On immunizing five-beta hybrid-stress element models from trapezoidal locking in practical analyses

When multiple trapezoidal four-node plane elements are used to model slender beams, it is found that the transverse bending stress/strain mode which should physically vanish is most detrimental to the element accuracy and leads to a de"ciency which is sometimes known as &trapezoidal lockingʹ. In this paper, immunity of four-node "ve-beta hybrid elements to &trapezoidal lockingʹ in practical analyses is obtained by a simple selective scaling procedure that judiciously reduces the sti!ness arising from the two bending stress/ strain modes in the elements