An Accurate Curved Beam Element Based on Trigonometrical Mixed Polynomial Function

A displacement-based, novel curved beam element is proposed for efficient and reliable analysis of frames composed of curved members. The accuracy of the proposed element is not controlled by the subtended angle of the element with the angle up to π. In contrast to the conventional method, the interpolation function for displacement is based on the infinitesimal straight beam sections extracted from the curved element. Consequently, the strain energy of the curved beam element can be integrated by the infinitesimal sections along the element length. The relationship between the displacements and the corresponding strains in the straight beam is simpler than that in the curvilinear co-ordinate description widely adopted by many researchers in their element derivations. This technique is formulated to avoid couplings between the tangential and radial displacement variables in the strain field and its successful utilization is also demonstrated herein. Furthermore, the relation between displacements and strains of the infinitesimal straight beam section is equivalent to that of the curved beam in the curvilinear co-ordinate description. Finally, the analysis results of several bench marked examples by the proposed curved beam element are presented. The results show the high accuracy and efficiency of the proposed element against the classical curved beam element.