New concept to include shear deformation in a curved beam element

Abstract

A horizontally curved beam element of arbitrary shape having three nodes and three degrees of freedom (vertical deflection, bending rotation, and twisting rotation) at each node is presented. The proposed element looks like an isoparametric curved beam element but it is based on a different formulation. The effect of shear deformation is incorporated in an efficient manner and to make the element free from locking in shear, which is a well-known problem of the isoparametric element. In this formulation, the field variables taken are vertical deflection, shear strain, and twisting rotation. It should be noted that shear strain is one of the field variables unlike isoparametric and other usual elements where bending rotation is the corresponding field variable. Moreover the order of interpolating polynomial used for the different field variables is identical in the isoparametric element, while it is different in the present case. Numerical examples are solved to validate the proposed element and to show its accuracy and range of applicability.