On the formulation of a multi-layered composite pipe finite element with an arbitrary variable wall thickness-Part 1: Static postbuckling analysis with unstable large deformation

A multi-layered composite pipe finite element is developed, in which the wall thickness and the reference surface of each layer can be arbitrary functions of circumferential and axial directions. The kinematics of this multi-layered composite pipe element is set up. Explicit formulations for the Jacobian matrix and its determinant are obtained. The high-order modal displacement test/trial function are applied. To satisfy the compatibility condition between adjacent layers, the interface traction DOF (degree of freedom) is induced and the mixed formulation is obtained. The Dirac's Delta function defined on the interfaces is used as the interpolation function of the traction field. The static condensation technique is applied so that the DOFs of traction are eliminated on the element level. The implementation details of the nonlinear finite element for the multi-layered composite pipe element are also presented. Large deformation and finite strain are both considered. The UL (Updated Lagrangian) form is applied. This multi-layered composite pipe element is applied to solve the multi-layered pipe buckling problem. The results are compared with those from ANSYS.