论文部分内容阅读
从工程实际的角度来说,一般不允许结构形式中包含重叠单元。目前桁架拓扑优化的基结构法在选定基节点的情况下一般不建重叠单元,这导致可行域缩小,使优化不能找到更优解,人为增删杆件缺乏科学依据。针对该问题,该文对重叠给出准确的数学描述,建立包含重叠杆的基结构,利用Heaviside函数将拓扑变量连续化处理,使之在优化过程中可以获取目标函数、约束函数的敏度信息,同时考虑在拓扑优化中加入基频约束以避免出现机构,并加入稳定性约束防止出现压杆失稳,通过优化模型实现重叠过滤。最后通过两个案例计算证明可以找到更优解,验证了该方法的有效性。
From an engineering point of view, it is generally not allowed to include overlapping units in a structural form. At present, the basic structure optimization method of truss topology optimization does not construct overlapping cells in the case of selecting the base nodes, which leads to the reduction of the feasible region, so that the optimization can not find a better solution. There is no scientific basis for the addition or deletion of artifacts. In order to solve this problem, this paper gives an accurate mathematical description of the overlap, establishes a base structure containing overlapping bars, and uses the Heaviside function to process the topological variables continuously so that the target function and the sensitivity information of the constraint function can be obtained in the optimization process At the same time, the fundamental frequency constraint is added to the topology optimization to avoid the emergence of mechanism, and the stability constraints are added to prevent the buckling of the bar, and the overlapping filtering is achieved by optimizing the model. Finally, two case studies prove that the optimal solution can be found, which verifies the effectiveness of the method.