Denting of internally pressurized tubes under lateral loads

The present work examines the structural response of tubular members subjected to lateral quasi-static loading, imposed by wedge-shaped denting devices, in the presence of internal pressure. First, tubes are modeled with shell finite elements, accounting for geometric and material nonlinearities, and the numerical results are in good agreement with available denting test data from internally pressurized pipes. Using the finite element tools, a parametric study is conducted and load-deflection curves are obtained for different levels of pressure, for various wedge shapes and for different types of boundary conditions. It is found that the presence of internal pressure increases significantly the denting force. The effects of yield anisotropy on the denting resistance are also examined. A simplified three-dimensional analytical model is also developed, based on rate-of-energy balance, which yields closed-form expressions for the denting force and the corresponding denting length. The model, introduced elsewhere for non-pressurized tubes, is enhanced to include the pressure effects, accounting for different types of pipe end conditions, as well as the effects of plastic anisotropy. The analytical solution compares very well with finite element results, and illustrates tube denting response in a clear and elegant manner.