On the formulation of a 3-D smooth curved pipe finite element with arbitrary variable cross-section

A smooth curved pipe finite element is developed. The cross-section can be defined by any shape geometrically variable along the axial direction of the curved pipeline. The curved axial line of the pipe can be defined by any curve and the exact smooth configuration is obtained. the kinematics of the local cross-section with arbitrary shapes is set up. Then, the global 3-D curved pipe is obtained by extruding the local cross-section along the curved pipe axial line. The Consistent Orthogonal Basis Function Space is developed, such that the basis functions are very similar to mode shape functions and the diagonal mass matrix is accurately obtained. The nonlinear finite element implementation details are presented. Numerical tests are presented for four kinds of curved pipes and the post buckling analysis is presented. The results are verified with a commercial FEM package.