Abstract
In this study, the buckling of functionally graded (FG) nanoporous metal foam nanoplates is investigated by combining the refined plate theory with the non-local elasticity theory. The refined plate theory takes into account transverse shear strains which vary quadratically through the thickness without considering the shear correction factor. Based on Eringen’s non-local differential constitutive relations, the equations of motion are derived from Hamilton’s principle. The analytical solutions for the buckling of FG nanoporous metal foam nanoplates are obtained via Navier’s method. Moreover, the effects of porosity distributions, porosity coefficient, small scale parameter, axial compression ratio, mode number, aspect ratio and length-to-thickness ratio on the buckling loads are discussed. In order to verify the validity of present analysis, the analytical results have been compared with other previous studies.
Highlights
Graded materials (FGMs) are advanced composite materials whose compositions and volume fraction of materials vary gradually in one or more direction
Combining nanoporous metal foams with the Functionally graded materials (FGMs) concept, the functionally graded (FG) nanoporous metal foams are proposed. Due to their excellent fracture toughness and high electrical conductivities, FG nanoporous metal foam nanoplates are ideal for use as thin film elements
In order to demonstrate the accuracy of the present method, firstly, a comparison study was conducted for a homogeneous nanoplate
Summary
Graded materials (FGMs) are advanced composite materials whose compositions and volume fraction of materials vary gradually in one or more direction. Karimi et al [24] investigated vibration, shear and biaxial buckling of rectangular nanoplates, by using the non-local two variable refined plate theory. Daneshmehr et al [25] studied the free vibration problems of functionally graded nanoplates via non-local elasticity and high order theories. Narendar [31] used the two-variable refined plate theory and non-local elasticity theory to analyze the buckling problems of isotropic nanoplates. Based on the two-variable refined plate theory, Nami and Janghorban [33] investigated the free vibration problems of rectangular nanoplates via the strain gradient elasticity theory. Barati and Zenkour [35] examined the post-buckling behavior of nanoporous metal foam nanobeams based on a non-local, non-linear refined shear deformation beam model. The effects of several factors on the buckling of FG nanoporous metal foam nanoplates are presented in detail
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