Main Types of Analysis

1. General

Four main types of analysis are available in RIFLEX:

  1. Static analyses.

  2. Static parameter variation analyses.

  3. Dynamic time domain analysis including eigenvalue analysis.

  4. 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 co-rotated finite element formulation applied in RIFLEX allows for unlimited translations and rotations in 3D-space.

The static analysis is based on a complete non-linear formulation. However, a pre-processor 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 three-dimensional.

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:

  1. Establishment of initial configurations based on catenary approximation.

  2. Iteration for equilibrium position by incremental reduction of unbalanced forces. (Newton-Raphson iteration) by application of nonlinear finite element analysis.

Step 1 is optional and may be replaced by a zero-load initial configuration.

Snap-through 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 position-keeping.

  • Clarify sensitivity to support vessel position, external force, or current variations.

For this purpose the following analyses are available:

  1. Stepwise increment supernode position in any direction.

  2. Stepwise increment of support vessel position.

  3. Stepwise increment of current velocity or direction.

  4. Stepwise increment force components.

Combinations of above basic cases are also possible.

3.1. Results

The same results as for the basic static analyses are available, but the main output consists of a set of key parameters to be presented as function of the varied parameter. E.g. tension or curvature at selected locations as function of position.

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:

  1. Eigenvalue analysis

  2. Harmonic (periodic) excitation

    • Forced displacements (harmonic) at one or more specified nodes

    • Regular waves

  3. 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 wind-turbine-specific coordinate systems are defined in order to present the results.

  • Shaft system \(\mathrm {(XS,YS,ZS)}\): Follows the non-rotating shaft element. Wind output, azimuth, and out-of-plane (OoP) tip deflection follow this system.

  • Rotor system \(\mathrm {(XR,YR,ZR)}\): Follows the rotating shaft element and 1st blade. The blade tip in-plane (IP) deflection follows this system.

shaft system 2
Figure 1. Rotor and shaft coordinate systems
shaft system 1
Figure 2. Out-of-plane deflection
in plane deflection
Figure 3. In-plane deflection

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:

  1. 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)

  2. Output from static parameter variation analysis:

    • Print/plot of selected response quantities during parameter variation

    • Plot of system geometries during parameter variation

  3. 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).