Parametric study for modified couple stress theory on postbuckling of size-dependent FG saturated porous mindlin microplates

Abstract

Using modified couple stress plate and Mindlin theories, the present study is a parametric study for revealing the effect of length scale parameter on postbuckling of saturated poroelastic rectangular microplates with pore distribution being functionally graded across thickness. The microplate postbuckling is a nonlinear eigenvalue problem with coupled partial differential equations of equilibrium. In order to find the mode shapes, the eigenfunctions have been approximated by some complete polynomial series expansions in accordance with the conventional Ritz approximation technique. After discretizing the governing equations throughout the microplate grid points, the assembled difference equations construct a nonlinear eigenvalue problem with coupled algebraic equations. The nontrivial coefficients of the expansions were calculated such that the eigenfunctions extremize the microplate potential energy for satisfying the equilibrium homogeneous equations. Variation of the potential energy have been derived with respect to the expansions coefficients from the vantage of using Maple software. By gradual reduction in the initial end shortening of the movable supports and solving the assembled difference equations via Newton-Raphson iterations, the critical postbuckling displacement imposed to the movable supports are found along with the nontrivial coefficients regarding eigenfunctions. The results of the parametric study have revealed how geometric parameters, pore distribution, the Skempton coefficient, porosity, and different boundary conditions modify the influence of length scale parameter on the microplate postbuckling.

Investigating forced vibration of an intelligent sandwich plate consisting of a metal foam core, stiff nanocomposite layers and active piezomagnetic face-sheets exposed to electro-magnetic potentials

“…Once the values of e1 are known, e2 and e3 are determined using equation (6). Subsequently, with the values of e 1 , e 2 , and e 3 achieved, e m1 , e m2 , and e m3 can be obtained using equation (5). Now, with the values of porosity and mass coefficients, the three types of porosity patterns can be applied according to equations (1)- (3).…”

“…Metal foams are among the best materials for employing as the core of a sandwich structure which are lightweight cellular materials that use a solid metal structure with gas-filled holes inspired by natural materials like wood, bone, and sponges [4,5]. Considering these properties, various scientists have tried to investigate the mechanical responses of sandwich structures containing metal foam cores.…”