Lattice and continualized models for the buckling study of nonlocal rectangular thick plates including shear effects. (September 2018) - Hache, F.; Challamel, N.; Elishakoff, I.
Highlights: The buckling behavior of a lattice plate that accounts for the shear effect is studied. Three different kinds of continuous nonlocal elasticity plate theories for capturing the small length scale effect of this bending-shear lattice plate have been compared. Lattice-based and phenomenological (or stress gradient) nonlocal Uflyand–Mindlin plate model are compared. Each nonlocal plate model is calibrated with respect to the lattice plate model. The length scale coefficients are constant for the continualized lattice-based nonlocal models. For the phenomenological model, these coefficients are structural dependent and vary with different parameters, such as the aspect ratio or the buckling mode. Abstract: The present study investigates the exact buckling behavior of a new lattice plate theory, called microstructured thick plate model, that accounts for the shear effect. Three different kinds of continuous nonlocal elasticity plate theories for capturing the small length scale effect of this bending-shear lattice plate have been compared: a fourth and a sixth order continualized models based on the derivation of continuous equations from discrete ones and a phenomenological nonlocal Uflyand–Mindlin plate model. The phenomenological nonlocal model is the stress gradient model of Eringen (1983) applied at the plate scale for the bending part and eventually the shear part of the constitutive law. Each nonlocal plate model is calibrated with respect to the lattice plate model. By definition, the length scale coefficients are constant for the two proposed continualized models. For the phenomenological model, these coefficients are structural dependent and vary with different parameters, such as the aspect ratio or the buckling mode. More especially, it is shown that the calibrated small length scale coefficient is influenced by the shear effect. The comparison of the nondimensional buckling loads calculated with the optimal value of the small length scale coefficient, which differ for each nonlocal model, shows that the continualized models constitute a much better, more consistent and more accurate approximation than the phenomenological nonlocal approach. Graphical abstract: Deformation of a unit cell in a microstructured beam-grid model. Image, graphical abstract