Shell analysis of thin-walled pipes. Part II – Finite element formulation

A finite element formulation is developed for the analysis of thin-walled pipes based on thin shell theory. The formulation starts with a Fourier series solution of the equilibrium equations developed in a companion paper and develops a family of exact shape functions for each mode. The shape functions developed are used in conjunction with the principle of stationary potential energy and yield a finite element that is exact within the assumptions of the underlying shell formulation. The stiffness matrix contribution for each mode n is observed to be fully uncoupled from those based on other modes m ≠ n. The resulting finite element is shown to be free from discretization errors normally occurring in conventional finite elements. The applicability of the solution is illustrated through examples with various loading cases and boundary conditions. A comparison with other finite element and closed form solutions demonstrates the validity and accuracy of the current finite element.