Towards the Procedure Automation of Full Stochastic Spectral Based Fatigue Analysis

Fatigue is one of the most significant failure modes for marine structures such as ships and offshore platforms. Among numerous methods for fatigue life estimation, spectral method is considered as the most reliable one due to its ability to cater different sea states as well as their probabilities of occurrence. However, spectral based simulation procedure itself is quite complex and numerically intensive owing to various critical technical details. Present research study is focused on the application and automation of spectral based fatigue analysis procedure for ship structure using ANSYS software with 3D liner sea keeping code AQWA. Ansys Parametric Design Language (APDL) macros are created and subsequently implemented to automate the workflow of simulation process by reducing the time spent on non-value added repetitive activity. A MATLAB program based on direct calculation procedure of spectral fatigue is developed to calculate total fatigue damage. The automation procedure is employed to predict the fatigue life of a ship structural detail using wave scatter data of North Atlantic and Worldwide trade. The current work will provide a system for efficient implementation of stochastic spectral fatigue analysis procedure for ship structures.


INTRODUCTION
Ships are prone to fatigue due to high cyclic loads predominantly caused by waves and varying loading conditions (Fricke et al., 2011).Fatigue strength evaluation is an important criterion in ship design as accurate prediction of the fatigue life under service loading is imperative for both safe and economic design and operation (Cui et al., 2011).The fatigue strength of ship structure is generally assessed either by simplified method or spectral based Method.These techniques are categorized based on the method used for determination of stress distribution (Bai, 2003).Excessive sensitivity of the estimated fatigue damage to the weibull shape parameter and selection of basic design SN curve, confine the use of simplified approach to complex structures and novel hull forms (ABS, 2003).On the contrary, spectral method is considered as the most reliable method for fatigue life estimation of ship structure due to its ability to cater different sea states as well as their probabilities of occurrence (Wang, 2010).It is a direct calculation method based on linear theory in the frequency domain of a stationary and ergodic but not necessarily narrow banded Gaussian random process with zero mean (Kukkanen and Mikkola, 2004).
Full stochastic spectral fatigue calculations are based on complex stress transfer functions established through direct wave load analysis combined with stress response analysis.In full stochastic analysis, hydrodynamic loads are directly transferred from the wave load analysis program to Global FE model.Wirsching and Chen (1988), Sarkani et al. (1990), Pittaluga et al. (1991) and Wang (2010) have presented in detail the theoretical background and method of spectral based fatigue analysis.Chun-Bo et al. (2012) investigated the fatigue strength of trimaran cross deck structure by spectral approach.Shehzad et al. (2012) applied spectral method to estimate fatigue life of selected critical details of trimaran structure.In spectral approach, wave loads in regular waves Or Response Amplitude Operators (RAOs) and corresponding wave induced stresses in ship structural components are computed for a specific range of frequencies and headings to obtain stress transfer functions at the hot spots.Each transfer function is valid for a specified ship velocity, wave heading angle and loading condition.Wave data in terms of a wave scatter diagram and a wave energy spectrum are incorporated to generate stress-range response spectra, which is used to define the magnitude and frequency of occurrence of local stress ranges at hot spots in a probabilistic manner.Fatigue damage from individual sea state is calculated using Rayleigh's probability density function describing the short-term stress range distribution, spectral moments of various orders and S-N curve  An automatic pressure loading technique was developed utilizing APDL based subroutine ALSFG (Automatic Load Step File Generator).ALSFG macro working include removal of line mesh, systematically reading of AQWA pressure files, conversion to corresponding ANSYS load step files and finally remeshing of the lines to generate beam elements.These load step files can be used directly in ANSYS to perform quasi static FE analysis.This pressure loading approach turns out to be a useful tool as it greatly enhances the study efficiency.

Boundary condition and solution:
Application of proper displacement boundary condition in quasi-static FE analysis to constrain body motion is a challenging task.Spring supports are generally used to restrain relevant degrees of freedom of the structure to ensure non singularity of structural stiffness matrix.However, proper selection of spring stiffness constant is vital in order to keep corresponding spring force to be small enough to obtain valid results.
In this study, Inertia relief method in ANSYS is used to solve the problem of displacement boundary condition.It is a latest technique, which perform inertia relief calculations, compute and apply equivalent accelerations that counterbalance the applied loads.An APDL macro IRBCS (Inertia Relief Boundary Condition and Solution) is developed that apply inertia relief boundary condition and solve all load step files generated in previous step.

Stress extraction and stress transfer function:
The hot spot stress based fatigue design is based on the stresses at a weld toe obtained by a linear or quadratic extrapolation of stresses over 2 or 3 points in front of the weld toe under consideration (Kim et al., 2009).Hot spot stress or geometric stress includes all stress-rising effects induced by the structural detail but excluding all stress concentrations due to the weld profile itself.Extraction of hot spot stress and formulation of stress transfer function, which represents the relationship between the stress at a particular structural location, wave frequency and heading, is the key step in spectral fatigue analysis.This tedious cumbersome job of hot spot stress extraction and generation of transfer function is automated using APDL macro "HSSTFG" (Hot Spot Stress Transfer Function Generator".HSSTFG macro working is based upon the hot spot stress extraction methodology of DNV classification notes for fatigue assessment of ship structure (DNV, 2010).It derives hot spot stress for each load case by linear extrapolation over reference points 0.5 and 1.5 x plate thickness away from the hot spot and saves the final stress value at appropriate location in the matrix to generate stress transfer function.
Fatigue damage calculation: Mathematically, spectral-based fatigue analysis begins after the determination of the stress transfer function.Wave energy distribution S η in short term sea state over various frequencies, is modeled by parametric Pierson-Moskowitz wave energy spectrum (DNV, 2010) and expressed as: where, H s = Significant wave height T z = Zero crossing period ω = Wave frequency Stress energy spectrum S σ is obtained by scaling Pierson-Moskowitz wave energy spectrum in the following manner.
where, H σ (ω/θ) is the stress transfer function and θ is the heading angle.The nth spectral moment m n of the stress response process for a given heading is calculated as follows: . | , , Assuming the short-term stress response to be narrow-banded, then stress ranges follow the Rayleigh probability distribution (ABS, 2004).Using spectral moments of various orders, Rayleigh probability density function g(s) describing the short term stressrange distribution and zero up-crossing frequency of the stress response f are calculated as follows: (4) (5) where, s = Stress range m 0, m 2 = Spectral moments Using SN curve of the form N=AS m , the short term fatigue damage D ij incurred in the ith sea-state is given by the relation: where, f 0ij is zero-up crossing frequency of stress response in Hz, T is design life in sec, m and A are constants of SN curve and p i is the probability of occurrence of individual sea state.Substituting the value of g(s) from Eq. ( 4) and after mathematical manipulations, above equation takes the form as: where, represents gamma function.Based on Palmgren Miner rule, the total or cumulative fatigue damage D is calculated by the linear summation of the damage in individual sea state and is expressed as: where, N load = Total number of loading conditions considered p n = Fraction of design life in loading condition n

RESULTS AND DISCUSSION
The result of fatigue damage calculation for various scatter diagrams and effect of Wirsching's rain flow correction factor on computed fatigue life is shown in Fig. 7. Predicted fatigue damage using WWT scatter diagram is lower than the North Atlantic scatter diagram.This is in accordance with the established fact of North Atlantic as the severest condition for fatigue damage calculation.
Also, an increase in predicted fatigue life is observed by the inclusion of Wirsching's rain flow correction factor in spectral fatigue calculations.

CONCLUSION
This study presents procedure automation of full stochastic spectral based fatigue analysis of ship structure using ANSY and 3D linear sea keeping code AQWA.Spectral fatigue analysis is considered as the most reliable among the numerous methods for fatigue assessment of ship structure.Stochastic spectral fatigue is a complex and numerically intensive technique and requires a robust automated workflow of the process for efficient implementation to ship structures.In this study, various technical aspects of spectral fatigue methods are discussed in detail.For each aspect, APDL macros are created and subsequently implemented to automate the workflow of the process and to reduce the pre/post processing time for efficient implementation of the method to ship structures.A MATLAB program is developed to calculate cumulative fatigue damage.A numerical case study is conducted and the automation procedure is employed to predict fatigue life of a structure detail of a multihull craft for different sea scatter diagrams.Effect of Wirsching's rain flow correction factor toward predicted fatigue life of the structure is also investigated.The research study will provide a system to perform spectral fatigue analysis efficiently and accurately.

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