Consistency aspects of out-of-plane bending, torsion and shear in a quadratic curved beam element

Abstract

Curved beams in civil engineering applications call for out-of-plane bending and torsion under the action of out-of-plane transverse shear loads. The design of a quadratic displacement curved beam element capable of representing shear deformation as in the Timoshenko beam theory requires special attention to the manner in which the shear strain is represented. Field-inconsistent representations of the out-of-plane transverse shear strain will result in a loss of efficiency and introduce spurious oscillations in the bending moment, torsional moment and shear force. The optimal field-consistent assumed strain interpolation for shear is derived and it is demonstrated to posses very high accuracy which is free from spurious force and moment oscillations.