材料多等级双向演化结构优化算法  

Bidirectional evolutionary structural optimization algorithm for multi-grade materials

作　　者：张鹄志 黄垚森 李永贵 尹斌 ZHANG Huzhi;HUANG Yaosen;LI Yonggui;YIN Bin(School of Civil Engineering,Hunan Provincial Key Laboratory of Structures for Wind Resistance and Vibration Control,Hunan University of Science and Technology,Xiangtan 411201,China)

机构地区：[1]湖南科技大学土木工程学院结构抗风与振动控制湖南省重点实验室,湖南湘潭411201

出　　处：《铁道科学与工程学报》2022年第6期1726-1733,共8页Journal of Railway Science and Engineering

基　　金：国家自然科学基金资助项目(51508182);湖南省自然科学基金资助项目(2021JJ30270)。

摘　　要：经典双向演化结构优化(BESO)算法采用单一材料非“生”即“死”的优化方式,过程中易产生边界问题,从而使结果陷入局优。为解决这一问题,在优化中线性内插多个弹性模量等级的材料,再构建基于变异系数的材料利用程度评价指标,以决定单元在不同材料等级间的升降,开发出材料多等级BESO算法。通过深梁算例对比新算法与经典BESO算法在优化能力上的差异,并探讨材料等级数对优化过程和结果的影响。研究结果表明:算例在优化运行至折算体积率为0.3时,单一材料的经典BESO算法,双材料、三材料和四材料的材料多等级BESO算法,解的柔顺度指标分别为0.818×10^(4),0.785×10^(4),0.775×10^(4)和0.768×10^(4)N·mm,耗时分别为4,8,12和18 min。算例在优化运行至绝对体积率为0.3时,三材料的材料多等级BESO解中占比高的材料2和材料3,变异系数分别为0.11和0.26,而经典BESO解中单一材料的变异系数为4.88。因此,与经典BESO算法相比,材料多等级BESO算法可以得到柔顺度更低,更符合优化目标的解,即更优的解。同时演化出的杆系结构拓扑更清晰,材料利用率更高。材料等级数越多,越能通过不同等级的材料分布反映构件受力机理,显微构件受力细节,但会引起耗时增加,实际优化应用时应权衡精度与效率以选择合适材料等级数。The classical Bidirectional Evolutionary Structural Optimization (BESO) algorithm always obtains local optimal solution only,due to boundary problems occurring in the optimization process since it uses an optimization policy of“life”or“death”for a single material.In order to overcome this problem,a BESO algorithm for multi-grade materials was achieved by introducing linearly interpolated materials with multiple elastic modulus grades and using the evaluation index of material utilization constructed based on variation coefficient to determine the upgrade and downgrade of the elements’properties between different materia grades.Then,through numerical examples of a deep beam,the optimization ability between the new algorithm and the classical BESO algorithm was compared,and the influence of quantities of material grades on optimization process and results was investigated as well.The results show that the solutions of the classical BESO algorithm for single material,and the BESO algorithm for bi-grade materials,tri-grade materials and tetragrade materials separately have compliance index values of 0.818×10^(4) N·mm,0.785×10^(4) N·mm,0.775×10^(4) N·mm and 0.768×10^(4) N·mm,as well as the time consumption is 4 min,8 min,12 min and 18 min,respectively,when the examples were all optimized to a converted volume rate of 0.3.Moreover,the variation coefficients of material 2 and material 3,which accounts for high proportions in the solution of the BESO algorithm for tri-grade materials,are 0.11 and 0.26 respectively,while that of single material in the solution of the classical BESO algorithm is 4.88,when the examples were all optimized to an absolute volume rate of 0.3.Consequently compared with the classical BESO algorithm,the BESO algorithm for multi-grade materials can obtain solutions with lower compliance and more in line with the optimization goal,that are,better solutions;meanwhile,its evolved topology of bar-system structures are clearer and have a higher material utilization.Besides,the more gra

关 键 词：结构优化 拓扑优化 BESO算法 材料多等级 结构柔顺度 

分 类 号：TU318[建筑科学—结构工程]