Effects of New Nonlinear Curvature Models and Non-Local Elasticity on Buckling investigation of FG Tapered Nano-Beams Locating on Elastic Foundations

Abstract

New nonlinear curvature models are proposed to show their effects on the compressive critical buckling load on functionally graded (FG) tapered nano-beams locating on elastic foundations in the presence of non-local elasticity. Fourth and fifth orders finite difference methods (bvp4c and bvp5c) are applied on the governing differential equation which is a highly non-linear, due to curvature and has variable coefficients, due to properties. Dimensional analyses have been applied on the governing system together with the problem conditions to produce their dimensionless forms. For different considered parameters, the critical buckling load is computed using the eigenvalue theorem. The effects of nonlinear curvature, variable Young modulus, variable moment inertia and foundation parameters are studied and displayed in tables and figures. The stability and convergence of the present solution are tested using more than one strategy as: comparison with available results, comparison between bvp4c and bvp5c with different mesh intervals and tolerances of truncation errors. These comparisons show that, the new curvature model affects the critical buckling with different ratios depending on variability of properties and foundation parameters. The new results show that the nonlinear curvature model reduces the critical buckling load in comparison with the classical linear model, which, leads to decreasing in factor of safety in design of structures. The new results show that the design of structures will be influenced with the new reduction of the compressive critical buckling load, since it may affect the factor of safety in design of structures. The new results can lead, generally, to more reduction of critical buckling load for large or small input parameters and it will affect other critical values such that frequencies. The introduced Tables and Figures of the present problem with comparisons of previously exact, analytical and numerical works establish the higher accuracy and stability of current findings using bvp4c or bvp5c with preferable of the later. This study is related to some practical applications such as aeronautical and structural engineering.