Based on differential quadrature (DQ) element of tubular with a radial constraint,an arc-length incremental iteration method is established.It is used for the post-buckling analysis of tubular in a deviated well bottom.Detailed iteration steps and method of determining initial values of iteration are given.Iterative calculations are carried out for nonlinear buckling of tubular under various end lateral constraints in deviated wells.Numerical results are compared with approximate analytical solution,experimental data and numerical results obtained with purely incremental methods in literature.It shows that the developed method overcomes difficulties encountered in finite element method in dealing with tubular weight.At the same time,it is capable to adjust automatically increment step and trace complex path in the space load/displacement of tubular nonlinear post-buckling.The method is of high efficiency,good convergence,easy to implement.It can be used to analyze nonlinear buckling of tubular in deviated wells.

Equilibrium equations of tubular in a deviated well are presented.A differential quadrature element(DQE)incremental iteration method is established to analyze nonlinear buckling of tubular in a deviated well.The method is verified with result of finite element method.It exhibits advantages of easy implementation,low computational cost and higher accuracy.Helical buckling by DQE agrees well with experimental data.The maximum constraint force increases with increasing of upper end load.It is found that the buckling of long tubular is a local buckling problem.The buckling starts from the lower end and propagates upward with increasing applied load.Boundary conditions at upper end have little influence on local buckling of lower tubular.