Investigation of the geometrical nonlinear action of doubly curved shell panels (DCSPs) in micro scale is the main target of this paper. The proposed microshell panels (MSPs) are assumed to be made of an auxetic honeycomb core (AHOC), leading to negative magnitudes of Poisson's ratio, covered by two nanocomposite enriched coating layers (NCECLs). To conduct the size-dependent nonlinear analysis and achieve the corresponding nonlinear equilibrium path (EQP) of the proposed MSPs, the nonlocal strain gradient theory (NLSGT) is utilized. The governing equations containing the equilibrium and compatibility nonlinear partial differential equations in terms of the deformation components are analytically solved based on the Galerkin technique for different types of simply-supported panels. The achieved results of the present solution exhibit the fact that nonlocal and material length scale parameters significantly affect the EQP of the proposed MSPs especially at their post-buckling stage during their snap-through instability. By solving several numerical examples, the effects of various parameters on the size-dependent EQP of the proposed MSPs are investigated. The results indicate that the influences of size-dependency are significantly affected by the curvature and also boundary conditions of the microshells.

中文翻译：

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微壳的非线性屈曲

研究微尺度双曲壳板（DCSP）的几何非线性作用是本文的主要目标。假设所提出的微壳面板（MSP）由拉胀蜂窝芯（AHOC）制成，导致泊松比为负值，并由两个纳米复合材料富集涂层（NCECL）覆盖。为了进行与尺寸相关的非线性分析并获得所提出的 MSP 的相应非线性平衡路径 (EQP)，利用非局部应变梯度理论 (NLSGT)。基于伽辽金技术，针对不同类型的简支板，解析求解了包含变形分量的平衡和相容非线性偏微分方程的控制方程。本解决方案所取得的结果表明，非局部和材料长度尺度参数会显着影响所提出的 MSP 的 EQP，特别是在其突跳不稳定期间的屈曲后阶段。通过求解几个数值例子，研究了各种参数对所提出的 MSP 的尺寸相关 EQP 的影响。结果表明，尺寸依赖性的影响受到微壳曲率和边界条件的显着影响。