This study investigates the buckling behavior of cylindrical shells composed of Functionally Graded Materials (FGMs) when subjected to axial compression, challenging conventional assumptions regarding the influence of Poisson’s effect in homogeneous materials. To address this, we utilize a numerical approach employing the Asymptotic Numerical Method (ANM). Contrary to the expected linear pre-buckling behavior associated with a zero Poisson’s ratio, our findings reveal significant non-linearity in the response of FGM structures, emphasizing the influence of additional non-linear factors inherent in the behavior of advanced composites. Through an extensive numerical analysis conducted using a customized Matlab code, we examine the buckling and post-buckling characteristics of FGM shells with varying surface compositions, particularly focusing on configurations incorporating Al2O3 and Al on the upper surface. To elucidate our findings, we present numerical examples comparing two FGM scenarios (Al2O3/Al and Al/Al2O3) in terms of critical buckling and FGM distribution. Additionally, we validate our results by employing the commercial software Abaqus with Riks-based finite element method and Newton–Raphson solver.

中文翻译：

---

使用高阶有限延拓方法研究 FGM 壳的非线性屈曲


本研究研究了由功能梯度材料 （FGM） 组成的圆柱壳在受到轴向压缩时的屈曲行为，挑战了关于泊松效应对均质材料影响的传统假设。为了解决这个问题，我们采用了一种采用渐近数值法 （ANM） 的数值方法。与零泊松比相关的预期线性预屈曲行为相反，我们的研究结果揭示了 FGM 结构响应中的显着非线性，强调了先进复合材料行为中固有的其他非线性因素的影响。通过使用定制的 Matlab 代码进行广泛的数值分析，我们检查了具有不同表面成分的 FGM 壳体的屈曲和后屈曲特性，特别关注上表面包含 Al2O3 和 Al 的配置。为了阐明我们的发现，我们提供了数值示例，比较了两种 FGM 情景（Al2O3/Al 和 Al/Al2O3）在临界屈曲和 FGM 分布方面的表现。此外，我们通过使用商业软件 Abaqus 和基于 Riks 的有限元方法和 Newton-Raphson 求解器来验证我们的结果。