基于非线性规划和有限元法的悬臂式桁架优化设计

为了对悬臂式桁架结构进行改进与优化,提出了一种更为简单可行的非线性规划模型。首先,在充分分析悬臂式桁架使用要求的基础上,创新性地将悬臂端节点挠度和结构的可靠性分别视为目标函数和限制条件,并通过静力学分析确定了目标函数和限制条件的具体表达式。然后,利用Python语言编程对优化方案进行求解,发现在给定的限制条件下,当桁架的总长为4 m、总高为2.6 m且杆件的横截面积为1 400 mm~2时,悬臂端节点的挠度最小。最后,利用ABAQUS软件并根据有限元法来判断优化方案的合理性。有限元法的计算结果表明:得出的优化方案是较为准确合理的,且适当减少桁架的总长并增大桁架的总高和杆件的横截面积,可以降低悬臂端节点的挠度。因此,基于非线性规划模型提出的目标函数和限制条件为其他类型桁架结构的优化设计提供了新思路。

Design optimization of cantilever truss based on nonlinear programming and finite element method

In order to improve and optimize the structure of the cantilever truss, a more simple and feasible nonlinear programming model was proposed. First of all, based on fully analyzing the requirements of cantilever truss, the deflection of the cantilever truss end node and the reliability of the structure were innovatively regarded as the objective function and the constraint condition respectively, and the static analysis was carried out to figure out the specific expressions of the objective function and the constraint condition. Subsequently, the optimization scheme was solved by Python language programming, which revealed that with the total length of this truss of 4 m, the total height of 2.6 m and the cross-sectional area of 1 400 mm², the deflection of the cantilever truss end node was minimum under the given constraints. Finally, ABAQUS software was utilized to judge the rationality of the optimization scheme based on finite element method. The calculation results of finite element method demonstrate that the optimization scheme is correct and reasonable to some extent. In addition, decreasing the total length of truss and increasing the total height of truss and the cross-sectional area of the bars appropriately can reduce the deflection of this cantilever truss end node. Therefore, the objective function and the constraint condition of the nonlinear programming model can provide a new idea for presenting better optimization design model of other types of truss structures.