Shear and Membrane Locking-Free Thin-Walled Curved Beam Element Based on Assumed Strain Fields^#

Abstract

Shear and membrane locking-free two- and three-noded thin-walled curved beam elements with nonsymmetric cross-section are developed based on the assumed strain fields. The two-noded element is formulated from constant strain fields and three-noded one is from linear strain fields. Both elements consider extensional and inextensional conditions, respectively, along the centroid axis of beam. Since strain functions are assumed independently, proposed both elements are perfectly free from any locking phenomena and especially give explicit stress expression at an arbitrary point of cross-sections of curved beam. In order to illustrate the validity and the practical usefulness of the present assumed strain curved beam elements, the displacements and the normal stresses of curved arch with double-, mono-, and nonsymmetric cross-sections and the horizontally curved box girder with nonsymmetric cross-section are evaluated and compared with the analytical solutions, results from shell elements, and the experimental test results. The emphasis is given in investigating the influence of inextensibility along the beam axis on the behavior of curved beam with respect to the subtended angle, the slenderness ratio, and the boundary condition.

Keywords:

• Assumed strain fields
• Curved beam
• Normal stress
• Thin-walled cross-section

Notes

^#Communicated by G. Hulbert.