Abstract

A porosity-dependent nonlinear postbuckling analysis for microplates prepared from a porous functionally graded material (PFGM) is performed based on the modified couple stress theory of elasticity (MCSTE). To accomplish this purpose, the modified couple stress-based nonlinear differential equations are derived by third-order shear deformation plate theory (TSDPT). To extract PFGM microplate effective mechanical properties, a power-law function is utilized which is capable of incorporating porosity dependency and material gradient, simultaneously. Thereafter, the non-uniform rational B-spline (NURBS)-based isogeometric analytical method is employed as an effective discretization method which could satisfy C⁻¹ continuity condition. It is demonstrated that the gap between equilibrium paths relevant to various couple stress length scales reduces by going deeper in postbuckling regime. Also, one can see that for certain porosity and material property gradient index values, by boundary condition transformation from simply supported to clamped, the contribution of the effect of couple stress size in PFGM microplate postbuckling response becomes more significant, especially for a higher maximum deflection values.

摘要

基于改进的耦合弹性应力理论（MCSTE），对由多孔功能梯度材料（PFGM）制备的微板进行了与孔隙率相关的非线性后屈曲分析。为了达到这个目的，通过三阶剪切变形板理论（TSDPT）推导了基于修正耦合应力的非线性微分方程。为了提取PFGM微板的有效机械性能，利用了幂律函数，该函数能够同时兼顾孔隙率依赖性和材料梯度。此后，基于不均匀有理B样条（NURBS）的等几何分析方法被用作可满足C ^-1的有效离散方法。连续性条件。结果表明，在后屈曲状态下，与各种耦合应力长度尺度相关的平衡路径之间的间隙会减小。此外，可以看到，对于某些孔隙度和材料特性梯度指数值，通过从简单支撑到夹紧的边界条件转换，偶应力大小对PFGM微板屈曲后响应的影响变得更加明显，尤其是对于更高的最大挠度价值观。