Search

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]

A family of new geometrically nonlinear finite elements is formulated for the simulation of the structural response in the elastic regime of straight pipes with circular cross-sections under various loading conditions. The first Piola–Kirchhoff stress tensor is employed within the principle of virtual work framework in conjunction with a total Lagrangian approach. The Green–Lagrange strain tensor is adopted to capture the finite deformation-small strain effects. The formulations are based on the kinematic assumptions of the thin shell theory and capture the follower effects due to pressure load. Three schemes are proposed to interpolate the displacement fields in the circumferential direction: (1) a Fourier series expansion, (2) a quartic spline interpolation, and (3) a mixed interpolation combining Fourier series and splines. The performance and prediction accuracy of the elements are assessed through comparisons with finite element models based on shell and elbow elements in ABAQUS under various loading conditions. The results demonstrate the ability of the elements to predict the displacement and stress fields. In particular, the element based on Fourier series interpolation is shown to provide accurate predictions. • A geometrically nonlinear finite element is developed for circular cylindrical shells. • The virtual work is expressed in terms of the First Piola–Kirchhoff stress tensor. • Various interpolation schemes are compared. • The formulation captures the follower effect of the pressure. [ABSTRACT FROM AUTHOR]