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中文摘要：
传统渐进结构优化法（ESO）删除的低效材料，仅是阶段性的低效材料，其中部分材料若不被删除，有可能成为后续优化中的非低效材料。误删材料可能使接下来的优化成为“将错就错”的优化。该文在ESO法基础上提出的“周期性扩大框架的渐进结构优化方法（PEFESO）”，周期性地恢复并检查保留材料周围被删除材料的效率，重新判定该部分材料是否应被恢复到结构中，有效地削弱了ESO法可能误删材料的不良影响。PEFESO法具备一定的全程寻优能力，计算结果优于传统的ESO法，易于在工程中推广使用。
英文摘要：
The inefficient material removed in the traditional Evolutionary Structural Optimization （ESO） is only inefficient in some stages. If some of this material is not removed, it possibly does not become inefficient in the later optimization. The faulty removal of material possibly makes the subsequent optimization to be based on the previous faulty result. The Periodically Expanding Frame for the Evolutionary Structural Optimization （PEFESO） method is put forward in this paper. On the basis of ESO, this method periodically restores and checks the efficiency of the material removed around the remaining material and determines whether it should be restored to the structure or not, thusly PEFESO can effectively reduce the undesirable effect of ESO resulted from possibly faulty removal. PEFESO has a global optimization capacity at a certain degree with a better result than that of the traditional ESO. It is easy to be widely used in engineering.
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