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Abstract
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Herein, a two-node beam element enriched based on the Lagrange and Hermite interpolation function is
proposed to solve the governing equation of a functionally graded porous (FGP) curved nanobeam on an elastic
foundation in a hygro–thermo–magnetic environment. The material properties of curved nanobeams change continuously
along the thickness via a power-law distribution, and the porosity distributions are described by an uneven porosity
distribution. The effects of magnetic fields, temperature, and moisture on the curved nanobeam are assumed to result in
axial loads and not affect the mechanical properties of the material. The equilibrium equations of the curved nanobeam
are derived using Hamilton’s principle based on various beam theories, including the classical theory, first-order shear
deformation theory, and higher-order shear deformation theory, and the nonlocal elasticity theory. The accuracy of the
proposed method is verified by comparing the results obtained with those of previous reliable studies. Additionally, the
effects of different parameters on the free vibration behavior of the FGP curved nanobeams are investigated
comprehensively.
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