A Simple and Efficient Three-Node Curved Beam Element for the Out-of-Plane Shear, Bending and Torsion, Based on the Linked Interpolation Concept

Abstract

The paper presents a new three-node curved beam finite element for out-of-plane actions constructed on the expanded linked interpolations used before on a straight beam. The shear strain constraints are immanent in displacement interpolations and the geometry is interpolated compatibly with the used kinematics, so that the element stiffness forming procedure is very simple and can easily be implemented in any programming code. Different than the standard, an equivalent curved beam kinematics is introduced, which enables the use of global displacement variables instead of mostly used displacement parameters in local coordinates, avoiding the coordinate transformation for nodal degrees of freedom. Timoshenko beam theory assumptions are taken into account and the element was tested on a set of benchmark problems to demonstrate that the element shows no shear or membrane locking.