Abstract
This article presents a finite element method (FEM) integrated with the nonlocal theory for analysis of the static bending and free vibration of the sandwich functionally graded (FG) nanoplates resting on the elastic foundation (EF). Material properties of nanoplates are assumed to vary through thickness following two types (Type A with homogeneous core and FG material for upper and lower layers and Type B with FG material core and homogeneous materials for upper and lower layers). In this study, the formulation of the four-node quadrilateral element based on the mixed interpolation of tensorial components (MITC4) is used to avoid “the shear-locking” problem. On the basis of Hamilton’s principle and the nonlocal theory, the governing equations for the sandwich FG nanoplates are derived. The results of the proposed model are compared with published works to verify the accuracy and reliability. Furthermore, the effects of geometric parameters and material properties on the static and free vibration behaviors of nanoplates are investigated in detail.
Highlights
Nowadays, with the sophisticated development of technology, the investigation of nanostructures has been widely concerned by scientists in the world
Based on the best of authors’ knowledge, the static and free vibration analysis of sandwich functionally graded (FG) nanoplates resting on the elastic foundation using the MITC4 element integrated with the nonlocal theory has not been published yet
We investigate the static bending response of the fully simple-supported (SSSS) sandwich (Type A) FG nanoplate resting on the Winkler foundation under the sinusoidal load qðx, yÞ = q0 sin ðπx/aÞ sin ðπy/bÞ
Summary
With the sophisticated development of technology, the investigation of nanostructures has been widely concerned by scientists in the world. Salehipour et al [25] developed the analytical solution for free vibration analysis of the FG micro/nanoplates using the three-dimensional theory of elasticity accounting small-scale effect. Panyatong et al [41] combined the nonlocal theory and the surface stress to investigate the bending behavior of nanoplates embedded in an elastic medium. Based on the best of authors’ knowledge, the static and free vibration analysis of sandwich FG nanoplates resting on the elastic foundation using the MITC4 element integrated with the nonlocal theory has not been published yet. This motivates us to develop the MITC4 element integrated with the nonlocal theory to accurately describe the stress-deformation and displacement of the FG nanoplates resting on the elastic foundation in this work. The effects of geometric parameters and material properties on the bending and free vibration responses of sandwich FG nanoplates are investigated in detail
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