article · Mechanics of Advanced Materials and Structures
A finite element formulation using four-unknown shear deformation theory examines the static bending and hygro-thermo-mechanical vibration of sandwich functionally graded porous doubly curved nanoshells resting on an elastic foundation. The structural design features a fully ceramic homogenous core surrounded by top and bottom layers with uneven porosity distributions across their thickness. The governing equations are derived using Hamilton's principle alongside Eringen's nonlocal elasticity theory. A four-node quadrilateral element with ten degrees of freedom per node, combining Lagrangian and Hermitian interpolation functions, approximates membrane and bending displacement fields. Numerical results evaluated against exact solutions demonstrate the performance of the model. The investigation details how material and geometric variables, including the power-law index, porosity coefficient, nonlocal scale effects, and foundation stiffness, influence the bending and free vibration behaviours of these nanoshell structures.
Engineers working on advanced nanoscale components need precise mathematical models to predict structural integrity under thermal, moisture, and mechanical strains. By accounting for nanoscale material effects and varying porosity, this numerical method provides a more accurate way to simulate the structural behaviour of complex sandwich nanomaterials before physical testing or manufacturing.
The abstract does not indicate a commercialisation pathway or direct application, as the research is an early-stage theoretical and numerical modelling study.
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This article presents the finite element method (FEM) used four-unknown shear deformation theory for the static bending and hygro-thermo-mechanical vibration analysis of sandwich functionally graded porous (SFGP) doubly curved nanoshells resting on the elastic foundation (EF). The configurations of SFGP nanoshells include a homogenous core made of full ceramic while the top and bottom layers vary through the thickness with the law of uneven porosity distribution. The governing equations are obtained by using Hamilton’s principle and the nonlocal elasticity theory of Eringen (nonlocal theory). For the first time, a four-node quadrilateral element with ten degrees of freedom (DOFs) for each node using Lagrangian and Hermitian interpolation functions to approximate the membrane and bending displacement fields are proposed to analyze the SFGP nanoshells. The numerical results are compared with other exact solutions to evaluate the performance of the proposed method. Furthermore, influences of geometrical parameters and material properties such as the power-law index n, the porosity coefficient ξ, the nonlocal coefficient μ, and EF-stiffness (Kw, Ks) on the static bending, free vibration of SFGP nanoshells are comprehensive studied.
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DOI: 10.1080/15376494.2021.1968549
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