Field-consistency rules for a three-noded shear flexible beam element under non-uniform isoparametric mapping

Abstract

Most studies on the three-noded quadratic Timoshenko beam element have been based on a 2-point Gaussian integration rule for the shear energy or on the use of a smoothed substitute shape function or assumed shear strain field to improve its performance. However, if the mid-node of the element is slightly displaced from the mid-point position, the consistency requirements for the constrained shear strain field are more complex. This paper investigates this problem and the findings throw more light on consistency procedures demanded for distorted quadrilateral plate and shell elements. The optimal element which emerges from this study has bending and shear strain fields which have a linear variation over the element under non-uniform mapping.