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Bending, buckling and vibration analyses of simply supported nonlocal higher-order shear plates using mixed field series methods
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DOI：10.1080/15376494.2026.2682450.png)
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Abstract
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In this paper, the authors present a comprehensive comparative study of explicit closed-form analytical solutions to investigate small-scale effects on the bending, buckling, and vibration analysis of a simply supported rectangular nanoplate. The analysis is grounded in Eringen’s nonlocal elasticity theory integrated with higher-order shear plate model, including the Reddy third-order shear deformation plate theory and Shi third-order shear deformation plate theory. The associated partial differential equations are then solved using three distinct methods based on mixed-field variational principles and series expansions. It is possible to derive a single tri-Laplacian equation of the displacement field for all families of considered nonlocal higher-order shear plate models. The obtained results are rigorously validated against well-established benchmark data available in the literature, demonstrating excellent agreement. The kinematic equivalence, in term of deflection, between all cubic-based nonlocal higher-order shear plate models is commented. A detailed parametric investigation is conducted to elucidate the influences of key parameters, including the nonlocal parameter, transverse shear deformation, plate aspect ratio, and side-to-thickness ratio. In particular, it is shown that the nonlocal higher-order shear plate model is a generalization of the two other nonlocal plate theories.
Keywords:
Nonlocal plates
higher-order shear plate theory
series method
mixed field theory
Tri-Laplacian equation
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