A Novel Solution to Compute Stress Time Series in Nonlinear Hydro-Structure Simulations

Abstract

Ship transport is growing up rapidly, leading to ships size increase, and particularly for container ships. The last generation of Container Ship is now called Ultra Large Container Ship (ULCS). Due to their increasing sizes they are more flexible and more prone to wave induced vibrations of their hull girder: springing and whipping. The subsequent increase of the structure fatigue damage needs to be evaluated at the design stage, thus pushing the development of hydro-elastic simulation models. Spectral fatigue analysis including the first order springing can be done at a reasonable computational cost since the coupling between the sea-keeping and the Finite Element Method (FEM) structural analysis is performed in frequency domain. On the opposite, the simulation of non-linear phenomena (Non linear springing, whipping) has to be done in time domain, which dramatically increases the computation cost. In the context of ULCS, because of hull girder torsion and structural discontinuities, the hot spot stress time series that are required for fatigue analysis cannot be simply obtained from the hull girder loads in way of the detail. On the other hand, the computation cost to perform a FEM analysis at each time step is too high, so alternative solutions are necessary. In this paper a new solution is proposed, that is derived from a method for the efficient conversion of full scale strain measurements into internal loads. In this context, the process is reversed so that the stresses in the structural details are derived from the internal loads computed by the sea-keeping program. First, a base of distortion modes is built using a structural model of the ship. An original method to build this base using the structural response to wave loading is proposed. Then a conversion matrix is used to project the computed internal loads values on the distortion modes base, and the hot spot stresses are obtained by recombination of their modal values. The Moore-Penrose pseudo-inverse is used to minimize the error. In a first step, the conversion procedure is established and validated using the frequency domain hydro-structure model of a ULCS. Then the method is applied to a non-linear time domain simulation for which the structural response has actually been computed at each time step in order to have a reference stress signal, in order to prove its efficiency.

A Comparative Study on the Structural Response of Multi-Linked Floating Offshore Structure between Digital Model and Physical Model Test for Digital Twin Implementation

“…In this study, we used a DBM with the largest autocorrelation coefficients. In addition, F ij is a scaling matrix that normalizes S so that the absolute size of the elements included in S may not affect the orthogonality evaluation due to the numerical errors, and the definition of F is shown in Equation (6). To this end, only a wave load of which autocorrelation coefficient of the first mode is 80% or higher may be included in the correlation evaluation step.…”

“…The calculation of the correlation requires two or more S vectors. Since S was not selected from the set of results of numerical analysis when selecting the first mode, an inner product may not be performed to calculate the correlations shown in Equation (5). Therefore, for the first mode, we used the analytical results in the case where the autocorrelation coefficient was large.…”

“…In addition, the sensitivity of the analysis process according to the mesh size and mode superposition assumption was investigated, which provided the theoretical background of the conversion model. Bigot et al [5] estimated the girder moment and stress on the hatch coaming corners in the numerical model of a real container ship-Magellan-through the conversion model employing structural response on the regular wave as the mode basis. They presented that the most accurate estimates are obtained when using the regular wave response as the modal basis among various types of hull structure responses.…”

“…On the other hand, when the structural responses on regular waves are used as a modal basis, there is no eigenvalue problem to identify them, thus the eigen mode selection criterion must be newly defined. Therefore, Bigot et al [6] proposed an iterative mode selection process based on the orthogonality between the hull structural responses.…”