基于广义逆矩阵理论的杆系结构形态创构方法

A structural morphogenesis method for frame structure based on generalized inverse matrix theory

广义逆矩阵理论被广泛应用于不稳定结构的形态分析。不稳定结构在荷载作用下,其形状会发生变化直至其势能达到最低,此时的结构处于无弯矩的平衡状态。根据该原理并结合广义逆矩阵理论提出一种适用于杆系结构的形态创构方法。该方法将杆系模型中杆单元进行分组,在每一组中杆单元总长度不变的条件下,建立控制结构形状变化的移形方程。利用广义逆矩阵理论和势能梯度确定使模型势能下降最快的方向,并逐步调整节点位置直至势能达到最低。临时单元和单元组的引入使得该方法可以应用于多种形式结构的形态创构,合理地设置单元组和临时单元可以实现单元长度与单元内力的重新分配进而实现诸多功能。算例分析说明该方法的特性并验证其有效性。

Generalized inverse matrix theory has been widely applied to the morphological analysis of unstable structures.The shape of unstable structure may change under load until its potential energy reaches the minimum, which corresponds to the equilibrium state of the structure without bending moment.Based on this principle and the generalized inverse matrix theory, a structural morphogenesis method suitable for frame structures is proposed.The bar members in the unstable structure are grouped, and the shape transformation equation governing the shape change of the structure is established under the condition that the total length of the members in each group is unchanged.The generalized inverse matrix theory and potential energy gradient are employed to determine the rapidest descending direction of the potential energy, and the positions of nodes shall be gradually adjusted until the potential energy reaches the minimum.With the introduction of element group and temporary elements, the proposed method can be applied to the morphogenesis of various forms of structures.Reasonable setting of element group and temporary element can realize the reasonable redistribution of element length and internal forces as well as many functions.Based on several numerical examples, the characteristics of the method are explained and its effectiveness is validated.