考虑压杆稳定性的桁架拓扑优化设计

Truss Topology Optimization Considering Structural Stability

目的初探用进废退思想在桁架拓扑优化设计中的应用，开发相应的优化程序并用算例进行验证．方法在桁架拓扑优化设计中考虑结构中受压杆的稳定性，同时考虑材料应力约束和压杆的稳定应力约束，通过杆件的实际受载情况及其应力约束值来调整各杆件的截面积，剔除优化结果中截面积小于阈值的杆件，以得到最优的拓扑结构和杆的截面大小，使各杆在保证结构稳定的前提下各尽所能，物尽其用．结果优化结果表明桁架达到减重和安全稳定的目的．结论该方法实用、可靠、收敛速度快，可以应用于复杂桁架结构的设计中．

Aim To develop the truss topology optimizing program by refering to the biology hypothesis of Lamarck. Methods The stability of the pressure bar was considered when optimizing the truss topology and the bar′s cross section area. The constraints included the allowable stress of the material and the allowable stress of the pressure bar′s stability. As the optimal result, the bars whose cross section areas are smaller than the threshold were removed, and each bar was made to bear the load as possible as the materials allow. Results The results of two optimization examples showed that the weights of the structure were reduced and the stability requirement was satisfied by this method. Conclusion This method is practical and reliable. It is an efficient optimization method. It can be used for the design of the complex truss structure.