THE LINEAR ELASTIC STRESS-ANALYSIS OF CURVED PIPES UNDER GENERALIZED LOADS USING A REDUCED INTEGRATION FINITE RING ELEMENT

This paper consists of a linear elastic stress analysis of curved pipe s having all the possible boundary conditions in structural engineerin g and submitted to a generalized in-plane or out-of-plane loading. A s emi-analytic displacement formulation ring element was developed, wher e simple first-degree polynomials were used to interpolate the global shell displacements along the longitudinal direction, and Fourier seri es were used along the meridional direction. The deformed shape of the curved pipe results from the superposition of the beam-type displacem ent to that of a toroidal shell. For the first case, the curved pipe w as considered as being a short thin-walled straight beam element joini ng two nodal sections. In this case, as the pipe element is not curved , it is natural to consider that the transverse section undergoes no o valization or warping. A C-0-continuity reduced integration beam eleme nt was adopted for this purpose, leading to a simple and economic defi nition for the stiffness terms. In the second case, the displacement f ield was assumed to result from a stressed toroidal shell, where the t ransverse section could ovalize and warp. The stiffness terms followin g these assumptions are combined with those of the straight beam to gi ve the complete stiffness matrix. This element has the important advan tage of generating a zero stress field along the curved centroidal lin e when submitted to pure in-plane bending and, consequently, to the sa tisfaction of the 'patch test'.