An effective analytical method for buckling solutions of a restrained FGM nonlocal beam

• Published in: Computational & applied mathematics Vol. 41; no. 2
• Main Authors: Civalek, Ömer, Uzun, Büşra, Yaylı, Mustafa Özgür
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.03.2022; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied physics; Beam theory (structures); Boundary conditions; Buckling; Computational mathematics; Computational Mathematics and Numerical Analysis; Euler-Bernoulli beams; Exact solutions; Fourier series; Functionally gradient materials; Mathematical analysis; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics; Nonlocal elasticity; Parameters; Size effects; Stability analysis; Stability; 05C50; Euler–Bernoulli beam theory; Functionally graded material; 74G60; Stokes’ transformation; Fourier series; 42A16; Nonlocal elasticity theory
• ISSN: 2238-3603; 1807-0302
• DOI: 10.1007/s40314-022-01761-1

This work studies the size-dependent stability analysis of restrained nanobeam with functionally graded material via nonlocal Euler–Bernoulli beam theory using the Fourier series. The nonlocal elasticity theory introduced by Eringen is utilized to show the size effect on the buckling response of restrained functionally graded nanobeam. In addition, buckling loads of functionally graded nanobeam are obtained by classical elasticity theory as well to highlight the size effects. The influences of various parameters such as the nonlocal parameter, rotational restraints and power-law index on the critical buckling load of the functionally graded nonlocal beam are investigated. The contribution of this paper is that it presents an efficient analytical solution for the buckling response of functionally graded nanobeam with non-rigid boundary conditions.