An investigation of effects of Chebysheve points on the convergence rate in theoretical modeling of elastic contact between the spherical rigid indenter and steel pipe API XB

In this paper, theoretical model of the contact between rigid spherical indenter with steel pipe API XB is presented to simulate dent on the pipes in working environments, and the results could be used to estimate the stress-strain distributions and as a result the useful life of pipes in denting area. Governing equilibrium equations for thin cylindrical shell is presented in the form of displacement components by the Navier method, which will be solved by higher order finite difference method. Richardson extrapolation technique and the effect of ChebyShev points on the convergence rate of responses in finite difference method will be discussed. Contact pressure between the pipe and indenter in each loading steps are estimated by contact mechanic theories and will be applied to the outer surface of the pipe. The finite element method will be used to compare the results. Finally, it can see that the results of two methods are in the good agreement with error less than 5% and theoretical model are applicable to variety of dimensions, material, boundary and loading conditions of pipe and indenter.