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Design optimization of FGM beam in stability problem

机译：稳定性问题中FGM梁的设计优化

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Purpose The purpose of this paper is to define and solve the problem of an optimized structural topology of the simply supported beam made from functionally graded material (FGM) enabling achievement of a maximum buckling load.Design/methodology/approach Two kinds of inclusions are considered: regular distribution of inclusions of different rigidities and non-uniform distribution of identical inclusions. It is shown that the optimal conditions are similar for both structural designs. The optimization problems are solved by using the homogenization method, and the target functions belong to the class of piece-wise continuous functions. Both optimized structures exhibit border zones free of any inclusions, and the largest amount of inclusions is localized in the central zone of the beams.Findings It has been shown that the final result of the carried out optimization of the internal structure for both studied types of FGM are similar. The relative increase in the buckling force of the FG beam with the optimized internal structure is on amount of 20 per cent while comparing it with the regular structure beam.Originality/value In contrary to a standard approach, this paper is aimed to detect and study a scenario of transition from heterogeneous to its counterpart homogeneous beam structure based on the consideration of the FGM inclusions. In addition, the problem of inversed transition from the optimized homogeneous structure to the optimal heterogeneous one is solved.
机译：目的本文的目的是定义和解决由功能梯度材料（FGM）制成的简单支撑梁的优化结构拓扑问题，以实现最大屈曲载荷。设计/方法/方法考虑两种夹杂物：不同刚度的夹杂物的规则分布和相同夹杂物的不均匀分布。结果表明，两种结构设计的最佳条件相似。通过均质化方法解决了优化问题，目标函数属于分段连续函数。两种优化的结构都表现出没有任何夹杂物的边界区域，并且最大程度的夹杂物位于光束的中心区域。研究结果表明，对两种研究类型的内部结构进行了优化的最终结果FGM是相似的。与常规结构梁相比，具有优化内部结构的FG梁的屈曲力相对增加了20％。原始数据/值与标准方法相反，本文旨在检测和研究基于对FGM夹杂物的考虑，从异质结构过渡到其对应的均质梁结构的场景。另外，解决了从优化的均匀结构到优化的异构结构的反向过渡的问题。

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