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A program for designing floating marinas, breakwaters and bridges
Dynamic analysis of long floating marine structures
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INTRODUCTION
Floating marinas, floating breakwaters and floating bridges are long structures made up of pontoons which are connected between them rigidly or with flexible connectors, and they are anchored at the bottom of the sea with mooring lines. They are usually placed in protected water regions. The waves in these regions are short crested waves. The dynamic analysis of long floating structures in short crested waves must take into account the special characteristics of the short crested wave loading, and the frequency depended load correlation along the structure. 

The structural modelling using finite element methods does not present any difficulties. However the part of the analysis which presents special problems is the modelling of the loading in a short-crested sea. General purpose finite element programs do not provide methods for calculating the loading in a stochastic, short crested sea, and additional routines should be included in order to do the job. In conclusion the use of general purpose finite element programs is - time consuming, uneconomic, and susceptible to errors.
The program cgFLOAT has been developed especially for long floating structures in short crested sea loading. The dynamic response can be calculated via a frequency or time domain analysis. Theories and methods for hydrodynamic loading, short-crested waves, directional wave spectra, sea state simulation, and stochastic dynamics are included in the calculation routines. The computer code has been optimized taking into account the special characteristics of the structure and the loading. For the response calculation a Monte-Carlo simulation is used. This method is considered to be more advantageous over the usual frequency domain analysis, which is the only alternative, because it reduces the computational cost considerably and can be used for frequency and time domain analysis. It is based in simulating sets of nodal load series and calculates the structural response by deterministic dynamic analysis in frequency or time domain. The expected response values are obtained in the end by calculating the ensemble statistics between the simulated cases. The basis for computing the sets of nodal load series is the wave coherence along the structure, which is obtained from the directional wave spectrum.

General Data

Load Correlation

Pontoons

Connectors

PROGRAM CAPABILITIES

The program combines fluid, structural, and stochastic process theories in one program. Thus the response computation of long floating structure is reduced to a routine analysis.
The following aspects have been implemented in the program:

  • Modelling of continuous structures and structures with flexible connectors between the pontoons.
  • Eigenvalue solution
  • Frequency domain analysis
  • Time domain analysis
  • Boat wake analysis
  • Short-crested waves defined by a wave spectrum and wave coherence.
  • Monte-Carlo simulation of the wave loading.
  • Statistical evaluation of the results for the simulated response.
  • Frequency dependent hydrodynamic coefficients.
  • Metric or Anglo-American units can be specified.
  • Graphical output, for mode shapes and response values along the structure.
INPUT

Structural input data are the characteristics of the pontoons, length, width, height, moments of inertia, shear areas, elasticity modulus, and elastic characteristics of moorings. In case of flexible connectors the characteristics of the connectors as bending and shear stiffnesses must be described. The geometry of the structure and the nodal points are automatically generated by the program after the basic pontoon and connector properties are supplied. In case (as in most cases) of similar pontoons the characteristics of one pontoon is necessary and the number of pontoons.


For pontoons of rectangular cross section the hydrodynamic coefficients (added mass, added dumping and hydrodynamic forces) for various frequencies are automatically evaluated by the program. For other cross sections you may input the hydrodynamic coefficients for certain wave frequencies and the program interpolates between them for the necessary values in the response calculations.

Hydrodynamic coefficients

Wave Data

The short-crested sea state is specified by the wave spectrum and the wave coherence. Typical wave spectra like Pierson-Moskowitz, JONSW AP, are computed from their parameters by the program. Other kinds of spectra can be used by inputting their f and S(f) values. Wave time series are simulated from the spectra, via various methods, by the program. The wave correlation is handled by specifying the coefficients of an exponentially decayed wave coherence, or by specifying the nodal load correlation directly.

In the case of boat wake analysis the speed and characteristics of the boat wake are specified.

For the frequency domain analysis, the frequencies for the computation of the frequency response function can be specified or they are computed by the program after their number is specified. For the time domain analysis, participating modes, integration method and parameters, accuracy, time interval and time length are specified. The user specifies the various analysis paths, units, simulation methods and number, and required printed or plotted output quantities. For all the cases if general parameters are not specified by the user, default values assigned by the program.
Mode Shapes
Mode shapes

Frequency response
Frequency response

Time domain response
Time domain response

OUTPUT

The results from the frequency or time domain analysis is a large number of values. To be useful they are printed in graphs.
A typical output of the program contains:

  • A printout with all the information of the structure, the wave field, assumptions and parameters used.
  • Printout of the eigenvalues
  • Graphs of mode shapes
  • Graphs of the structure response to unit amplitude short crested waves of various frequencies.
  • Graphs of ensemble maximum, mean, and standard deviation values, between the simulated responses, for displacements, bending moments, and shearing force, along the structure for the three directions of motion (sway, heave and roll).
  • The computations are for frequency domain analysis and for time domain analysis.


    From the displacements in sway motion the mooring forces can be computed.
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Publications

13) Georgiadis, C. "CGFLOAT A Computer Program for the Dynamic Analysis of Floating Bridges and Breakwaters ", journal of Advances in Engineering Software, Vol. 5, No. 4, October 1983, CML Publication Southampton, England, pp. 215-220.

16) Georgiadis, C. "Time and Frequency Domain Analysis of Marine Structures in Short-Crested sea by Simulating Appropriate Nodal Loads ", Offshore Mechanics and Arctic Engineering, proceedings of American Society of Mechanical Engineers ASME book I00171, Vol.1, 1984, New York, pp. 177-183.

17) Georgiadis, C. "Modelling Boat Wake Loading on Long Floating Structures ", Journal of computers and structures, Vol.18,No. 4, 1984, Pergamon Press, London, pp. 575-581.
19) Georgiadis, C. "Finite Element Modeling of the Response of Long Floating Structures Under Harmonic Excitation ", Transactions of ASME, Journal of Energy Resources Technology, Vol. 107, March 1985, pp. 48-53.

GENERAL REMARKS
The program is well documented. In addition to the user manual, references 1-6 explain in detail the theoretical aspects behind the computational and simulation methods as well as the concept of hydrodynamic forces and short-crested waves. Detailed examples are included to show the correct use of the program.

The accuracy of the program has been checked with in situ measured response values at the Hood-Canal floating bridge and other floating breakwaters in the Puget Sound area.(1)

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Revised: Απριλίου 14, 2016.  

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