基于节点竖向移动的正交正放网架结构形态优化研究

Research on Structural Shape Optimization of Orthogonal Grid Structure Based on Vertical Movement of Nodes

研究了节点竖向位置对于正交正放网架结构承载力的影响.建立了以节点竖向坐标为设计变量,以结构储存应变能最小为目标函数,以结构允许变化空间作为约束条件的优化数学模型.在优化方法上,首先计算正交正放网架结构的总应变能;然后计算节点应变能对竖向坐标灵敏度,通过调整节点竖向坐标,进一步减小结构总应变能,改善结构受力状态;反复迭代,直至结构形态最优.通过算例表明本文提出的正交正放网架结构形态优化方法是可行的,通过对不同阶段结构矢跨比进行对比,得出了最合理矢跨比.

The influence of the vertical position of the nodes on the bearing capacity of the orthogonal grid structure is studied.An optimization mathematical model is established,which takes the vertical coordinates of nodes as the design variable,the minimum strain energy of the structure as the objective function,and the allowable variation space of the structure as the constraint condition.In the optimization method,the total strain energy of orthogonal grid structure is calculated firstly.Then,the sensitivity of the node strain energy to the vertical coordinate is calculated.By adjusting the vertical coordinate of the node,the total strain energy of the structure is further reduced and the stress state of the structure is improved,whichiterates repeatedly until the structure is optimal.An example is given to illustrate the feasibility of the proposed optimization method for the structural form of orthotropic grids.