含自重载荷作用下桁架拓扑优化的功射极法  

WORK-RATIO-EXTREMUM METHOD FOR TOPOLOGY OPTIMIZATION OF TRUSSES SUBJECTED TO LOADS INCLUDING SELF-WEIGHT

作　　者：欧笛声[1,2] 周雄新[2] 

机构地区：[1]广西大学土木建筑工程学院,南宁530004 [2]广西工学院工程训练中心,柳州545006

出　　处：《工程力学》2011年第7期136-142,164,共8页Engineering Mechanics

基　　金：广西壮族自治区科技厅项目(0728013);广西工学院项目(0977109)

摘　　要：由含自重载荷功约束下桁架重量最小化问题的一阶极值条件导出功-重量分配准则,即结构重量应按外力功与自重载荷所做功之差的大小来正比分配才能达到最优。桁架拓扑优化的功射极法是依据不等式约束的Kuhn-Tucker极值条件以及射线步对功函数一阶偏导数的影响规律而构造的,它包括3个步骤,即:解析确定最佳射线步步长与乘子、求解功准则方程组。利用各设计变量的等比变化对不动点迭代求解式及其Jacobi矩阵的影响规律,证明所构造的求解式具有全局收敛性。基于功约束与应力约束的不相容性,可用应力比法对经拓扑优化的结构做进一步的优化。以多工况下三杆和十杆桁架结构为例验证所述方法的有效性。The work-weight-distribution criterion is derived from the first-order extremum conditions of minimal truss weight under the work constraint with self-weight loads.It indicates that structural weight can be optimally distributed according to the difference of external force work and self-weight work.The work-ratio-extremum method of the truss topology optimization is derived from the Kuhn-Tucker conditions with inequality constraints and the regular influences of a ratio step on the first order derivations of the work function.The method includes three steps,i.e.,formulate the optimal ratio step and the multiplier,and solve the work-criterion equations.Using the regular influences of a scale of all design variables on the fixed-point iterative solution and its Jacobi matrix,it is proved that the algorithm is globally convergent.Based on the incompatility of the work constraint and the stress constraints,the stress ratio method can be used to optimize the structure next to the topology optimization.Numerical examples of a three-bar truss and a ten-bar truss for multiple loadings show that the methods are effective.

关 键 词：桁架拓扑优化 自重载荷 功射极法 全局收敛性 反变仿射变换法 

分 类 号：TU323.4[建筑科学—结构工程] TB21[一般工业技术—工程设计测绘]