结构优化导重准则及其意义与合理性

MEANING AND RATIONALITY OF GUIDE-WEIGHT CRITERION FOR STRUCTURAL OPTIMIZATION

导重准则是根据数学规划的库恩-塔克极值条件严密推导的结构优化理性准则,导重准则可表述为"最优结构应当按照导重正比分配结构重量",意义明确、形式简捷,便于应用.导重准则法克服了虚功准则法无法考虑载荷随设计变量变化导数的缺陷,具有优化效果好、优化迭代前几步收敛快的明显优势.论文从结构优化基本形式出发给出导重与导重准则更加规范、更具一般性的数学表达与力学意义,创新之处在于对照优化设计基本理论对导重准则的合理性以及导重准则对结构优化寻优迭代的指导意义给出深入思考与剖析,解决了最优结构为什么要按导重正比分配重量的问题,并首创了衡量结构设计最优化程度的最优性定量指标,为导重准则法在工程结构中的广泛应用奠定可靠理论基础.

The guide-weight criterion for structural optimization is introduced here, which is rigorously educed from Kuhn-Tucker extremum conditions and rational. This criterion is expressed as that in an opti-mum structure the weight and guide-weight of any component group should be directly proportional. Its meaning is clear,and its form is very simple, guide-weight criterion method overcomes the drawback of vir-tual work criterion method which can not consider derivative of load to design variable. Moreover, guide-weight criterion can obtain excellent optimization results and a fast convergence. In this paper,more norma-tive and more general mathematical expressions and mechanical meanings of guide-weight and Guide-weight criterion are presented. The rationality of guide-weight criterion and the supervise sense of guide-weight criterion for optimization iterative are lucubrated and discussed, and a newly created index measuring the optimization degree is also proposed.