影响结构优化理性准则法优化效果的关键问题研究

深入仔细分析决定理性准则法优化效果与优化效率的关键问题——准则是否准确和迭代计算是否收敛。首次提出：在结构优化中，重量作为设计资源除有改善结构性能的一面之外，还会有作为载荷导致结构性能劣化的矛盾的另一面。虚功准则方程组忽略载荷导数，无法考虑重量矛盾作用的另一面，这种忽略不能视为合理近似。因为对于航空航天器、高精度天线和高速运行的机械、车辆等以自重和惯性载荷为主的一大类工程结构，这种忽略导致虚功法，得到的解离最优解相差甚远。导重准则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，优化效果大幅度提高。理性准则法最后归结为非线性准则方程组的迭代求解，由于工程结构优化的准则方程组难以满足其严格的收敛条件，而可采用步长因子法求解，可以证明使迭代收敛的步长因子一定存在，并可给出步长因子理论取值范围和实际取值方法。以十杆桁架考题和两个天线结构优化为例验证了以上论点。

Study on Keys Influencing Optimization Effect of Rational Criterion Methods of Structural Optimization

Keys influencing optimization effect of rational criterion methods of structural optimization are correctness of criteria equation groups and astringency of iterative algorithm, these keys are dissectionally lucubrated. It is firstly pointed out that structural weight plays two ambivalent roles in structural optimization: As design resource, weight can improve structural performances; On the other hand, as structural load, weight may make structural performances bad. Criteria equation group of virtual work method has ignored derivatives of structural load to design variables, can not consider the other hand of ambivalent roles of structural weight, this ignoring can not be treated as a rational approximation. For aircraft, spacecraft, high-precision antenna, high-speed train, vehicle and machine etc., their structural main load is structural weight or inertial load, the result obtained through Virtual Work method is 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. Rational criteria methods come down to directly iterative solution of nonlinear criteria equation group, which is a fixed point mapping problem with strict convergence condition. The step factor method is often used to ensure iteration convergence. It can be proved that the step factors making iteration convergence must be existent. And theoretic value range and practical selection methods of step factors making iteration convergence has been educed and proposed. Optimization examples of a truss with 10 bars and two antenna structures can validate above contention.