prediction and analysis of critically stressed · dynamic behaviours of ship structures. the...

Prediction and analysis of critically stressed ship sections

H. K. A. Lee, Z. J. Liu, S. W. Gong & K. C. Hung

Institute of High Performance Computing, Computational Multi-Physics

Abstract

Whole ship shock analysis (WSSA) is becoming a mandatory requirement in the design of naval platform. One of the key technical challenges in WSSA is the reduction of a complex ship design to a reasonable FE model size. An approach known as “smearing” is commonly used to idealise the ship to a manageable number of DOFs, by using equivalent stiffness. This paper presents a novel technique to study the localized stress and deformation of a ship section using global parameters obtained from the WSSA. A 3D explicit finite element code is used to compute the critically stressed areas in the whole ship and predict the localized stresses in the ship section. This paper expounds the methodology of stress recovery through the conversion of the displacement time history from the whole ship to obtain the stress distribution for the ship section. The expedience of exploiting stress recovery to inspect the localized stresses in the beam and shell elements will also be clearly exemplified. Last but not least, a displacement accuracy comparison will be performed on the ship section and the “unsmeared” whole ship.

1 Introduction

The response of the whole ship subjected to underwater explosion is greatly complicated by the detonation of a high explosive, shock wave propagation, bulk and local cavitations, complex fluid-structure interaction phenomena, and the dynamic behaviours of ship structures. The simulation of the whole ship shock analysis (WSSA) is an essential step in the early phase of the ship design spiral. Computational results of shock loadings on the ship structures and the acceleration/forces on equipments in the ship will be valuable to the ship design.

Damage and Fracture Mechanics VIII, C. A. Brebbia & A. Varvani-Farahani (Editors)© 2004 WIT Press, www.witpress.com, ISBN 1-85312-707-8

Modeling Division, Singapore

With the purpose to counter the high DOFs in the ship model, an approach called smearing is employed. Consequentially, the stresses at the secondary stiffeners do not depict the true value and a detailed model of a critically stressed ship section has to be performed to determine the actual value.

2 General characteristics

A box-like structure is used to carry out this case study. The dimensions of the length, width and height are 20m, 10m and 8m respectively. Three models are used for comparison. The first model is the full ship model, where all the beam elements are modeled. The second is the timo ship model, where smearing is done using the Timoshenko formulation and the third is the detailed model, showing a critically stressed bulkhead. The FE models are shown in Figure 1a, 1b and 1c respectively. The shock impact is distributed over a small area from the keel to the mid-deck on the starboard.

2.1 Shell and beam elements

All of the shell elements in the first model use the Belystschko-Lin-Tsay type and those in the second and third models use the Hughes-Liu Integration shell type. Although, the former is computationally more efficient, the latter enables the user to determine the stresses at the upper, middle and lower surface of the shell elements. The number of DOF for the three models is 20679, 5067 and 1359 respectively. For the beam elements, the timo ship model uses the Belytschko-Schwer resultant beam because of its computational time expedience. However, for the detailed model, in order to analyse the stress distribution, and hence the failure risk, the Belytschko-Schwer resultant beam cannot be used. Instead, the beam utilized is the Hughes-Liu beam, with cross-section integration. For complete comparison with the detailed model, the beam type assigned to the full ship is the also the Belytschko-Schwer resultant beam. With the T-beam type, the analysis becomes more computational efficient and robust, as every beam element consists of nine integration points. Using a post-processor, LS-POST, the axial stress for each part can be shown. Thus, it is easy to predict if any beam would exceed its yield strength and fail. The T-beam type is shown in Figure 2.

2.2 Material model

The beam elements in the timo ship model use the Johnson-Cook material model (*MAT_JOHNSON_COOK). For the beam elements in the full ship and detailed ship models, the elastic with plastic hardening material model (*MAT_PLASTIC_KINEMATIC) is employed. The advantages of using the (*MAT_PLASTIC_KINEMATIC) model are that it is simplified and more conservative than the (*MAT_JOHNSON_COOK) material model.


196 Damage and Fracture Mechanics VIII

(c) Figure 1: Cross-sectional view of FE models for (a) full ship & (b) timo ship.

(c) Front view of FE model for detailed model.

Figure 2: Hughes-Liu T-beam type with 9 points of integration.

Shell elem 4003

Beam elem 37826

(a) (b)


Damage and Fracture Mechanics VIII 197

Figure 3: Time history plot for maximum von Mises shell stress.

The elasto-plastic behaviour is simplified using the Johnson-Cook formulation:

( )( )*m*pTεCεBAσ

n

−+

+= 1ln1 (1)

whereσ is yield stress, pε is effective plastic strain,

0εεε

p* = is effective

plastic strain rate for 0ε =1s-1, roomTmeltT

roomTT*T−

−= is homologous

temperature, A, B, C, n and m are constants.

3 Detailed stress analysis

The rationale for performing a detailed stress analysis is that after smearing has been done, the local stress distribution, except at the primary stiffeners, is no longer of plausible accuracy. As a result, it is of absolute necessity to perform a detailed stress analysis on some critically stressed areas, namely hotspots, to inspect the localized stresses at the beam and shell elements. This is done to



determine if the elements at these hotspots would exceed the yield strength and fail. If this happens, it is probable that the ship would capitulate. The dynamic loading for the detailed model is obtained using the following procedures. The ASCII format output file, called NODOUT, is required to obtain all the displacement DOF data. Next, an in-house developed FORTRAN program, called GETDATA, is essential to output the critical information to the correct format. Thereafter, another in-house developed MATLAB program is written to perform surface interpolation and also to output the displacement-time history as inputs for the detailed model. This type of boundary conditions is termed prescribed motion. Using this methodology, the detailed stress analysis can be executed on any ship section that is critically stressed. In this paper, the ship section of interest is a bulkhead to the left of the midship section.

4 Results

One of the bulkheads is identified as a critically stressed ship section. For each shell element in the bulkhead of the timo ship model, it is split into four to achieve the fine FE meshing shown in Figure 1c. The total computation time taken to complete the full ship model is about 1710s, for the timo ship model about 1359s, and for the detailed model about 130s. This amounts to sizeable time saving. Considering that these three models are considerably scaled down from actual computational ship models, where the DOFs can be at least ten times as large, the time expedience would be significantly augmented. Now, the maximum von Mises stress for the shell elements is 449MPa and occurs in element 4003 at 0.0505s. It is located near to the bottom on the starboard side (see Figure 1c). The von Mises stress with time history for this element 4003 is shown in Figure 3. As for the beam elements, the maximum axial stress, beam integration point 1, found in element 37826 is 353MPa. This occurs at time 0.024s. The location of the beam element is shown in Figure 4. From the results presented, it shows that in the event of failure, the shell elements would fail before the beam elements. This finding harmonizes with an actual ship subjected to shock loadings, where the beams take the brunt of the impact. Having found the stress distribution in the critically stressed bulkhead, the user is able to determine the possible areas of failure. Modifications can be easily made to the bulkhead to overcome this, and the repercussion of these modifications can be quickly assessed. All this happens in the design phase, ensuring unnecessary wastage of materials, thus cost. For verification purposes, the nodal displacement of the full ship model and detailed model are compared, shown in Figure 5. This node is found in the middle of the critically stressed bulkhead of interest. From the curves, it is shown that the displacements are in good agreement, although some of the points do not coincide. The reason for this is attributed to the approach of the surface interpolation and draws to the conclusion that for maximum accuracy, all the



grid points in the detailed model have to be used to perform the surface interpolation. Consequently, this approach of stress recovery is verified and shown to be reliable.

Figure 4: Time history plot for maximum axial beam stress.

Figure 5: Z-Displacement time history for element 8192.

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.00E+00 1.00E-02 2.00E-02 3.00E-02 4.00E-02 5.00E-02 6.00E-02 7.00E-02 8.00E-02 9.00E-02 1.00E-01

Time (s)

z-di

spla

cem

ent (

m)

Detail Full



5 Conclusion

The objective of the detailed stress analysis is to correctly predict the stress distribution of a critically stressed ship section, subjected to an underwater explosive shock. From the simulation results, it is possible to obtain the stress distributions of the beam and shell elements, whereupon, recommendations can be made to improve the highly stressed ship section. This is critical to facilitate design guidelines and in some cases, stealth can also be significantly increased. In addition, adopting this stress recovery approach leads to time expedience and unnecessary wastage of raw materials to build the ship.

References

[1] Hallquist, J., LS-DYNA3D Theoretical Manual, Livermore Software Technology Corporation, USA, 1994.

[2] LS-DYNA3D User’s Manual, Version 936, LSTC, Livermore, Ca 94550, 1995.

[3] Timoshenko, and Woinowsky-Kreiger, Theory of Plates and Shells, McGraw-Hill, New York, 1959. 580 pp.

[4] Z.J. Liu, etc, An Approach For Stress Prediction Of Stiffened Panel Under Shock Loading, Proceedings of the 4th Asia-Pacific Conference on Shock & Impact Loads on Structures, Singapore, 2001.



prediction and analysis of critically stressed · dynamic behaviours of ship structures. the...

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