带损伤平面桁架结构位移解析

 采用解析方法,研究了带损伤平面桁架结构的静力问题。对于含有n个子结构的平面桁架结构,建立一个与理想桁架结构等价的循环周期结构体系,对其中一个子结构建立控制方程,将杆件损伤处理为方程的荷载项,运用U 变换法对静力学方程组进行解耦,推导出各个节点位移的解析表达式。应用解析表达式分析带一个杆件损伤桁架结构的节点位移,并与无损伤时结构的解相比较,结果显示,有损伤时相关节点位移较无损伤时有所增大,且其位移变化合理,验证了解析表达式的可行性。

Analytical study of the plane truss structure with damage

This paper presents an analytical static study of the plane truss with rigidity damage. Firstly, an equivalent structure with cyclic periodicity is built. The rigidity damage of the bar can be expressed as an additional loading in the governing equations of a substructure. Then, by using the U-transformation technique, the equations may be uncoupled into independent equations. The nodal displacements are solved in the analytical form. Lastly, a calculation example is taken, and the obtained nodal displacements are compared to the those of a perfect structure. It is shown that the variations of the displacements are reasonable. This paper provides a means for analyzing the influence of the rigidity damage on the plane truss structure.