Non-linear buckling analysis of inclined circular cylinder-in-cylinder by the discrete singular convolution

The lateral buckling and helical buckling problem of a circular cylinder constrained by an inclined circular cylinder under a compressive force, torsion, and its own weight is complicated and difficult to obtain an exact analytical solution. Thus, the non-linear differential equation is solved incrementally using the discrete singular convolution (DSC) algorithm together with the Newton–Raphson method. Detailed formulations are worked out. A simple way to numerically simulate the helical buckling is proposed and solution procedures are given. Four examples with various inclined angles, weights per unit length of the inner cylinder, axial applied loads, and boundary conditions are investigated. To verify the formulations and solution procedures, comparisons are firstly made with data obtained using the finite element method. It is verified that under certain circumstance, only lateral or helical buckling alone will occur. On some other circumstance, both lateral buckling and helical buckling may occur and the critical helical buckling loads are higher than the critical lateral buckling loads if frictions are not considered. Some conclusions are made based on the results presented herein.