Structural capability assessment of a double-shell panel by a non-linear finite element analysis

1.Objective of the study

The objective of the study is the structural assessment of a double-bottom structure of a bulk-carrier for different mesh sizes, loading and boundary conditions by a non-linear analysis. The more precise objective is to assess which parts of the double-bottom structure enter plastic deformation as the wave height increases.

From the whole structure of the ship only the double-bottom region for the length of one cargo hold was considered for this study. Two models with different mesh sizes were created and 40 non-linear analyses were made: for two sets of boundary conditions and five wave heights. For each wave height and boundary conditions set four analyses were made for the two models for sagging and hogging conditions.

2.Ship data

The main dimensions of the ship considered in this study are the following: -Length between perpendiculars: 168 m -Length at waterline: 170 m -Breadth: 26.6 m -Depth: 12 m -Draught: 9 m

3.FEM Models

For the ship having the main dimensions from the previous chapter, scantling of the midship section was determined using DNV-GL Poseidon software.

For the structure information obtained from Poseidon two structural models were created in Femap: a coarse-mesh model with elements size maximum 200 millimeters and a fine-mesh model with elements size maximum 100 millimeters. The length of the models was taken as the length of one cargo hold, 25.6 meters.

For the fine-mesh model an overall view and structural detail are shown in the pictures below:

For the coarse-mesh model an overall view and structural detail are shown in the pictures below:

4.Boundary conditions

Two sets of boundary conditions were used for two sets of analyses. The first set of boundary conditions is the one recommended by DNV GL register, and are as follows: -symmetry conditions on the nodes in centerline, translations around y-axis and rotations around x-axis and z-axis being blocked, as the axis system is shown in the next slide -vertical translations are blocked in the nodes corresponding to the side and inner side panels -vertical translations are blocked in the nodes corresponding to the fore and aft ends of the innerbottom

For the second set of boundary conditions, recommended by Bureau Veritas register, two additional boundary conditions are considered: -for the double-bottom fore and aft ends the rotation around the transverse axis is blocked -for the nodes located in correspondence of the side and double-side panels the rotation around longitudinal axis is blocked

The boundary conditions considered for the analyses sets are shown below, the two sets of boundary conditions are applied to the same nodes.

5.Loading cases

Four simultaneous loading conditions we’re considered: -gravitational acceleration, corresponding to the weight of the structure: 9.81 m/s^2. This loading condition is the same for all cases investigated. -cargo hold pressure on the double-bottom.The bulk carrier is considered loaded with cereals having a density of 0.6 t/m^3.This loading condition is the same for all cases investigated. -Hydrostatic water pressure on the bottom of the ship, which depends on the wave characteristic. -Global loading of the ship’s hull, considered as forces applied on the nodes of the bottom and double-bottom aft and fore ends of the structure.Also depends on the wave characteristic.

The main parameter that changes for the loading scenarios is the wave height, which changes the values for the water pressure on ship’s bottom and the forces representing the global bending of the hull.

The values for the W modulus at deck and bottom and the moments of inertia of the midship section were provided by the Poseidon software.The bending moments were calculated according to DNV GL register rules for the sagging and hogging conditions.

Knowing the W modulus and the bending moments the stress σ was calculated. By multiplying the sectional area of the double-bottom and bottom plates with the stress the force representing the global bending moment was calculated.The calculated force was divided at the number of nodes on the bottom and the double-bottom plates ends and a force was applied to each node.

Five wave heigths were considered, the first one being calculated according to register rules:

The wave height calculated according to DNV GL register rules was 9.23 m. For this study, analyses were also made for 9.5m,10m,10.5 m and 10.75m.

General overview of the ship loading conditions:

The cargo pressure on the double-bottom and the forces representing the global loading of the hull:

The five loading cases depending on the wave height considered:

6.Non-linear analysis for DNV-GL boundary conditions

Because of the multitude of analyses and results only a few will be shown here. The drawn arrows are highlighting the plastic deformation areas of the structure.

Fine mesh model, hogging,wave height=9.23 m:

For the element in the picture below the following charts have been created using FEMAP software: stress as a function of the virtual time step , elastic strain-plastic strain and stress-strain. The element selected for representing the charts is a part of the floor structure, as shown in the picture below:

The chart on the left represents the stress as a function of the virtual time step, of the element highlighted above, from the analysis of the fine mesh model, hogging, wave height 9.23 m. As can be seen from the chart, the element enters plastic state at virtual time 320, from 400 time steps.

The charts below show the stress-strain variation and elastic strain-plastic strain variation, for the same element:

Hogging, coarse mesh model, wave height 10 m. The plastic zone is in the same areas of the structure, but is extended more:

Fine mesh model, hogging, wave height= 10.75 m analysis result is shown below. The extent of the plastic deformation area is clearly visible compared to the 10 m wave height case.

7.Non-linear analysis for Bureau Veritas boundary conditions

For Bureau Veritas boundary conditions, small fluctuations appear in the stress, mainly in the hopper tank sloped plates, as shown in the pictures below: coarse mesh model, hogging,hw=9.23 m, BV conditions (first image) and DNV-GL conditions(second image).

Fine mesh model, hogging, hw=9.23 m, DNV-GL boundary conditions(first picture) and BV boundary conditions (second picture).

8.Conclusions

As a result of the numerous cases of loading and boundary conditions analyzed, the following conclusions have been reached: -the stress and plastic zones are much more reduced in the sagging case. That is because the pressure of the water on the bottom of the ship is decreasing as the wave height increases, and the loading from the global bending increases but not enough to produce a significant increase in stress -there are significant differences between the two models, for the same loading and boundary conditions. Mainly the plastic zones are much more extended for the fine-mesh model. -for the hogging case, the main area in which plastic strain appears is the bottom of the ship. The conclusion, also considering the difference between hogging and sagging cases, is that the water pressure on the bottom of the ship is the main loading acting on the structure. -There are small differences between the two boundary condition cases, mainly in the hopper tank sloped plates. -because the structure has plastic stress areas, even for the register-calculated wave height, it means that the structure obtained from Poseidon must be improved to correspond to the register standards.

9.References

For a better understanding of the phenomena described in this project lecturing the following books is recommended: 1.Leonard Domnisoru-Structural analysis and hidroelasticity of ships, The University Foundation “Dunarea de Jos” Publishing House, Galati, 2006 2.Bergan P.G.,Bathe K.J.,Wunderlich W.-Finite Element Methods for Nonlinear Problems, Springer Verlag, Berlin, 1986 3.Baguley D.,Hose D.R.-How to Interpret Finite Element Results, NAFEMS, Bell and Bain Ltd, Glasgow, 1997 4.Bathe K.J.-Finite Element Procedures in Engineering Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, 1982   5.Arthur P. Borest,Ken P. Chong, James D. Lee-Elasticity in engineering mechanics, John Wiley& Sons, 2011 1.Peter Wriggers-Non-linear finite element methods, Editura Springer, 2008