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首页> 外文期刊>Proceedings of the institution of mechanical engineers >A buckling analysis of perfect and imperfect functionally graded columns
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A buckling analysis of perfect and imperfect functionally graded columns

机译：完善和不完善的功能梯度柱的屈曲分析

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Due to the asymmetry of the material properties about the middle plane, perfect columns made of functionally graded materials (FGMs) may not remain straight when a com-pressive axial point load is concentrically applied. This article analytically derives the displacement functions and the buckling load of both perfect and imperfect Euler-Bemoulli functionally graded columns. The method of derivation is based on the translation of the reference plane to the position at which the coupling between the axial and bending deformations is eliminated, i.e. the physical neutral surface position. Then, all the governing equations and their solutions turn out to have the same form as those of homogeneous columns subjected to an eccentric axial load. The effects of geometric imperfection are studied with the main purpose of finding imperfect shapes that make an imperfect column stronger than a perfect one. Further, the governing equations that are used to find those analytical solutions are expanded so that the equations can deal with large deformation and large strain analysis. These new governing equations are solved by finite element (FE) method based on linear exact shape functions. Then, the FE solutions are used to compare and validate the analytical solutions obtained earlier.
机译：由于材料特性关于中间平面的不对称性，当同心施加压缩轴向点载荷时，由功能梯度材料（FGM）制成的理想圆柱可能不会保持笔直。本文通过分析得出了完善的和不完善的Euler-Bemoulli功能梯度柱的位移函数和屈曲载荷。推导方法基于参考平面到消除轴向变形和弯曲变形之间的耦合的位置（即物理中性表面位置）的平移。然后，所有控制方程及其解都具有与均质柱承受偏心轴向载荷相同的形式。研究几何不完美的影响的主要目的是找到使不完美圆柱比理想圆柱更坚固的不完美形状。此外，扩展了用于找到这些解析解的控制方程，从而使这些方程可以处理大变形和大应变分析。这些新的控制方程通过基于线性精确形状函数的有限元（FE）方法求解。然后，将有限元解决方案用于比较和验证先前获得的分析解决方案。

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