一种求解索杆张力结构整体自应力模态的能量方法

摘要

索杆张力结构通过预应力来获取刚度和承载能力,因此预应力态的确定是进行其他分析的基础.针对这种柔性结构体系,提出一种求解整体自应力模态的能量方法,通过特征值分析获取使结构初应变能取驻值的自应力模态.分析表明,这其中包含了结构各个线性独立的满足整体对称性要求的自应力模态,其实质是求得整体自应力模态解空间的一组满足初应变能驻值条件的标准正交基.该方法无需预先根据结构的对称性人为对杆件分组,降低了工作难度和出错的可能性,可作为整体可行预应力法的补充,应用于拓扑复杂的结构.算例分析结果显示,对于单整体自应力模态的结构,该方法与整体可行预应力法的找力分析结果一致.而对于多整体自应力模态的情况,初应变能取驻值这一约束条件的引入使求得的多组整体自应力模态中更易包含可行解,从而有利于将索杆张力结构的预应力设计问题转化为相对简单的单变量(预应力水平系数)优化问题进行求解.%Cable-strut tension structures can provide stiffness and load carrying capacity when prestressed,so the subsequent analysis is based on the prestressing mode.An energy method for overall self-stress modes calculation of flexible structureal system is proposed.The eigenvalue analysis was conducted to determine a set of self-stress modes where the linear independent overall self-stress modes are included.Essentially,the proposed method can achieve a special orthonormal basis of overall self-stress modes space,which satisfies the stationary condition of initial strain energy.Since the process of grouping members in terms of the structural integral symmetry is avoided,it is particularly applicable for the structures with complicated topology.The numerical examples show that for the single-overall selfstress mode,the force finding results agree well with those results by using integrity feasible prestressing method.For the multi-overall self-stress modes,the analysis results are more likely to include the solution which satisfies the feasible condition of cables in tension and struts in compression.So the prestressing design problem can be transformed into the single-target optimization problem about prestress level coefficient and can be solved easily.