基于改进双向渐进结构优化法的桁架结构拓扑优化

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...

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

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.