Main Types of Analysis
1. General
Four main types of analysis are available in RIFLEX
:

Static analyses.

Static parameter variation analyses.

Dynamic time domain analysis including eigenvalue analysis.

Frequency domain analysis.
The method of analysis is based on finite element technique which has
proved to be a powerful tool for several applications. The corotated
finite element formulation applied in RIFLEX
allows for unlimited
translations and rotations in 3Dspace.
The static analysis is based on a complete nonlinear formulation. However, a preprocessor based on catenary theory is also implemented. The reason for this is to reduce computing time by giving the nonlinear iteration a good starting point, but also to analyse simple problems without use of the finite element method.
Time domain analysis is based on step by step numerical integration of the dynamic equilibrium equations. It is possible to apply a complete nonlinear method based on the incremental dynamic equilibrium equations, or alternatively, a linearized approach by linearization of mass, damping and stiffness matrices at the static equilibrium position. Nonlinear hydrodynamic loading is, however, included in the linearized time domain analysis.
The frequency domain analysis is based on the linearized dynamic equilibrium equation at static equilibrium position by application of stochastic linearization of the hydrodynamic loading.
All analyses are threedimensional.
The mathematical models are described in detail in the Theory Manual.
2. Static Analysis
This is the elementary mode of analysis and is used for establishing pipe configuration for a specified set of conditions.
The computations include:

Establishment of initial configurations based on catenary approximation.

Iteration for equilibrium position by incremental reduction of unbalanced forces. (NewtonRaphson iteration) by application of nonlinear finite element analysis.
Step 1 is optional and may be replaced by a zeroload initial configuration.
Snapthrough behaviour and multiple equilibrium configurations can be discovered by incremental static analysis from different initial positions. The program will be able to discover the appearance of kinks. However, a detailed study of kinks including contact forces between pipe elements is not included in the analysis.
Basic results are:

Nodal point coordinates

Curvature at nodal points

Axial force

Bending moment

Shear force  Torsion
The bending moments and the torsion moment are calculated about the area center and the shear center, respectively. Note that all results refer to the element coordinate system. The results are available as print (tables), and stored on file for post processing and graphic presentation.
3. Static Parameter Variation Analysis
The purpose of these analyses is to study the influence of varying key parameters in the system.
Key problems:

Establish static stiffness characteristics in order to specify support vessel requirements with regard to positionkeeping.

Clarify sensitivity to support vessel position, external force, or current variations.
For this purpose the following analyses are available:

Stepwise increment supernode position in any direction.

Stepwise increment of support vessel position.

Stepwise increment of current velocity or direction.

Stepwise increment force components.
Combinations of above basic cases are also possible.
4. Time Domain Dynamic Response Analysis
The purpose of these analyses is to study the influence of support vessel motions as well as of direct wave induced loads on the system.
A static analysis to define equilibrium condition is assumed to be carried out before starting a dynamic analysis. The last step of a parameter variation analysis can also be used as starting point for a dynamic analysis.
The following types of dynamic analyses are included:

Eigenvalue analysis

Harmonic (periodic) excitation

Forced displacements (harmonic) at one or more specified nodes

Regular waves


Irregular excitation

Stochastic, stationary excitation due to support vessel motions and irregular waves

Transient excitation. Special options available to simulate release or rupture, slug flow, time dependent current and external force variations

The mathematical models used in these analyses are described in the Theory Manual.
4.1. Results
The basic results from the eigenvalue analysis will be the system’s eigenfrequencies and eigenvectors. The basic result format from the dynamic excitation analysis will be as time series of a selected, limited number of response parameters:

Nodal point coordinates

Axial force

Shear force

Curvature

Bending moment

Torsion
The bending moments and the torsion moment are calculated about the area center and the shear center, respectively. Note that all results refer to the element coordinate system. The parameters may be given as total values or as difference from static equilibrium condition. In addition, the total system configuration may be stored for a limited number of time steps.
4.1.1. Wind Turbine Results
An additional output file is created for analyses which include a wind turbine. A columnwise description of the outputs is given in the witurb key file. Several windturbinespecific coordinate systems are defined in order to present the results.

Shaft system \(\mathrm {(XS,YS,ZS)}\): Follows the nonrotating shaft element. Wind output, azimuth, and outofplane (OoP) tip deflection follow this system.

Rotor system \(\mathrm {(XR,YR,ZR)}\): Follows the rotating shaft element and 1st blade. The blade tip inplane (IP) deflection follows this system.
5. Result Post Processing and Graphic Presentation
Results from static and dynamic analyses are stored on file for subsequent post processing and graphic presentation. An overview of main types of output is given in the following:

Output from static analysis:

2D and 3D plot of system geometry

2D plot of projected line geometries

Plot of force variation along lines

Print of forces, coordinates and element projection angles, optionally element by element, segment by segment or line by line (direct output from static analysis)

Calculation/graphic presentation of pipe wall force (i.e. axial force including hydrostatic pressure)


Output from static parameter variation analysis:

Print/plot of selected response quantities during parameter variation

Plot of system geometries during parameter variation


Output from dynamic time domain analysis:

Computation of time series derived from basic response quantities

calculation of curvature from nodal coordinates

calculation of support forces

wall force calculation (e.g. axial force including effects from internal and external hydrostatic pressure)

element angle calculation (e.g. angle between elements, vessel and element and global axis and elements)

calculation of distance time series (e.g. clearance between lines, vessel and lines, global axis and lines)


calculation of velocities and accelerations from wave and vessel motion time series

Plot/print of response time series

Statistical time series analysis (e.g. estimation of spectral densities, probabilistic distribution for maxima/minima, sample moments, spectral moment, etc.)

Animation of the dynamic behaviour of the complete system including support vessel and exciting waves

Graphic presentation of vessel motion transfer functions

Envelope curves for displacements, curvature and forces showing static value, mean value and response range

In addition to the post processing features available in RIFLEX
it is
also possible to export results via standardized file formats to general
purpose statistical analysis programs (e.g. STARTIMES
) and a advanced
graphical presentation/animation tools (e.g. GLVIEW
).