On the Advances of Computational Nonclassical Continuum Theories of Elasticity for Bending Analyses of Small-Sized Plate-Based Structures: A Review

Abstract

Nonclassical continuum theories of elasticity (NCTE) have been extensively used in the mechanical analyses of small-sized structures due to their effective and tremendous ability of incorporating the small size effects into account than the classical continuum theories. The prevalent usage of these theories has to do with the necessity of understanding the mechanics of these small-sized as they are being used in serval areas of applications and today's nanotechnological applications. Consequently, a glimpse into this extensive open literature of NCTE for static bending characteristics of small-sized structures is paid. Subsequently, in this piece of work, by focusing on plate-based structures, we present an ample and novel review on the advances of NCTE for linear and nonlinear bending characteristics of microplate/nanoplate-based structures. We consider several classifications of documents while presenting these advancements. These categorizations of documents involve those reported on linear and nonlinear bending characteristics of small-scale plates (microplates and nanoplates), with a sub classification of documents within the investigated/reported plate types. Further, at the end, a summary, comparison and discussion of some significant studies are presented. At large, in this piece of work, we intent to deliver the existing research trends and primary gaps in static bending behaviors of microplates and nanoplates.