A reduced integration mindlin beam element for linear elastic stress analysis of curved pipes under generalized in-plane loading

Abstract

This paper presents a ring element for the analysis of in-plane bending of curved pipes. The element is derived from the arch bending theory using short, straight elements as an approach to the curved structure. Each curved pipe element is considered as a straight thin-walled C0-continuity beam element for the purpose of the derivation of the beam stiffness matrix terms. The assumption of the straight elements does not involve ovalization and warping of the transverse section; for the stiffness terms concerning the distortion of the transverse section, the pipe element is assumed curved. This method leads to the important advantage of generating a zero stress field along the curved centroidal line of the element under pure in-plane bending and to the satisfaction of the ‘patch test’.