Application of a p-version curved C1 finite element based on the nonlocal Kirchhoff plate theory to the vibration analysis of irregularly shaped nanoplates

Nanoplates have been widely used as elementary components for ultrasensitive and ultrafine resolution applications in the field of nano-electro-mechanical systems because of their potentially remarkable mechanical properties. The accurate analysis of their mechanical behavior is currently of particular interest in the function design and reliability analysis of nano-scaled devices. To examine the size-dependent bending and vibration behavior of nanoplates with curvilinear and irregular shapes, a new p-version curved C-1 finite element is formulated in the framework of the nonlocal Kirchhoff plate model. This newly developed element not only enables an accurate geometry representation and easy mesh generation of curvilinear domains but also overcomes the difficulty of imposing C-1 conformity required by the nonlocal Kirchhoff plate model, particularly on the curvilinear inter-element boundaries. Numerical examples show that this element can produce an exponential rate of convergence even when curved elements are used in the domain discretization. Vast numerical results are presented for nanoplates with various geometric shapes, including rectangular, circular, elliptic, annular, and sectorial. The high accuracy of the present element is verified by comparing the obtained results with analytical and numerical results in the literature. Additionally, a comprehensive parametric analysis is conducted to investigate the influences of nonlocal parameters, plate dimensions, and boundary conditions on the nonlocal behavior of nanoplates. The present element can be envisaged to allow large-scale mechanical simulations of nanoplates, with a guarantee of accuracy and efficiency.