Abstract
This paper presents the effects of temperature and the nonlocal coefficient on the bending response of functionally graded (FG) nanoplates embedded in an elastic foundation in a thermal environment. The effects of transverse normal strain, as well as transverse shear strains, are considered where the variation of the material properties of the FG nanoplate are considered only in thickness direction. Unlike other shear and deformations theories in which the number of unknown functions is five and more, the present work uses shear and deformations theory with only four unknown functions. The four-unknown normal and shear deformations model, associated with Eringen nonlocal elasticity theory, is used to derive the equations of equilibrium utilizing the principle of virtual displacements. The effects due to nonlocal coefficient, side-to-thickness ratio, aspect ratio, normal and shear deformations, thermal load and elastic foundation parameters, as well as the gradation in FG nanoplate bending, are investigated. In addition, for validation, the results obtained from the present work are compared to ones available in the literature.
Highlights
Nanotechnology is the study of small objects and their applications and has many uses in scientific fields, such as physics, materials science, engineering, chemistry, and biology
Graded materials (FGMs) consist of a mixture of metal and ceramic materials, which range from one material to the other following the law of volume fractions of the two materials through the thickness of the nanoplate [6,7,8]
A refined plate theory is used for the nonlinear and linear thermal analyses of functionally graded (FG) nanoplates resting on an elastic medium under thermal loading using two power-law distributions
Summary
Nanotechnology is the study of small objects and their applications and has many uses in scientific fields, such as physics, materials science, engineering, chemistry, and biology. Zenkour and Sobhy [4] discussed the thermal buckling of nanoplates resting on Winkler–Pasternak foundations utilizing the nonlocal elasticity theory. Graded materials (FGMs) consist of a mixture of metal and ceramic materials, which range from one material to the other following the law of volume fractions of the two materials through the thickness of the nanoplate [6,7,8] Due to their distinct physical and thermal properties, the FGMs are preferable in many real-life applications. A refined four-unknown higher-order normal and shear deformations theory (RHT) for bending analysis of FG nanoplates embedded in elastic foundations is presented in this work where only four independent known functions are used. The effects of foundation parameters, temperature, transverse normal deformation, plate aspect ratio, side-to-thickness ratio, nonlocal coefficient, and volume fraction on deflections and stresses are investigated
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