不同荷载工况下钢筋混凝土深梁的拓扑优化设计

Topology optimization design for RC deep beams under different load conditions

为探讨不同荷载工况对钢筋混凝土深梁拓扑优化的影响,同时改进当前深梁设计方法,采用渐进演化类拓扑优化算法寻求钢筋混凝土开洞深梁在不同集中加载工况和荷载集度工况下的最优拓扑结构,再依据这些最优拓扑结构建立相应的压杆-拉杆模型,并分析这些最优拓扑结构和压杆-拉杆模型的差异。结果表明:压杆-拉杆模型均为较符合满应力分布的Michell结构;集中荷载作用在梁顶时,荷载从加载点通过最短直线压杆以压力的形式向支座传递;集中荷载作用梁腹和梁底时,荷载则通过伞状拉杆悬吊在主压拱上,再向支座传递;随着荷载集度降低,最优拓扑结构向拱或拱-组合压杆的组合体系演化。在工程设计中,对于不同荷载工况条件下的钢筋混凝土深梁,可以参照最优拓扑结构在内部有针对性地设计隐藏的受压加强构件或受拉钢筋。

To discuss the influence of load conditions on the topology optimization for RC deep beams,and improve their current design methods as well,in this paper the optimal topology structures for RC deep beams with openings under different concentrated loading conditions and different load concentration conditions were separately evolved based on the evolutionary topology optimization algorithm.Then,the corresponding Strut-and-Tie models were constructed according to these optimal topology structures.The diversities among these optimal topology structures and among these Strut-and-Tie models were discussed next.The results show that all these Strut-and-Tie models conform better to Michell structures which have full stress distribution.The loads are always transmitted from the loading point to the support in the form of pressure through the shortest straight struts when a concentrated load is applied on the top surface of the beams,while the loads are suspended on the main pressure arch by umbrella shaped ties and then transmitted to the support when a concentrated load is applied on the web or bottom of the beams.The optimal topological structures always evolve into arch structures or hybrid system of arch-and-composite-strut as the load concentration decreases,especially those are close to uniform loads applied on the beam.Furthermore,the RC deep beams under different load conditions may be designed with some hidden reinforced compression parts and tensile reinforcements in beam body by the light of the optimal topology structures in engineering designs.