3D Stress Analysis of Multilayered Functionally Graded Plates and Shells under Moisture Conditions

Salvatore Brischetto,Roberto Torre

doi:10.3390/app12010512

Abstract

This paper presents the steady-state stress analysis of single-layered and multilayered plates and shells embedding Functionally Graded Material (FGM) layers under moisture conditions. This solution relies on an exact layer-wise approach; the formulation is unique despite the geometry. It studies spherical and cylindrical shells, cylinders, and plates in an orthogonal mixed curvilinear coordinate system (α, β, z). The moisture conditions are defined at the external surfaces and evaluated in the thickness direction under steady-state conditions following three procedures. This solution handles the 3D Fick diffusion equation, the 1D Fick diffusion equation, and the a priori assumed linear profile. The paper discusses their assumptions and the different results they deliver. Once defined, the moisture content acts as an external load; this leads to a system of three non-homogeneous second-order differential equilibrium equations. The 3D problem is reduced to a system of partial differential equations in the thickness coordinate, solved via the exponential matrix method. It returns the displacements and their z-derivatives as a direct result. The paper validates the model by comparing the results with 3D analytical models proposed in the literature and numerical models. Then, new results are presented for one-layered and multilayered FGM plates, cylinders, and cylindrical and spherical shells, considering different moisture contents, thickness ratios, and material laws.

Highlights

The environmental conditions characterizing the service life of structural components can be adverse in many applications
Besides verifying the accuracy of this solution, this phase helps define how many mathematical layers should be used to consider with confidence the effects of the curvature and those of the Functionally Graded Material (FGM) law and the order of expansion to use in the exponential matrix calculation
Consistent with the previous test case, the results show that the 3D shell model always gives comparable results with the 3D FE model, despite the thickness ratio and the considered variable, when the number of mathematical layers is sufficiently high

Summary

Introduction

The environmental conditions characterizing the service life of structural components can be adverse in many applications. Zenkour studied how the thermal and hygrometric fields affect the bending and the buckling of plates embedding FGMs [39] In this case, the authors considered a material grading in the thickness direction of the structure. Multilayered structures under hygrometric fields have been the target of the finite element model by Khoshbakht et al [51]; Kundu and Han studied buckling and vibration in multilayered shells with double curvature [52] through a finite element model grasping the hygrothermal effects They extended this research to dynamic instability of doubly-curved shells embedding composite materials through a nonlinear finite element under orthogonal curvilinear coordinates [53].

Fick Moisture Diffusion Equation

Assumed Linear Moisture Content through the Thickness Direction

Results

Assessments

New Benchmarks

Conclusions