Nonlinear finite element free and forced vibrations of cellular plates having lattice-type metamaterial cores: a strain gradient plate model approach

The main objective of this paper is to develop a theoretically and numerically reliable efficient methodology based on combining finite element method strain gradient shear deformation plate model accounting for the nonlinear free forced vibrations cellular plates having lattice-type metamaterial cores. proposed provides modelling framework computationally more than conventional three-dimensional elasticity simulation underlying dynamics with microarchitectures. corresponding governing equations follow Mindlin’s theory including micro-inertia effect applied first-order along von Kármán kinematics. Standard higher-order computational homogenization methods determine classical material constants, respectively. A C1-continuous 6-node adopted discretization in spatial domain, an arc-length continuation technique time-periodic implemented solve resulting time-dependent problem. Through set comparative studies 3D full-field models as validation references triangularly prismatic example cores, accuracy efficacy dimension reduction are demonstrated diverse range problem parameters analyzing large-amplitude dynamic structural response. results show that can accurately capture microarchitecture effects low costs, which signifies relevant contribution particularly analysis dynamics.