On the finite element analysis of functionally graded sandwich curved beams via a new refined higher shear deformation theory

TL;DR

This paper introduces a new shear deformation theory and finite element model to accurately analyze the bending behavior of functionally graded sandwich curved beams, eliminating shear correction factors and providing benchmark results.

Contribution

A novel parabolic shear deformation theory combined with a finite element approach for FG sandwich curved beams, enhancing accuracy and stability without shear correction factors.

Findings

The proposed model is accurate and converges rapidly.

Results are consistent with existing literature.

Numerical analysis reveals effects of various parameters on beam behavior.

Abstract

In the present paper, a new parabolic shear deformation beam theory is developed and applied to investigate the bending behavior of functionally graded (FG) sandwich curved beam. The present theory is exploited to satisfy parabolic variation of shear stress distribution along the thickness direction thereby obviating the use of any shear correction factors. The material properties of FG sandwich beam change continuously from one surface to another according to a power-law function. Three common configurations of FG beams are used for the study, namely: (a) single layer FG beam; (b) sandwich beam with FG face sheets and homogeneous core and (c) sandwich beams with homogeneous face sheets and FG core. The governing equations derived herein are solved by employing the finite element method using a two-noded beam element, developed for this purpose. The robustness and reliability of the developed finite element model are demonstrated by comparing its results with those available by other researchers in existing literature. The comparison studies show that the proposed model is: (a) accurate and comparable with the literature; b) of fast rate of convergence to the reference solution; c) excellent in terms of numerical stability and d) valid for FG sandwich curved beams. Moreover, comprehensive numerical results are presented and discussed in detail to investigate the effects of volume fraction index, radius of curvature, material distributions, length-to-thickness ratio, face-to-core-thickness ratio, loadings and boundary conditions on the static response of FG curved sandwich beam. New referential results are reported which will be serve as a benchmark for future research.