New method in mechanics to determine Euler critical force in bar structures

Abstract

The forced displacement method [2], [3] allows us to immediately obtain the critical forces and the vibration frequency of the bars. It is different from traditional methods, such as the Rayleigh method, which only gives us the fundamental frequency of vibrations, or the commonly used method today, which brings the determinants of the stability and vibration equations to diagonal form to get the product of that term gives us a characteristic polynomial equation to determines the eigenvalues. In this paper, the author uses the forced displacement method combined with the finite element method to determine the Euler critical force of the bar's eigenvalue problem taking into account the effect of the lateral shear strain.