An exact closed-form solution for buckling of an elastically connected nano-size multi-bonded system subjected to axial load

Abstract This work’s primary objective is to create and demonstrate a low-cost computational technique and an easy-to-implement formulation for estimating buckling capacity of multiple parallel nano-scale elements elastically connected by a Kerr-type foundation subjected to axial load. To accomplish this goal, the system of governing equilibrium equations of the considered multi-bonded structure, which includes n coupled linear differential equations of order 8th, is extracted using the calculus of variations approach and after eliminating the deformation of the inner shear spring layers. A set of explicit and parametric formulas for predicting the stability strength of the system under-investigation, focusing on the double-bond system, is ultimately obtained after the resulting system of equations is solved using trigonometric functions for simply-supported boundary conditions. The attained closed-form formulations require a minimal computational cost, which greatly decrease the central processing unit time, and the extracted expressions, along with their correctness and precision, can be used to achieve the critical loads associated with both in-phase and out-of-phase buckling mode deflections. An exhaustive parametric study is conducted to precisely examine the sensitivity of endurable buckling loads of double-bonded nano-scale elements after the accuracy of the extracted closed-form solution formulations is evaluated. This study considers the effects of various parameters, including the non-locality parameter, the shear layer stiffness constant, the stiffness of Winkler-type elastic medium, including the top and bottom layers, mode number, and axial load ratio, taking into account the effects of applying compressive and/or tensile axial force.