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

Applied Sciences

Salvatore Brischetto¹  Roberto Torre¹ 

[1] Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy;

关键词: functionally graded materials;    3D shell model;    steady-state hygro-elastic analysis;    Fick moisture diffusion equation;    moisture content profile;    layer-wise approach;   

DOI  :  10.3390/app12010512

来源: DOAJ

【 摘 要 】

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 ($\alpha$, $\beta$, 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.

【 授权许可】

Unknown