Progress in the Analysis and Design of Marine Structures

Proceedings of the 6th International Conference on Marine Structures (MARSTRUCT 2017), May 8-10, 2017, Lisbon, Portugal

Carlos Guedes Soares, Y. Garbatov, Carlos Guedes Soares, Y. Garbatov

• Publisher: CRC Press
• Year: 2017
• ISBN:
  9781351653404
• Edition: 1
• Topic: Technology & Engineering
• Subtopic: Civil Engineering
• Index: Technology & Engineering

Progress in the Analysis and Design of Marine Structures collects the contributions presented at MARSTRUCT 2017, the 6 th International Conference on Marine Structures (Lisbon, Portugal, 8-10 May 2017).

The MARSTRUCT series of Conferences started in Glasgow, UK in 2007, the second event of the series having taken place in Lisbon, Portugal in March 2009, the third in Hamburg, Germany in March 2011, the fourth in Espoo, Finland in March 2013, and the fifth in Southampton, UK in March 2015. This Conference series deals with Ship and Offshore Structures, addressing topics in the areas of:

- Methods and Tools for Loads and Load Effects
- Methods and Tools for Strength Assessment
- Experimental Analysis of Structures
- Materials and Fabrication of Structures
- Methods and Tools for Structural Design and Optimisation, and
- Structural Reliability, Safety and Environmental Protection

Progress in the Analysis and Design of Marine Structures is essential reading for academics, engineers and all professionals involved in the design of marine and offshore structures.

Collision and grounding

A simplified method to assess the damage of an immersed cylinder subjected to underwater explosion

K. Brochard & H. Le Sourne

GeM Institute, ICAM Nantes Campus, France

G. Barras

Direction Générale de l’Armement—Techniques Navales, Toulon, France

ABSTRACT: This paper presents a simplified method for assessing the damage of an immersed cylinder subjected to the primary shock wave produced by an underwater explosion. The interaction between the water and the cylinder is divided into two phases for simplicity. In the first phase, a kinetic energy transmitted to the cylinder by the shock wave is calculated. In the second phase, the cylinder deforms and the related shell displacements create an additional pressure loading. A simplified mechanical model of the shell is proposed. Closed-form expressions for evaluating the final deflection profile of the shell are presented and compared to finite element results. The presented method is in quite good agreement with numerical results. Further developments are needed for improving the modelling of the cylindrical shell mechanical behavior.

1 INTRODUCTION

The design of a submarine’s hull is crucial for its operability and crew’s safety, but also complex. Indeed, engineers need to balance lightness, acoustic discretion and resistance to both immersion pressure and environmental attacks. Submarine explosions represent a first-rate threat for the integrity of the hull, whose behavior needs to be properly analyzed. In the design process of submarines, numerous calculations must be performed to minimize the amount of damage produced by underwater explosions, with various characteristics of shell, material and scenarios of explosion.

Experimental analysis are extremely expensive, time-consuming, as shown by Brett (2008) and are not to be used for design analysis, even though, they provide precious understanding of the physics of the problem. In recent decades, numerical methods have been developed for simulating the dynamic response of a submerged structures to an underwater explosion, and have been applied to cylindrical shell and ring-stiffened cylinder by Hung (2009) and Li (2012). However, numerical simulation are also time-consuming and not well-suited at design stage. Hence, present research aims at developing a simplified method that allows to perform quick resolution of the problem of an immersed cylinder subjected to an underwater explosion.

The presented work relies on a methodology developed by Wierzbicki & Hoo Fatt (1993), the so-called plastic string-on-foundation method, which enables to obtain closed-form solutions for the deformation and velocity profiles of a cylindrical shell when subjected to impact or explosive loading. However, this method is inappropriate when shell is immersed, because fluid-structures interactions are not considered. The work presented here focuses on coupling this method with an approximate formulation of the fluid-structure interaction. In order to obtain closed-form expression of an immersed cylinder’s final deflection when it is impacted by an underwater explosion primary shock wave.

2 EXPLOSIVE LOADING

2.1 Theoretical foundations

Consider a cylindrical shell of length L, radius R and thickness h, clamped at both ends. It is filled with air and fully immersed in water. An explosive charge of mass C detonates at a distance D₀ from the stand-off point S₀, located at the intersection of cylinder’s planes of symmetry, as shown in Figure 1.

On a current point S of the shell, shock wave’s amplitude may be calculated with the following expressions proposed by Cole (1965):

pI(S|t)=pse−t/Ts(1)

Figure 1. Initial configuration of an immersed cylinder subjected to an underwater explosion.

With,

Ps=Kp(C1/3/D)APTs=KTC1/3(C1/3/D)AT(2)

Here, D is the distance between S and the charge’s location and K_P, K_T, A_P and A_T are characteristic parameters of the explosive. In the following developments, the fluid is supposed to be infinite, inviscid and incompressible so that a potential flow can be assumed. In a point far enough from the charge, pressure field in the fluid also verifies Bernoulli linear equation. When the shockwave generated by the underwater explosion impacts the shell, fluid-structure interactions lead to a pressure field in the fluid of the following form:

p(P|t)=pI(P|t)+ps(P|t)(3)

where p_S is the so-called scattered pressure, i.e. the sum of the reflected wave on the cylinder fixed and rigid and of the radiated wave from shell’s deformatin. It constitutes the unknown of the problem.

2.2 Retarded Potential Formula applied to a cylinder

For a structure immersed in an infinite fluid medium, pressure field and its components must satisfy the Helmholtz equation, which is expressed from the velocity potential φ:

Δφ−1cf2∂2φ∂t2=0(4)

where c_f is the speed of sound in the fluid. At the fluid-cylinder interface, in the case where cylinder’s spe...