Small size-effect isogeometric analysis for linear and nonlinear responses of porous metal foam microplate

Abstract

The main objective of this paper is to explore the linear and nonlinear responses of porous metal foam micro-plate using a modified couple stress theory coupled with isogeometric analysis. The material properties of metal foam micro-plate are derived from three porosity variation models, namely uniform, symmetric and asymmetric variation across the thickness of the microplate. The stress-strain and the modified couple stress constitutive relations are obtained using a seventh order distributed function based on the general shear deformation theory. Furthermore, the Hamilton’s principle is utilized to establish the size-effect equilibrium equations for metal foam micro-plate. The presented numerical solution is able to capture the small size effect of microplate by considering the material length scale parameter in the classical continuum theory. The reported results demonstrate the effect of small size-effect, porosity variation, porosity coefficient, slenderness ratio on free vibration, linear and nonlinear static bending of porous metal foam micro-plate. The role of pattern porosity variation in the nonlinear responses becomes more important by increasing the porosity coefficient. The pattern of symmetric porosity presents the best performance of linear and nonlinear responses.