基于改进双向渐进结构优化法的桁架结构拓扑优化  

Topology optimization of truss structure based on improved bi-directional evolutionary structural optimization method

作　　者：才琪 冯若强[1] CAI Qi;FENG Ruoqiang(The Key Laboratory of Concrete and Prestressed Concrete Structures of the Ministry of Education,Southeast University,Nanjing 211189,China)

机构地区：[1]东南大学混凝土与预应力混凝土结构教育部重点实验室,江苏南京211189

出　　处：《建筑结构学报》2022年第4期68-76,共9页Journal of Building Structures

基　　金：国家自然科学基金项目(51778283,51978151),东南大学优秀博士学位论文培育基金(YBPY1958)。

摘　　要：为了将双向渐进结构优化法应用于桁架结构优化设计中,结合能量原理和满应力设计准则,推导了以结构最小应变能为目标函数的优化计算公式,提出了可以应用于桁架结构优化的桁架-双向渐进结构优化(T-BESO)法。T-BESO法以杆件截面面积为设计变量,以结构应变能为目标函数,以应力约束和满应力设计准则为约束条件。在T-BESO法中,将BESO法表示单元密度的二元离散设计变量修改为表示截面面积的连续设计变量,这使得可以同时对桁架结构进行拓扑优化和尺寸优化;采用能量原理和满应力设计准则简化了桁架结构的灵敏度推导;相比BESO法每次迭代一般只能优化2%的设计变量,T-BESO法可以同时优化所有设计变量;T-BESO法不需要设置体积约束,可以克服传统BESO法由于体积系数设置不合理而导致程序不收敛的缺点。数值算例的优化结果表明,当采用合理的基结构时,T-BESO法的计算结果与解析解的误差在1%以内,这表明了T-BESO法的有效性。In order to apply the bi-directional evolutionary structural optimization(BESO)method to the optimization of truss structures,a novel algorithm named truss-BESO(T-BESO)is proposed.The BESO method,energy principle and fully stressed design criterion are combined in the T-BESO method.The cross-sectional areas of the bars are used as the design variables.The structural strain energy is used as the objective function,and the stress constraints and fully stressed design criteria are used as constraints in the T-BESO method.In the T-BESO method,the binary design variable representing the member density in the BESO method is modified to a continuous design variable representing the cross-sectional area of the bar.This makes it possible to optimize both the cross-sectional area of the bar and the topology of truss structure simultaneously.The energy principle and fully stressed design criteria are used to simplify the sensitivity calculation of the truss structure.All design variables can be optimized in one iteration in the T-BESO method.However,in the BESO method,only 2%of the design variables can be optimized.In addition,the T-BESO method does not contain the structural total volume constraint,which can overcome the shortcomings of the BESO method that the code does not converge due to the unreasonable total volume constraint.The optimization results of the numerical examples show that when a reasonable ground structure is used,the errors between the optimization results of the T-BESO method and the analytical solutions are less than 1%,which illustrates the effectiveness of the T-BESO method.

关 键 词：桁架结构 桁架-双向渐进结构优化法 拓扑优化 应变能 满应力设计 

分 类 号：TU393.304[建筑科学—结构工程] TU311.41