Shell finite element formulation for geometrically nonlinear analysis of curved thin-walled pipes.

A family of shell finite elements is developed for the geometrically nonlinear analysis of pipe bends. The constitutive description follows the Saint-Venant-Kirchhoff model. The first Piola–Kirchhoff stress and the conjugate gradient of the virtual displacement fields are adopted within the framework of the virtual work principle. Three C 1 continuous schemes are used to interpolate the displacement fields in the longitudinal direction while Fourier series are used for circumferential interpolation. Eigenvalue analyses are conducted to assess the ability of the elements to represent rigid body motion. Comparisons with other shell and elbow models demonstrate the accuracy and versatility of the formulation. • Finite elements are formulated for geometric nonlinear analysis of pipe bends. • Solution adopts First Piola–Kirchhoff stress within the virtual work principle. • Eigenvalue analyses assess the ability of elements to capture rigid body motion. • The formulation properly tackles the effect of follower loads (e.g., pressure). • The formulation accurately captures the nonlinear response. [ABSTRACT FROM AUTHOR]