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added amplitude analysis applied approach ASME bending body bottom boundary calculated capacity coefficients collision compared comparison computed configuration considered Copyright coupled curve damage damping deck defined developed direction displacement distribution domain dynamic effects element energy Engineering equation estimate experimental experiments fatigue field Figure floating flow force frequency function given heave height hull hydrodynamic impact increase International joints length linear load locations mass maximum mean measured Mechanics method mode mooring motion natural nonlinear numerical obtained Ocean offshore operation parameters performed period pile pipe plate platform position predicted presented pressure problem ratio reduced reference relative represents respectively response riser sensor ship shown shows simulation soil solution static stiffness stress structure surface Table tank tension transverse unit values vertical vessel water depth wave weld wind