静定桁架结构截面最优化设计的功定向配置法

WORK METHOD OF DIRECTIONAL ALLOCATION FOR CROSS-SECTION OPTIMIZATION OF STATICALLY DETERMINATE TRUSS

以Kuhn-Tucker函数的极值条件为出发点,证明多节点位移与多杆内应力约束下结构重量最轻化问题可转化为单约束问题来求解,可将位移—重量分配准则和应力—重量分配准则转化为功定向分配准则。利用功能互等定理,将位移与应力约束统一为功的定向约束,以此为基础构造出功定向配置法,以各承受节点载荷的节点位移作为约束控制点,组成具有正定性质的位移约束;或用位移约束与应力约束的组合,构成具有正定性质的位移与应力约束;结合位移极射法和满应力法获取最优解。并用二杆和六杆静定桁架结构的算例验证相关理论和算法。

According to the extremum condition of Kuhn-Tucker function,it is proved that the weight minimization problem,under displacement constraints of multiple nodes and stress constraints of multiple bars,can be transformed into several optimization problems under single constraint.And,the displacement-weight and the stress-weight distribution criterion can be turned into the directional work-distribution criterion.On the basis of external work being equal to internal energy,the displacement and stress constraints can be changed into uniform constraints of directional work.Thus,the work method of directional allocation is proposed： the nodal displacements of carrying nodal loads are used as controlled points,and are made up of the displacement constraints which constitute a positive definite set.Or,a combination with displacement and stress constraints also constitutes a positive definite set.The optimal solution is obtained by the displacement-extremum-scale method,or a method of combinating with it and fully stress design.At last,two numerical examples of statically determinate 2-bar and 6-bar trusses are used to verify the mentioned theories and algorithmic rules.