Influence of initial geometric imperfection on static and free vibration analyses of porous FG nanoplate using an isogeometric approach

Abstract

In this paper, the size-dependent analysis of geometrically imperfect porous functionally graded (FG) nanoplates is studied by an isogeometric approach based on a new refined plate theory. Simultaneous effects of initial geometric imperfection and porosity on the natural frequency and deflection of the FG nanoplates are investigated. The initial geometric imperfection is considered as an initial curvature and modeled by an analytical function in the governing equations of the nanoplate. Material properties of porous FG nanoplate are defined by a modified power-law function, and two types of distribution for porosity are used. A four-variable refined plate theory with a new polynomial shape function is proposed. Based on Hamilton’s principle, a weak form of static and free vibration problem for nonlocal plate is derived. The discrete system of equations is solved by an isogeometric approach based on NURBS basis functions, and the accuracy of the present study is verified by comparing the results with solutions given in published papers. Present results indicate the importance of porosity parameter, porosity distributions, nonlocal parameter, material index, plate geometrical parameters, and specially imperfection amplitude on the static and free vibration behavior of FG nanoplates.