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基于对传统双向渐进结构优化(BESO)方法的改进,通过均匀化方法建立微观尺度多相材料布局分布与宏观结构材料弹性张量之间的联系,集成宏观结构所得到的位移场,推导出带有宏观结构力学特性的微观灵敏度。提出以宏观结构最大刚度为目标、对极小尺度周期性排列的材料微结构胞元进行布局优化设计的方法。本文算例结果表明,该方法在微结构多相材料布局优化设计过程中,不仅克服了拓扑优化领域常见的“棋盘格”现象,得到了边界清晰、受力合理的多相材料合理分布布局优化结果,而且整体优化过程稳定,具有很强的工程实际应用价值。
Based on the improvement of traditional BESO method, the relationship between the distribution of microscopic multiphase materials and the elastic tensor of macrostructure material is established by means of homogenization method, and the displacement field obtained by macrostructure is integrated, and the band Micro-sensitivity of macro-structural mechanics. In this paper, aiming at the maximum stiffness of macrostructures, a method to optimize the layout of microstructural cells with periodically arranged microscopic structures is proposed. The results of numerical examples show that this method can not only overcome the common “checkerboard” phenomenon in the field of topology optimization, but also obtain reasonable distribution of multiphase materials with clear boundaries and reasonable forces Layout optimization results, and the overall optimization process is stable, with strong engineering practical value.