Buckling and vibrations of microstructured rectangular plates considering phenomenological and lattice-based nonlocal continuum models. (1st August 2016) - Challamel, N.; Hache, F.; Elishakoff, I.; Wang, C.M.
Abstract: The present study investigates three different kinds of nonlocal plate theories for capturing the small length scale effect of microstructured plates in elasticity. One kind is the classical stress gradient Eringen's theory as applied to the Kirchhoff–Love plate model, another kind is based on the continualization of the discrete lattice model and the last kind is a combination of Eringen's model with some additional gradient curvature terms. From the three associated governing equations, analytical vibration and buckling solutions of these equivalent continuous systems are obtained for simply supported rectangular plates and their accuracies are assessed by comparison to the reference exact lattice model. The exact lattice solution is derived for the discrete microstructured plate model via the resolution of a linear difference boundary value problem. It is found that the continualized model (nonlocal continuum model constructed from the lattice equations) provides more accurate results than the traditional Eringen's theory. This model introduces some nonlocal terms both in the constitutive law and in the balance equations. It appears that this new nonlocal continuum perfectly fits the lattice plate model with a length scale factor that only depends on the element size of the microstructured plate, independently on the kind of analysis, static versus dynamics. However, when considering the Eringen stress gradient model, the small length scale coefficient determined by comparing the solutions from the continuous models and the microstructured beam–grid model, is shown to be dependent on the buckling mode and the geometry of plate. Ultimately, the models are evaluated based on their ability to capture microstructured scale effects.