A simplified boundary condition method for conducting shock resistance analyses of ship piping systems

Highlights

• A numerical model of pipe systems based on multi-span beam bending moment theory is introduced to address the shock resistance of ship piping systems.

• The proposed method can be generally used to analyze the target piping whether the pipeline models are in a plane space or a three-dimensional space.

• The simplified five-span method will save 60% of the time.

Abstract

The shock resistance of ship piping systems is very difficult to study owing to the large scales of such systems, and the high level and variability of the impact loading involved. To address these issues, the present work establishes a numerical model of pipe systems based on multi-span beam bending moment theory. An analysis of the bending moments of different multi-span continuous beams under static loading demonstrates that the simplified model employing just five spans provides a bending moment for target equal diameter straight tube (EDST) segments that deviates from theoretical calculations by less than 1%. Moreover, the bending moments obtained by the five-span model for a target EDST segment deviate by only about 4% from corresponding results obtained by the finite element (FE) method under both uniformly distributed static loading and complex static loading. The proposed simplified five-span model is then employed to calculate the stress responses obtained at individual critical points in a complex piping system under impact loading. The results obtained deviate at most by less than 15% from corresponding results obtained from the FE method based on the overall piping system model. Moreover, the average deviation for all critical points considered was only 5.87%. The results show that the shock response obtained using the simplified five-span model is essentially equivalent to that of the complex model. The proposed simplified five-span method is thereby demonstrated to be reasonable for simplifying large-scale complex piping systems when conducting shock resistance research.

Introduction

Ships suffer structural damage when attacked by explosive weaponry such as missiles, mines, and torpedoes. Among the many crucial ship components vulnerable to damage, ships employ widely distributed and complex piping systems that are mainly used for transporting various essential fluids such as fuel, drinking water, cooling water for equipment, and fluids for fire control systems. As such, damage to a ship piping system will directly endanger the survivability and safety of the ship. Therefore, evaluating the shock resistance of ship piping systems is of critical importance.

At present, finite element (FE) method and the numerical analysis methods are widely applied worldwide for studying the shock resistance performance of ship piping systems. For example, Yang [1] experimentally studied pipe-on-pipe impact with numerical simulation using LS-DYNA (Livermore Software Technology Corp.). Wang [2] experimentally studied the lateral impact properties of a water filled ultra-light cement composite (ULCC) tube by drop hammer impact testing coupled and with numerical simulation using LS-DYNA (Livermore Software Technology Corp.). Alshahrani [3] developed and experimentally validated an FE model of a glass fiber reinforced epoxy (GFRE) tube, and derived a failure criterion according to predictions of layer damage sustained under low velocity impacts based on the three-dimensional stress state of the tube. Kristoffersen [4] adopted experimental investigation and numerical simulation to calculate and analyze an offshore pipeline under a no-load condition and water filling. Liu [5] demonstrated the significant impact of vibration on the structural integrity of pipelines, and through the finite element simulation calculation, proposed several methods to adjust natural frequency to solve the vibration problem of pipeline system. Z.L. Yu [6] used numerical simulation to design an effective pipeline defense system to reduce the damage of the structure under the blast impact. W.H.Semke [7] studied the dynamic structural response of pipeline system. Zhou et al. [8] applied the transfer matrix method toward an analysis of the shock resistance of a warship piping system. Here, the transfer matrix of a spatially complex cooling pipe system was first established, and a numerical solution was obtained for determining its impact response.

While substantial progress has been made for evaluating the shock resistance of ship piping systems numerically, these methods require considerable time and manpower when applied to complex ship piping systems such as fire control piping systems. This problem is compounded by the complexity of the most critical points of a ship piping system under impact, which include elbows and three-way pipe intersections. Therefore, the task of simplifying the structure of tube systems is of particular practical importance. For example, Okeil [9] et al. calculated the inelastic seismic response of a nuclear power plant cooling water pipeline system using an ideal pipe model consisting of four equal length pipes in conjunction with an existing pipeline system model. Zhu et al. [10] adopted an experimental procedure to study pipeline deformations obtained for different pipe diameters under lateral impacts, and accordingly proposed a method for determining local and global system deformations. The dynamic characteristics of pipelines under lateral impacts were then established based on the deformation mode of the pipeline obtained under impact testing. The primary drawback of these simplified models is that they consider only a subset of an overall piping system, but fail to clearly define the boundaries of the model. As a result, the influence of conditions external to the calculation model are not considered, which limits the applicability and accuracy of the evaluation approaches.

To address these issues associated with past work, the present study applies the theory for evaluating the bending moment of a multi-span beam for evaluating the impact resistance of a ship piping system. The proposed method mainly simplifies the boundary conditions of complex piping systems for greatly improving the tractability of numerical calculations evaluating their impact responses. Three kinds of five - span piping models are introduced in this paper, respectively (a) straight tube; (b) elbows; (c) three-way pipes (see Fig. 13). When the pipelines are of the above three models, the proposed method can be generally used to analyze the target piping whether the pipeline models are in a plane space or a three-dimensional space. We obtain the stress responses at individual critical points in a complex piping system under impact loading by the proposed simplified five-span method and compare them with the corresponding results obtained from the FE method of the overall piping system model. The favorable comparisons demonstrate that the proposed simplified five-span method is reasonable for simplifying large-scale complex piping systems when conducting shock resistance research.