MOSES Conventions and Coordinates


  • General:

  • All axes are right handed. Directions for environments are the direction from which the environment comes. The body system is used for simulations. In most cases, the body system will be identical to the part system of the part which has the same name as the body. The axes of the body system are parallel to the global system when roll, yaw, and pitch are zero. The orientation of the body system defines the orientation of the body by three Euler angles, yaw, followed by a pitch, followed by a roll. An illustration of the global and part coordinate system along with a jacket and vessel body system during a launch is shown below.


  • Vessel Motion :

  • In the frequency domain, the motions are reported in the body system. The Surge motion is along the X, positive aft, Sway is along the Y axis,positive Starboard, and Heave is along the Z axis, positive Up. Roll is a rotation about X positive from Y toward Z (i.e. positive Roll is Starboard up). Pitch is a rotation about Y positive from Z to X (i.e. positive Pitch is Stern down). Yaw is a rotation about Z positive from X to Y (i.e. positive is Bow to Port or Stern to Starboard).


  • Motion Phases:

  • RAO phases are relative to the wave elevation at the point being reported. Clearly the phase relative to a point on the body depends upon the location of the vessel origin. Normally its location is that shown above. In any event, there is an additional phase shift due to spatial separation of the point of interest and the origin.

    The Wave Elevation, eta, is given by

       eta  = a*cos(w*t + k*x*cos(beta) + k*y*sin(beta))
    
    where a is the wave amplitude, w the encounter frequency, k is the wave number, x and y are the global coordinates of the point of interest, and beta is the wave heading angle and shown above. The heading is the angle from which the sea comes, measured relative to the X axis; i.e. beta equal 180 corresponds to a head sea, beta equal 90 corresponds to a sea striking the Starboard beam.

    The resulting Vessel Response is then given by

       r   = R*cos(w*t + phi)
       RAO = R/a
    
    where phi is the phase.


  • Structural Elements:

  • The element system for a beam is used in defining the section of the beam, local offsets, releases, and k factors. It is also the system in which loads and stresses will be reported. The origin of the element system is located at the beginning end of the beam, and the beam X axis lies along the axis of the beam and is positive from the first end to the second end. The remainder of the element system depends upon several things. First, if one specifies the -REFN option, then the beam Z axis (or "weak axis") points toward *REFNOD.

    If the -REFN option is specified, then the beam Y axis is defined as the vector cross product of the vector from the beginning of the beam to *REFNOD with the beam local X axis. The beam Z axis is then given by the cross product of the beam X axis with the beam Y axis.

    If -REFN is not specified, then the local axes are defined based on the -STGAXIS option of a &MODEL_DEF command. This defines two vectors: SAV1 and SAV2 which define local Y and Z as follows:

    • If the beam X axis is not parallel to the SAV1 vector, then the beam Y axis will be defined by the cross product of the SAV1 vector and the beam X axis.
    • If the beam X axis is parallel to the SAV1 vector, then the beam Y axis is determined by the cross product of the SAV2 vector with the local X axis.
    In either case, the local Z axis is obtained from a cross product of the local X and Y axes. Thus, the SAV1 vector serves the same purpose as a reference node - defining the direction of the local z axis or weak axis. The choice of values defining the SAV vectors should be made based on the manner in which the model is defined. If one wants the strong axis of beams to be "horizontal", the SAV1 vector should be the vector defining "vertical" in the part system. In other words, if Z is the part "vertical" then SAV1 would be 0, 0, 1. Alternately if Y is the part "vertical" then SAV1 would be 0, 1, 0. In either case, SAV2 simply handles the special case and can be chosen to either suit ones fancy or to conform to some existing practice.

    After the local system has been defined, it can be rotated about the local X axis with the -CA option. Here, CHANG is the beam chord angle (degrees). The rotation of the system is about the beam x axis, positive towards the beam negative Y axis (right hand rule). The relationship of the local coordinate system is shown;


  • Joint coordinate system:

  • When discussing tubular joints, the joint coordinate system is used. This system is defined for each brace in a joint as follows:

    Let

    • e be a unit vector along the brace X axis acting from the joint toward the other end of the brace and

    • c be a unit vector from the chord "left joint" to the joint

    then e is the force direction and the directions for inplane (mi) and out of plane bending (mo) are given by:

    • mi = (exc) / ||exc||

    • mo = (exmi)/ ||exmi||

    When doing fatigue of a joint, the CDRs are computed at eight points shown below.