A Nonlocal Numerical Solution Based on Carrera Unified Formulation for Static and Free Vibration Analysis of Laminated Composite Nanoplate

Abstract

This paper presents an advanced numerical model based on Carrera unified formulation (CUF) and isogeometric analysis (IGA), the size-dependent finite element unified formulation model is proposed to investigate the static bending and free vibration of laminated composite nano-plate. The CUF type of trigonometric function with nine degrees of freedom is used to simulate the displacement fields of laminated nano-plate. The size effect of nano-plate structures is included through the Eringen’s nonlocal elastic theory. The size-dependent governing equations for static bending and free vibration of laminated are established based on CUF, IGA and nonlocal theory. The correctness of the presented numerical model is verified by comparison with existing solutions. Furthermore, with the addition of a nonlocal effect, the plate’s stiffness decreases correlating to an increase in nonlocal parameter. Through different calculations, the changes in the static and free vibration responses of laminated composite nano-plate are effected by nonlocal parameter, plate length-to-thickness ratio, and boundary conditions including Young’s modulus ratio.