A 3D nano scale IGA for free vibration and buckling analyses of multi-directional FGM nanoshells.

Abstract

In this article, we explore a three-dimensional solid isogeometric analysis (3D-IGA) approach based on a nonlocal elasticity theory to investigate size effects on natural frequency and critical buckling load for multi-directional functionally graded (FG) nanoshells. The multi-directional FG material uses a power law rule with three power exponent indexes concerning three parametric coordinates. Nanoshell s geometries include the square plate, cylindrical and spherical panels with the side length considered in a nanoscale. Because 3D-IGA utilizes an approximation of NURBS basic functions to integrate from geometry modeling to discretized domain, it is the best promising candidate to fulfill a higher-order derivative requirement of the nonlocal theory on nanoshells. The numerical solutions are verified by those published in several pieces of literature to determine the current approach s accuracy and reliability. After a convergence solution is examined, a quartic NURBS basic function can yield ultra-converged and high-accurate results with a low computational cost. The findings show the size effect parameters which significantly impact the frequencies and the critical buckling factors of the multi-directional FG nanoshells. Generally, increases in the size effect parameters will cause declines in the frequencies and the critical buckling factors of the nanoshells.