A co-rotational curved beam element for geometrically nonlinear analysis of framed structures

Abstract

Curved beams are sometimes used in practical framed structures due to good mechanical properties and artistic design. In a framed structure, curved beams may undergo large displacement and experience nonlinear behavior as same as the other straight slender beam-column members. Thus, a geometrically nonlinear curved beam element plays an important role in the analysis of framed structures with curved beams. However, most existing curved beam elements are not accurate enough and still need several or even dozens of elements to accurately describe the behavior of a curved beam with a large subtended angle. To fill this gap, this paper presents a novel geometrically nonlinear curved beam element based on the element-independent co-rotational (EICR) method. The proposed element can simulate a curved beam using only one single element in the analysis and design of most practical framed structures. Moreover, this element is directly derived in a Cartesian coordinate system and can be directly and conveniently used with straight beam-column elements in nonlinear structural analysis. In this manuscript, the derivation of the proposed geometrically nonlinear curved beam element is detailed and several benchmark problems are proposed to verify its accuracy and efficiency.