Nonlinear post‐buckling analysis of viscoelastic nano‐scaled beams by nonlocal integral finite element method

Abstract

AbstractThe viscoelastic buckling and nonlinear post‐buckling behavior of nano‐scaled beams are analyzed using the nonlocal integral elasticity theory. Eringen's nonlocal theory is one of the well‐known and popular size‐dependent theories, which has been used by several researchers to study the mechanical behavior of, mostly, the elastic nanostructures. A finite element method is developed using Hamilton's principle based on the two‐phase nonlocal integral theory and taking into account the buckling related terms and viscoelastic effects. The corresponding formulations are derived by implementing the Euler–Bernoulli beam theory and Kelvin–Voigt viscoelastic model. Furthermore, for analyzing the post‐buckling and viscoelastic buckling behavior, the nonlinear strains, and initial displacement (imperfection) have been considered. By employing the variational relations, the governing equations are obtained and then solved numerically using the finite difference and Newton–Raphson methods. Because of the finite element nature of the current method, various boundary conditions can be properly implemented. The results of the current study are compared with those available in the literature and the effects of nonlocal parameter, viscoelastic parameter, axial compressive load and boundary conditions on the viscoelastic buckling, and postbuckling behavior have been investigated.