On the formulation of a pipe element for a pipe structure with variable wall thickness

In this paper, a pipe element is developed for a pipe structure with variable wall thickness. The variable wall thickness field tw can be an arbitrary function about circumferential and axial directions. A local dimensionless cylindrical coordinate system is set up. The displacement expression is defined based on the local dimensionless cylindrical coordinate system. The map from the local dimensionless cylindrical coordinate system to the pipe structure configuration is established. In the circumferential and radial dimensions, the series is used as the displacement basis functions. In the axial direction, Lagrangian interpolation is applied. Furthermore, the referential surface R can also be defined as an arbitrary function about circumferential and axial directions as tw. Thus, this pipe element has wide applications. The complicated problems with geometrical nonlinearity (large deformation and finite strain) can be analyzed well by this element. The pipe buckle crossover problem is analyzed in this paper. In this problem, the pipe model has an axially variable wall thickness field. The eccentric pipe collapse problem is also analyzed. In this problem, the pipe model has a circumferential variable wall thickness field. The results are compared with those from other well-established FEM simulations.