Computational Mechanics Australia Pty Ltd
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QUAD-PLATE
Semi-Submersible Mobile Offshore Drilling Unit (MODU) of Catamaran Type.
MODUs are used for offshore oil prospecting and production at depths up to 200 meters.

As an example, consider a MODU structure consisting of two pontoons, eight stabilizing columns, and a top platform. The platform length and width are 108 and 67.4 meters correspondingly. Each column is 27.3 meters in height. There are four cylindrical columns of 5.8 meters in diameter and four cylindrical columns of 7.9 meters in diameter. The pontoons' length and width are 92.5 and 13 meters, correspondingly. The pontoons' height is 7.2 meters.
Structural model of MODU (undeformed)
A derrick of 27.3 meters in height is located at the platform center.

The columns, the platform and the pontoons are connected by horizontal and diagonal bracing beams. The top platform is stiffened by beams as well.

The pontoons are divided by vertical plates into compartments that are partially filled with water ballast (water height in pontoons is 4.75 meters as measured from the pontoons' bottom). The pontoons are completely submerged in water.

The stabilizing columns are stiffened by horizontal plates. The columns are partially submerged in water; they are empty inside (i.e. no added ballast). Therefore, the pontoons and the submerged parts of the columns bear the action of hydrostatic forces.

In order to make the numerical modeling as accurate as possible, parts of the stabilizing columns located above the water surface, as well as the derrick beams and the bracing beams have been subjected to the wind action. The wind speed was assumed to be 30.5 meters per second. Further numerical experiments indicated that the influence of such wind on the catamaran overall strenth was negligible and could be ignored.

The top platform is also subjected to equally distributed operating load of 2 kN per square meter.
It is assumed that the structure is made of steel plates and beams. For modelling purposes, plates' thickness is taken to be 5 cm for the catamaran pontoons and columns, and 5 cm for the top platform.

The MODU structure is anchored to the seabed.

Structural analysis of MODU included numerical evaluation of bending and shear stresses, location of stress concentrations, and calculation of nodal displacements that comprise the deformed state.

Elastic structural response of the MODU was analysed using the following loading conditions:

  • weight of the unit;
  • external water pressure load on the submerged parts of the structure;
  • internal water pressure on pontoons' hulls (including vertical internal plates);
  • wind pressure applied to parts of the structure exposed to wind load;
  • top platform operating load.

  • Deformed state of catamaran (deflections shown with 3 times magnification):
    Deformed Catamaran Structure
    For each quadrilateral finite element, the minimum and the maximum principal stresses, the stress intensity and the von Mises (equivalent) stress were calculated at the middle plane as well as at the two outer planes of the element.

    As expected, the largest equivalent stress values were obtained at the outer (external and internal) surfaces of the plate elements located along the bottom edges of the catamaran pontoons. Those plates and their edges are subjected to heavy hydrostatic load and represent the locations of stress concentrators. The bending moments acting at such locations are the largest. The deflections are also the largest for the vertical plates of the pontoons' hulls. Compared to that, the intensity of shear stresses observed at mid-planes of the pontoons' plates are insignificant.

    This model was developed in order to demonstrate capabilities of QUAD-PLATE-3D - our newest product, intended for Finite Element Analysis of spatial structures consisting of plates and beams. The original model (presented ot top of this page) consists of 70886 quadrilateral elements based on the Mindlin hypothesis. In order to verify the results we also ran the same problem with a more accurate mesh, this time containing 182553 quadrilateral elements; the von Mises stresses shown for that model. Generally, less accurate meshes appear to deliver somewhat underestimated stress values. This example serves as an illustration that models represented by very fine finite element meshes are necessary to provide high quality numerical results, corresponding to the real-life situations as close as possible.
    von Mises stresses in catamaran pontoon
    QUAD-PLATE-3D is available with complete source codes and the full commercial lisence allowing easy incorporation into your own applications. All our codes are written in ANSI C and will compile and run on all UNIX and Windows platforms without changes. They are also fully commented, allowing easy modification at user discretion.

    QUAD-PLATE-3D is available on no-royalties and no-annual-renewals basis: there is a one-off price for the unlimited commercial lisence.

    QUAD-PLATE-3D standard distribution kit includes:

    - fully-commented source codes of the program in ANSI C and C++.

    - the product's User Manual containing detailed description of input and output data structures and an example driver program;

    - a graphical application that allows the user to visualize the input and output data of QUAD-PLATE-3D.

    QUAD-PLATE-3D is completely developed by our company and contains no third party code.

    To learn more about the full range of our products please follow this link.

    We also invite you to contact us with any questions, preferably by e-mail on comecau@ozemail.com.au or comecau1@bigpond.net.au.