NURBS-based finite element analysis of functionally graded plates: static bending, vibration, buckling and flutter

TL;DR

This paper presents a NURBS-based finite element method for analyzing the static and dynamic behavior of functionally graded plates, including bending, buckling, vibration, and flutter, with validation and parametric studies.

Contribution

It introduces an iso-geometric finite element approach using NURBS for FGM plates, incorporating shear locking alleviation and multiple analysis types.

Findings

Validated accuracy against 3D solutions

Demonstrated influence of gradient index on responses

Provided insights into effects of aspect ratio and thickness

Abstract

In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material properties are assumed to be graded only in the thickness direction and the effective properties are computed either using the rule of mixtures or by Mori-Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation plate theory (FSDT). The shear correction factors are evaluated employing the energy equivalence principle and a simple modification to the shear correction factor is presented to alleviate shear locking. Static bending, mechanical and thermal buckling, linear free flexural vibration and supersonic flutter analysis of FGM plates are numerically studied. The accuracy of the present formulation is validated against available three-dimensional solutions. A detailed numerical study is carried out to examine the influence of the gradient index, the plate aspect ratio and the plate thickness on the global response of functionally graded material plates.