Size and surface effects on mechanical behavior of thin nanoplates incorporating microstructures using isogeometric analysis

Abstract

In this paper, we present an effective plate formulation based on isogeometric analysis (IGA) and non-classical Kirchhoff plate theory for the study of static bending and buckling behaviors of nanoplates, taking into account microstructure and surface energy effects. In this setting, the modified couple stress theory is used to capture microstructure effect, while the Gurtin-Murdoch surface theory is adopted to consider surface energy effect. The C1-continuity requirement of the non-classical Kirchhoff plate theory is effectively fulfilled with the aid of inherent high-order continuity of non-uniform rational B-splines (NURBS), which serve as basis functions in IGA. Several numerical examples are presented to illustrate the effects of microstructure and surface energy on mechanical responses of nanoplates. The results reveal that microstructure and surface energy effects increase the nanoplate stiffness, which gives rise to a reduction in bending deflection and an increase in buckling loads. The surface energy effect becomes dominant for ultrathin nanoplates.