A nonlocal strain gradient isogeometric nonlinear analysis of nanoporous metal foam plates

Abstract

We investigate the nonlinear bending behavior of nanoporous metal foam plates within the framework of isogeometric analysis (IGA) and higher-order plate theory. The nonlocal strain gradient theory (NSGT) taking into account the length scale and nonlocal parameters has been adopted to establish a scale dependent model of metal foam nanoscale plates. Von Karman nonlinear strains are then used to take up the geometric nonlinearity. Different pore dispersions, namely uniform, symmetric and asymmetric, are confirmed. By using the principle of virtual work, nonlinear governing equations are derived and then solved by using an isogeometric analysis and iterative Newton-Raphson method. Influences of the length scale parameter, porosity distributions, nonlocal parameter and nanoporous coefficient on the nonlinear deflection of the plate are numerically experimented in detail. Some findings would play an important role for designing metal foam structures.