质量对结构优化理性准则法计算结果的影响研究

在结构优化中,质量作为设计资源能改善结构性能,但质量会引起自重与惯性载荷等问题,因而质量还会导致结构性能劣化。虚功准则方程组忽略了载荷对设计变量的导数,不能考虑质量导致结构性能劣化的一面。对于航空航天器、高速运行的车辆、机械和高精度天线等以自重和惯性载荷为主的工程结构,这种忽略导致虚功法得到的解与最优解相差甚远。导重法是严密推导的理性准则法,克服了虚功法准则不准的缺陷,优化效果较虚功法大幅提高。但对于考虑自重载荷的三杆、五杆桁架等简单结构优化问题,虚功法也可以得到与导重法相同的最优解计算结果,从拉格朗日条件出发解释该问题,给出考虑载荷对设计变量的导数时虚功法也可求得最优解的条件,这对于结构理性准则法及其工程应用的深入研究均具有重要理论与实践意义。

The influence of structural mass on optimization effect of rational criterion methods

Structural mass plays two ambivalent roles in structural optimization:As design resource,mass can improve structural performances; On the other hand,as structural load,mass may make structural performances bad.Criteria equation group of virtual work method has ignored derivatives of structural load to design variables,cannot consider the other hand of ambivalent roles of structural mass.For aircraft,spacecraft,high-speed train,high-precision antenna etc.,whose structural main load are structural weight or inertial load,the result obtained through Virtual Work method are far away from the optimum solution.In Guide-weight method,the criteria equation groups of are strictly deduced,the limitation of Virtual Work method has been overcome,and its optimization result is improved greatly.But for some simple trusses composed by 3 bars or 5 bars,the result obtained through Virtual Work method is the same as the result obtained through Guide-weight method.According to Lagrange condition,this enigmatic problem is explained.The condition,that the result of Virtual Work method is the same as the result of Guide-weight method,is firstly presented.For rational criterion methods of structural optimization and its engineering applications,the study has important academic and practical value.