Study on Spectral Fatigue Assessment of Trimaran Structure

This study presents fatigue strength assessment of the trimaran platform by the spectral approach. Spectral fatigue calculations are based on complex stress transfer functions established through direct wave load analysis combined with stress response analysis. In this study, ANSYS software with 3 dimensional linear seakeeping code AQWA is used to compute frequency response functions of the vessel at zero forward speed. Finite element analysis of global trimaran structure is performed in ANSYS software utilizing hydrodynamic wave loads. Hot spot stress approach is used to compute stress transfer functions of the selected critical details. A MATLAB program, based on direct calculation procedure of spectral fatigue is developed to calculate total fatigue damage using wave scatter data of North Atlantic. Damage incurred during individual heading direction is also calculated and presented by means of polar diagrams to study its contribution towards cumulative fatigue damage.


INTRODUCTION
Trimaran platform design has gained enormous attention in recent years owing to its superior seagoing performance.The trimaran offers significant advantages in terms of low resistance at high speed, excellent seakeeping characteristics, massive deck space and stealth (Blanchard and Ge, 2007).Due to its unique configuration and high operating speed, trimaran experiences severe structural loads, which include splitting moment, wet deck slamming and stress concentration in the cross deck region.These loads accelerate fatigue damage; hence, evaluation of fatigue strength is vital for trimaran design.
The research work focusing on sea keeping aspects of the novel trimaran platform emerged after launching of RV Triton in 2000, being the world's largest trimaran of that time (Pei-Yong et al., 2002;Varyanik et al., 2002;Xiao-Ping et al., 2005;Fang and Too, 2006;Fang and Chen, 2008;Kang et al., 2008).However, very little material is available on fatigue strength assessment of trimaran structure (Chun-Bo et al., 2012).The fatigue strength of a ship structure is generally assessed either by simplified method or spectral based Method (Bai, 2003).These techniques are categorized based on the method used for determination of stress distribution.In simplified method, long-term stress distribution in structure is specified by Weibull probability distribution, whereas, short term stress range distribution in spectral method is defined by Rayleigh probability density functions for each short term sea state.Application of simplified method for trimaran is complex, since guidelines of the classification societies for fatigue loads, load cases and loading conditions are not available.Moreover, excessive sensitivity of the estimated fatigue damage to the Weibull shape parameters and selection of basic design SN curve confine the use of simplified approach to novel ship structures.
Spectral fatigue analysis 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).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.This research is focused on fatigue strength assessment of trimaran by spectral method.
In this study, frequency response functions representing the ship response to a sinusoidal wave with unit amplitude for different frequencies and wave headings are computed using linear sea keeping code ANSYS AQWA utilizing 3-dimensional potential flow based diffraction-radiation theory.Considering hot spot stress approach, stress transfer functions are calculated by global FE analysis of the trimaran.Finally direct calculation procedure of spectral based fatigue is employed to estimate cumulative fatigue damage of the hot spots.The study also investigates the effect of Wirsching's rain flow cycle correction factor and contribution of fatigue damage caused by individual heading direction towards cumulative fatigue damage of the hot spots.

LITRETURE REVIEW
Spectral-based fatigue analysis is a complex and numerically intensive technique.Theoretical background and method of spectral fatigue are presented in detail in numerous publications (Wirsching and Chen et al., 1988;Sarkani, 1990;Pittaluga et al., 1991;Wang, 2010).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, S-N curve of the structural detail and zero crossing frequency of the response.Based on Palmgren-Miner linear damage accumulation hypothesis with occurrence probabilities of the different operational and environmental conditions, total or cumulative fatigue damage is determined by combining the short-term damages over all the applicable sea states (Siddiqui and Ahmad, 2001).The analysis procedure of spectral based fatigue is shown in Fig. 1.
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-Moskowitzwave 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) : The stress transfer function θ : The heading angle The n th spectral moment m n of the stress response process for a given heading is calculated as follows: . | , , Effect of directional spreading can be included in spectral moment calculation using cosine squared approach 2 ⁄ cos to model confused short crested sea conditions.Spreading limitation of the cosine squared function is generally assumed from +90 to -90°C on either side of the selected wave heading.Revised spectral moment formulation after inclusion of wave spreading function is 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 and the bandwidth parameter of Wirsching's rain flow correction are calculated as follows: (5) ( 6) where, s : Stress range m 0, m 2, m 4 : Spectral moments Using SN curve of the form N = AS m , the short term fatigue damage D ij incurred in the i th sea-state is given by the relation:   Eq. ( 5) and af quation takes t  ull with wet de ran structure, h ate stress trans size't x t' is us is coarse mesh cing (Fig. 4).