Stability analysis of non-local Euler-Bernoulli beam with exponentially varying cross-section resting on Winkler-Pasternak foundation

Abstract

In this paper, linear stability analysis of non-prismatic beam resting on uniform Winkler-Pasternak elastic foundation is carried out based on Eringen's non-local elasticity theory. In the context of small displacement, the governing differential equation and the related boundary conditions are obtained via the energy principle. It is also assumed that the width of rectangle cross-section varies exponentially through the beam’s length while its thickness remains constant. The differential quadrature method as a highly accurate mathematical methodology is employed for solving the equilibrium equation and obtaining the critical buckling load of simply supported beam. Several numerical results are finally provided to demonstrate the effects of different parameters such as elastic foundation modulus, nonlocal Eringen’s parameter and tapering ratio on the critical loads of an exponential tapered non-local beam lying on Winkler-Pasternak foundation. The numerical outcomes indicate that the critical loads of pinned-pinned beam decrease by increasing nonlocal parameter. Furthermore, results show that the elastic foundation enhances the stability characteristics of non-local Euler-Bernoulli beam with constant or variable cross-section. It is finally concluded that the effect of non-uniformity in the cross-section plays significant roles on linear stability behavior of non-local beam.