Isogeometric finite element analysis of functionally graded plates using a refined plate theory

TL;DR

This paper introduces a novel isogeometric finite element method using a refined plate theory for analyzing functionally graded plates, accurately capturing shear stresses without shear correction factors.

Contribution

It develops a new inverse tangent shear deformation formulation combined with IGA and RPT for improved analysis of FGM plates.

Findings

Accurate static, vibration, and buckling analysis of FGM plates achieved.

Shear stresses described without shear correction factors.

High accuracy with computational efficiency.

Abstract

We propose in this paper a novel inverse tangent transverse shear deformation formulation for functionally graded material (FGM) plates. The isogeometric finite element analysis (IGA) of static, free vibration and buckling problems of FGM plates is then addressed using a refined plate theory (RPT). The RPT enables us to describe the non-linear distribution of shear stresses through the plate thickness without any requirement of shear correction factors (SCF). IGA utilizes basis functions, namely B-splines or non-uniform rational B-splines (NURBS), which achieve easily the smoothness of any arbitrary order. It hence satisfies the C1 requirement of the RPT model. The present method approximates the displacement field of four degrees of freedom per each control point and retains the computational efficiency while ensuring the high accuracy in solution.