Analytical Modeling of Sandwich Beams with Functionally Graded Core

Abstract

This study investigates several available sandwich beam theories for their suitability of application to one-dimensional sandwich plates with functionally graded core. Two equivalent single-layer theories based on assumed displacements, a higher-order theory, and the Fourier—Galerkin method are compared. The results are also compared with the finite element analysis. The core of the sandwich panel is functionally graded such that the density, and hence its stiffness, vary through the thickness. The variation of core Young's modulus is represented by a differentiable function in the thickness coordinate, but the Poisson's ratio is kept constant. A very good agreement is found among the Fourier—Galerkin method, the higher-order theory, and the finite element analysis.

Bending behavior of sandwich structures with flexible functionally graded core based on high-order sandwich panel theory

“…Lateral displacement of the lower face-sheet of the current study falls between the results from FSDT and FourierGalerkin theory which is good since Fourier-Galerkin theory is very accurate in this area as shown in the benchmarks of the Ref. [5]. Also as it can be seen the shear stress obtained from the present study is very close to that of FSDT theory.…”

“…Figure 10 presents lateral displacement of the lower face-sheet and shear stress through the core obtained from the present solution compared to two other theories presented in Ref. [5] under sinusoidal loading of p(x) = sin(px/l) N/m 2 . Although it's worth mentioning that in the Fig.…”

“…Second benchmark is the comparison of the results of the present study, FSDT and Fourier-Galerkin theory applied on a beam with FG core presented in Ref. [5] with same boundary conditions as this study.…”

“…6 of Ref. [5] there seems to be a mistake in the description of the figure since the Fig. 6a is said to be related to a beam with functionally graded core which is symmetric with respect to geometrical neutral axis of the beam, which means the core is stiffer at Fig.…”

“…Apetre et al [5] compared four analytical and one finite element methods found in literature for modeling of sandwich beams with functionally graded core. The analytical models were two equivalent single-layer theories based on assumed displacement, a higher-order theory and the Fourier-Galerkin method.…”