Effect of nano-porosity on postbuckling of non-uniform microbeams

Abstract

This study is accomplished to investigate the effect of different types of porosity distribution on the static postbuckling response of non-uniform microbeams under the simply supported boundary conditions. The modified couple stress theory is used to capture the size effect in microscales, and the von-Karman strain-displacement relation is employed to describe the nonlinearity effect. The relative elasticity characteristics, e.g., Young's modulus and the material length scale parameter, are considered as a function of relative mass density. The nonlinear governing equations for Euler-Bernoulli porous microbeams with non-uniform cross section are derived by a variational energy method and solved using a closed-form solution. The critical buckling load and the static postbuckling response of porous non-uniform microbeams, non-porous non-uniform microbeams and porous uniform microbeams are compared with together. Therefore, effects of nano-porosity and non-uniformity on the postbuckling behavior of the microbeam are investigated.

Finite element formulation of metal foam microbeams via modified strain gradient theory

“…Post-buckling of metal foam simplysupported microbeams with variable material length scale parameter (MLSP) is investigated by MCST and Euler-Bernoulli theory [42]. Under periodic excitation, the vibration responses of silicon foam nanobeams are examined via surface elasticity theory [43]. IGA is used to present the nonlinear flexural responses of metal foam plate with NSGT [44].…”

A Levy solution for bending, buckling, and vibration of Mindlin micro plates with a modified couple stress theory

“…To mention some more recent ones, some researchers used the strain gradient theory to study the behavior of micro/ nano beams [12] and plates [13,14], while some others used the non-local elasticity theory to analyze the size dependent beams [15,16] and plates [17][18][19]. Among different non-classical continuum theories, the modified couple stress theory [11] incorporates only one length scale parameter and is preferred over the others due to its simplicity and has been intensively used to study the size dependent structures [20,21]. Here, the studies on isotropic and homogenous micro plates including bending, buckling, and vibration behaviors using the MCST are reviewed.…”