On lateral buckling of end-loaded cantilevers, including the effect of warping stiffness

摘要

We investigate the numerical consequences of the presence of certain non-linear terms in the expressions for the components of transverse shearing strain which occur in the derivation of one-dimensional equations for small finite deflections of straight beams from three-dimensional finite elasticity through use of the principle of minimum potential energy. While particular emphasis is placed on the effect of warping stiffness, the paper also includes results of interest in connection with the classical Michell-Prandtl-analysis of lateral buckling of endloaded cantilevers. Comprehensive numerical results are obtained for the entire range of the relevant dimensionless parameters, using power series, asymptotic expansion and modern numerical methods procedures.