基于敏感度的杆系结构形态创构方法

The sensitivity-based morphogenesis method for framed structures

针对杆系结构,利用单元、节点坐标参数与结构应变能的关系,提出能够兼顾拓扑与形状的杆系结构形态创构方法。该方法基于有限元平衡方程,分别计算节点自由移动、约束移动、单元增加和单元消除等四种应变能敏感度,并利用这些敏感度与应变能变化关系生成或修正结构的拓扑形状,调整节点位置,最终得到应变能最小的合理结构形态。支座条件、空间条件等设计参数对最终结构形态的影响较大,利用该方法的此特点,可以调整设计参数得到多种合理的结构几何形状,在方案设计阶段可供设计人员参考。算例表明,该方法所得到的结构以轴力的形式传递荷载,而且能够保证刚度要求。

Based on the relationship between element or nodal coordinates and structural strain energy, the morphogenesis method, considering both topology and shape of framed structure, is proposed. In the method, the sensitivity numbers based on the finite element equilibrium equations were calculated for free nodal shift, restricted nodal shift, elemental increase or elimination. The change relations of this sensitivity and strain energy are used to generate or amend structure topology shape, adjust the location of the nodes to attain reasonable morphology with minimum strain energy. Design parameters such as support conditions, space conditions, etc. will influence the final morphology. According to this feature of the method, the design parameters can be adjusted to get diverse reasonable geometry shapes as reference in the design phase. Numerical examples show that the structures derived by the method can not only transfer load in the form of axial force but also guarantee the stiffness requirements.