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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。
By using analytical method, the static problem of the planar truss structure with damage is studied. For a planar truss structure with n substructures, a periodic cyclic structure system equivalent to the ideal truss structure is established, a governing equation is established for one of the substructures, the damage of the bar is treated as the load term of the equation, The equations of mechanics are decoupled and the analytical expressions of displacement of each node are deduced. The analytic expression is applied to analyze the joint displacement of a truss structure with one rod and compared with the solution of the structure without damage. The results show that the displacement of the relevant node increases with the damage and the displacement changes reasonably , Verify the feasibility of parsing the expression.