A novel numerical approach for the stability of nanobeam exposed to hygro‐thermo‐magnetic environment embedded in elastic foundation

Source abstract

Abstract In this paper, a novel numerical technique, namely, shifted Chebyshev polynomials based Rayleigh‐Ritz method has been employed to analyze the buckling characteristics of the nanobeam. The main advantage of the shifted Chebyshev polynomials is that, due to the orthogonality of the polynomials, ill‐conditioning of the system is being avoided with higher number of terms in the approximation. The nanobeam is exposed to both hygroscopic and thermal environments while being subjected to a longitudinal magnetic field. Further, the beam is modeled with Winkler‐Pasternak elastic foundation and nonlocal Euler–Bernoulli beam theory. The governing equation of motion of the proposed model has been derived using the Hamilton's principle, and critical buckling loads for Hinged‐Hinged (HH), Clamped‐Hinged (CH), and Clamped‐Clamped (CC) boundary conditions have been computed. The proposed model is validated against the existing model in special cases, exhibiting excellent agreement. Then a convergence study is performed to ensure the correctness and effectiveness of the method. Furthermore, a comprehensive parametric study has been carried out to determine the impact of various parameters such as the small scale parameter, Winkler modulus, shear modulus, magnetic field intensity parameter, hygroscopic parameter, and temperature parameter.