On the NURBS-based isogeometric analysis for couple stress-based nonlinear instability of PFGM microplates

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.