretical guidance and improve applicability for structural dynamic optimization design of multivariate complex cross sections.
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