Versatile and Improved Higher‐Order Beam Element

Abstract

The degeneration of two classes of deep beam elements is conducted, one (DB6) based on the conventional Timoshenko beam assumptions and the other (DB7) based on the assumed cubic order longitudinal displacement profile. While an adjustable shear correction factor is required for the DB6 element to compensate for the unrealistic distribution of a shear strain across the beam depth, the DB7 element assumes the more realistic quadratic profile of shear strain at the outset. With the plane‐stress continuum solution serving as reference in static and free‐vibration analyses, solutions obtained by these two element models are compared with the analytical Timoshenko solution, the analytical thin beam solution and several available solutions of existing beam elements. The result indicates that the performance of the higher order beam element DB7 is seen to be more versatile than other models previously developed by various investigators. Also, superior accuracy of the results is evident in both analyses over a wide range of the beam aspect ratios.