SIMO Modeling Tutorial 1. Applications 1.1. Various vessels and structures 1.1.1. General comments Standard modelling of large bodies is based on hydrodynamic data calculated by diffraction theory programs, such as WAMIT or WADAM. A 6 DOF - time domain body should be chosen if: Couplings to other bodies or to globally fixed points are expected to have any influence on first order wave induced motion. Viscous damping has not been included in the analysis by the diffraction theory program. Hydrodynamic forces for the body is modelled as a sum of distributed hydrodynamic forces. If not, the less time consuming analysis for a 6 DOF - separated analysis body can be chosen. 1.1.2. Ships It is often necessary to add roll damping due to bilge keels and flume tanks to the hydrodynamic damping calculated from diffraction theory (linear damping). 1.1.3. Semisubmersibles Viscous damping in heave roll and pitch can be significant. Due to the small waterplane area, the weight of catenary mooring lines will pull the vessel down to a larger draught. The static set-down can be compensated by a constant upward specified force model element in the vessel’s centre of gravity. Other comments as for ships. 1.1.4. TensionLeg Platforms Tethers are preferably modelled as finite element lines, with drag forces. Simplified modelling with simple spring elements (fixed elongation coupling) without drag forces is not recommended on deep water. The vertical reference point Zref for the hydrostatic stiffness model element, should be adjusted to give correct tether tension at the design water line, Z0. The unstretched length of the tethers, L0, should be found in order to adjust the tether lengths from the attachment point, Za, to the water depth (i.e. the seabed foundation strucuture): \[ F=k_{33}(Z_{ref}-Z_0)\] \[ L_0=\frac{Z_a-D-F}{k_t}\] \[ L_0=\frac{(Z_a-D)}{1+\frac{F}{EA}}\] 1.1.5. Spar buoys The hydrostatic stiffness for angular (roll and pitch) motion and the coupling to heave will be non-linear, which will not be expressed correctly by these programs. A way to improve the model is to represent the buoyancy by a vertical slender element, which will give correct buoyancy effects (vertical force and restoring moment). Avoid doubling of force components: If wave forces from a diffraction theory program are used, no wave forces should be calculated for the slender element. The hydrostatic stiffness for heave motion (from the diffraction theory program) should be set to zero if a slender element is introduced to calculate the buoyancy effects. For roll and pitch, a stiffness representing the local moment of inertia of the waterplane minus internal free surface effects may be maintained in the hydrostatic stiffness data. 1.1.6. Articulated towers Hydrodynamic force coefficients should be calculated by diffraction theory programs, with the actual stiffness matrix (expressing the hinge at the seabed), and with the origin at the hinge point. In case high frequency ringing forces are focused, the quadratic transfer function (QTF) for sum frequencies should be requested. In SIMO the tower can be modelled in two alternative ways: As a rigid body with realistic mass and gyration radii, fixed at the seabed (lower end) by means of 3 stiff springs (fixed elongation couplings). Ringing response can be calculated if the vertical stiffness is correct. As a body with a huge mass and realistic gyration radii about lower end. The ringing forces can be calculated without disturbing influence from structure elasticity, in order to serve as input to other types of structural analysis. In both cases, the non-linear hydrostatic stiffness can be modelled by slender elements or fixed body elements, similar to spar buoys. 1.1.7. Gravity base structures Hydrodynamic force coefficients should be calculated by diffraction theory programs. If vertical vibration caused by higher order wave forces is thought to cause fatigue problems, ringing forces should be focused. Sum frequency QTFs should then be calculated by the diffraction theory program and given as input to SIMO, and the option to calculate ringing forces should be activated. 1.1.8. Jackets There are mainly two cases where a SIMO analysis of a jacket is relevant: Jacket installation or removal Installation of the superstructure Feasible models are summarised here: Jacket structure Mudmats / soil interaction Comments 6 DOF body Twin-crane lift 6 DOF body + slender elements Bumpers, docking cones Support springs 3 DOF body with soil forces Coupled to main structure Prescribed body (couplings incl. jacket stiffness) 6 DOF body Soil springs or 3 DOF body with soil forces Coupled to main structure 1.1.9. Jackups The installation phase may be critical for a jacket, possibly with large lateral forces on the legs at touchdown on the seabed due to roll/pitch motion of the (still floating) platform. A relevant SIMO model: Floating platform body: 6 DOF body (hydrodynamic data from diffraction theory program) Legs: Slender elements Mudmat units: 3 DOF body with small body hydrodynamic data and depth dependent soil data, coupled to the main body with 3 springs (fixed elongation couplings) representing vertical and horizontal leg stiffness. If the jack-up operation shall be analysed, the model must be changed significantly. It must be possible to move the legs downwards and lifting the main hull out of water must be included: Floating platform body: 6 DOF body, with several slender elements modelling position-dependent buoyancy and wave forces. Legs: 6 DOF bodies with slender elements, coupled to the main body by 4 stiff horizontal springs (fixed elongation couplings), preventing transverse and angular motion and a vertical spring (fixed elongation coupling) from the top of each leg to the main body, with a winch function included. Mudmat units: 3 DOF bodies (as in first model except for the stiffness of the fixed elongation couplings, which here act together with the springs (fixed elongation couplings) between the leg and the main body. The combined stiffness must be adjusted to the real leg stiffness). The gravity force should be included for all the bodies/units. The calculated wave forces on the main body will not be as accurate as the wave forces calculated by standard diffraction theory program. 1.1.10. Subsea structure with mudmats Hydrodynamic data for various subsea structures are not easily found by standard diffraction theory programs. Often the structure can be simplified by division into structural parts that each can be considered as a small-body object or a slender element attracting hydrodynamic forces. For splash zone analysis, depth dependent coefficients can be defined for each part. As the structure is a 6 DOF body, the sub-structures can be modelled in two methods: 3 DOF bodies attached to the main body, each by 3 springs (fixed elongation couplings) (in X[line-through],Y, and Z-direction). Slender elements or concentrated force elements defined as a part of the main body. Soil forces can only be modelled for 3 DOF bodies. If penetration into the soil shall be included in the analysis, it is advised to model the foundation buckets as 3 DOF bodies with position dependent hydrodynamic data and soil forces, and to express the hydrodynamic forces on the remaining structure by slender elements. 1.1.11. Pipes Distributed hydrodynamic forces on a pipe can be accounted for by defining an imaginary main body, containing one or more slender elements, which are subject to dynamic forces. This model assumes that the pipe is rigid. Redistribution of load due to pipe elasticity is thus not included. Any segment decomposition can be modelled. Depth-dependent hydrodynamic coefficients can be used to analyse splash zone crossing of horizontal pipe segments. Example: Spool piece Here is described an L-shaped spool piece with segment lengths 20m and 12m and diameter 0.5m. The coordinates indicated in the figure are local coordinates of the imaginary body introduced for definition of the spool piece. image::e_spool.gif[image] Simplified depth dependent coefficients are given for water surface crossing. 1.2. Positioned or coupled vessels 1.2.1. Introduction A DP system can in its simple form be regarded as a dampened spring system. If either the resonance period or the equivalent stiffness of the system, \(K_{eq}\), is known for surge, sway and yaw motion, a simplified model can be established, in two alternative ways: Stiffness and damping matrix Insert realistic DP stiffness values for surge \(k_{11}\), sway \(k_{22}\) and yaw \(k_{66}\) motion in the existing hydrostatic stiffness editor (or create a new hydrostatic stiffness model element on the body). Insert realistic DP damping values for the same degrees of freedom in the linear damping editor (or create a new linear damping model element on the body), assuming that the damping from the DP system is 70 % of critical damping, \(C_u=0.7(2\sqrt{k_{ii}M_{ii}})\space | \space i=1,2,6\) The mass terms are inclusive the added mass. Horizontal springs (fixed elongation couplings) Arrange a number of (e.g. n = 4) linear stiffness elements as symmetrically as possible: Equal angular spacing Equal distance to the vessel’s centre of gravity Select spring stiffness The required stiffness in each line is \(K_L = 2*K_{eq}/n\) for surge and sway motion Tangential component for yaw motion The easiest way of obtaining the required yaw stiffness, is to arrange the springs with tangential component for yaw motion. Surge and sway stiffness: \(K_{11}=K_{22}=\frac{n}{2}K_{L}\) Yaw stiffness: \(K_{66}=\frac{n}{2}K_{L} r^{2}\) Pre-tensioned springs Alternatively, if the spring directions go through the vessel centre the springs should be pre-tensioned. Surge and sway stiffness: \(K_{11}=K_{22}=\frac{n}{2}K_{L}\) Yaw stiffness: \(K_{66}=nF\frac{r^2}{L}\) 1.2.2. Two ships lying side-by-side This is relevant for load transfer operations. The most accurate method is to include full hydrodynamic coupling as well as mechanical coupling between the two vessels. The effect of hydrodynamic coupling can be found by WAMIT or similar programs, in which the hull geometry of the two vessels must be modelled completely, as there will be no symmetry in the hydrodynamic forces. When the results from the hydrodynamic calculations are read and converted to SIMO input, the data will be found in the Couplings/Hydrodynamic couplings folder. Both vessels must be defined as large body types. The calculated hydrodynamic data will be valid only for small deviations from the modelled relative position between the vessels. The mechanical coupling can be modelled by means of : Coupling fenders (fixed or roller fenders) Hawsers (spring and breast lines) modelled as fixed elongation couplings, which gives several possibilities to model non-linear stiffness, winch hysteresis etc. An accurate adjustment of the hawser lengths is required in order to ensure an even tension distribution between the hawsers. This can be done by iterative static analyses. Make sure that the coupling lines are arranged so that they prevent relative slowdrift motion, but that the hawser arrangement is elastic enough to allow first order wave induced motion. 1.2.3. A vessel alongside berth The most accurate method is to include the proximity of the quay and shallow water in the hydrodynamic analysis program (WAMIT or similar) The hull geometry must be modelled completely, as there will be no symmetry in the hydrodynamic forces. The input data groups read into SIMO will be the same as for a free-floating vessel. Notice that the calculated hydrodynamic data will be valid only for small deviations from the modelled water depth and distance between the vessel and the quay. The mooring can be modelled by means of: Berthing fenders (fixed or roller fenders) Hawsers (spring and breast lines) modelled as fixed force elongation, which gives several possibilities to model non-linear stiffness, winch hysteresis etc. A very accurate adjustment of the hawser lengths is required in order to ensure an even tension distribution between the hawsers. This can be done by iterative static analyses. Make sure that the coupling lines are arranged so that they can take the environmental forces and prevent slowdrift motion, but that the hawser arrangement is elastic enough to allow first order wave induced motion. 1.2.4. Offshore float-over mating Feasible models are summarised here: 1.3. Other simplified models 1.3.1. Forces on a fixed structure There may be a need to calculate the external forces on a rigid structure, either if the structure is fixed to land or the sea bed, or to control that a sensible model has been established, and that the calculated dynamic forces (neglecting any influence from the structure motion) are correct. There are mainly three ways of modelling a stationary body: by applying a high positioning stiffness by specifying an unphysically large body mass. A variant of the latter is a body with huge mass, but still allowing rotation by modelling an unmoveable body (prescribed body type) A summary of pros and cons for these methods is given here: Method Description Advantages Disadvantages Stiff springs Motion (in all degrees of freedom!) reduced by stiff positioning springs, or a specified stiffness matrix The body keeps its position, also when subject to a constant force The resonance periods must be significantly below the excitation periods, which requires very short simulation time step Huge mass and moments of inertia No positioning stiffness. Motion kept acceptably low by the large inertia No resonance periods, long time steps accepted, determined by the excitation period. Drift due to static load components Huge mass, realistic moment of inertia about one axis No positioning stiffness. Realistic angular motion about a selected fixed axis No resonance periods, long time steps accepted. Drift due to static load components Prescribed body type No body motion Forces are calculated for a truly fixed body The gravity force should not be included if a huge mass is specified for the body. If it is necessary to include a realistic gravity force, an additional mass (with corresponding gravity force) can be specified in one of the data groups: + * Time dependent volume mass * Time dependent point mass * Slender element * Fixed body element 1.4. Lifting operations 1.4.1. Crane and Lifting gear There are several alternative ways to model an object suspended in a liftwire system. Which model that should be selected, depends on the scope of the study and the over-all system configuration. An overview of modelling alternatives, and comments to suitable application and limitation are found here: Model Body type Lifting gear Typical application Comments Module: 6 DOF body Hook: 3 DOF body The hook is modelled as a separate body. Slings and hoist wire modeled individually, as simple wire connections from padeye points to hook and from hook to crane point Lift in air or in the wave zone, angular motion of the load and forces in individual slings focused. Hook mass significant for the dynamic behavior of the system. (hook mass not negligible compared to load mass) The most accurate model. Short, internal resonance periods require very short time steps in the integration. Module: 6 DOF body Slings and hoist wire modelled as a multiple wire connection, from padeye points via hook to crane point. The hook is modelled only as a branch point Lift in air or in the wave zone, angular motion of the load and forces in individual slings focused. Hook mass has little influence on the dynamic behaviour of the system The model is acceptably accurate in most cases. Short time steps normally required Module: 6 DOF body Simple wire coupling from crane top to sling branch point Individual sling forces not focused. Object at large water depth, below wave zone Simple model, extremely short time steps not required Module: 3 DOF body Simple wire connection from crane point to centre of gravity of the load Individual sling forces and angular object motion not focused. Object at large water depth, below wave zone Simplest model 1.4.2. Pendulum damping There are two possible ways of preventing excessive pendulum motion in air: Wires from the load to locked winches Wires from the load to winches working in constant tension mode, with a hysteretic dead band In particular for heavy loads, the first method require a high pretension to ensure that the wire will not experience slack and snatch loads due to vessel motion, and it is unpractical in combination with lowering or lifting. The second method is recommendable, because it adds damping to the system, thus reducing the resonance amplification at the natural pendulum period. A line from the crane base to the load is often used to add damping in radial direction. The crane operator often provides tangential damping, by slewing motion of the crane. In SIMO, however, the tangential damping must be provided by a modelled damping element. A suitable model is two orthogonal directed springs (fixed elongation couplings) with specified relation between distance, force and damping. In the example below, the two springs (fixed elongation couplings) are horizontal, one in X and one in Y direction. The tension in each line is 50 ± 10 kN. 1.4.3. Load positioning at landing Landing control with guidewires Guidewires are used for lateral position control during the final approach to the target position, e.g. prior to landing a module on a seabed structure. The tension at upper end is controlled either by a constant-tension winch or a cylinder compensator, both with hysteresis damping. The lateral stiffness of the guidewires (assuming small horizontal deflections) can be approximated by: \(K_{l}=\sum \frac{F_i}{L_i}\) All the guidewire sections (above and below the module) shall be included in the sum. Just before landing, the stiffness contribution from the guidewire sections above the module can be neglected. Landing control with guidewires can be modelled by use of positioning lines between the module and the guideposts arranged at the target area (fixed force elongation). The guidewires between the ship and the module can be modelled as general coupling lines (fixed elongation coupling). Example: Assume a module that shall be landed on 300 meters water depth. Horizontal position control at landing by means of two guidewires. Crane vessel position: (0, 0, 0) Crane top position: (10, 25, 30) Start position of module: (10, 25, \–290) Mass of module: 30 tonne Hoist wire diameter: 50 mm Guidewire tension: 30 ± 5 kN Notice also that the lower guideline attachment points and the landing support spring are adjusted so that the module lands before the line length become zero (as this may result in a division by zero error) 1.4.4. Load positioning with bumpers / cursors Bumpers or protection bars can be used in order to guide a module down to its specified position on a vessel or at a fixed point, and to protect existing equipment close to the landing area against impact loads from the module. Bumper elements can be modelled, and realistic positioning forces, inclusive impact loads, can be calculated. A closer description, with examples is found here. Precision landing with guideposts and docking cones Docking cones can be modelled for final positioning of a body onto the landing position, and for calculation of impact forces prior to landing. Positioning at a global position as well as final connection to another body can be modelled. A more detailed presentation, with examples is found here. 1.4.5. Heading control for a subsea module during installation Heading control can be obtained by using a wire from a dead-man load suspended from a second winch or crane. The wire can either be attached directly to the module, or to a bridle. A bridle arrangement increases the restoring moment and the moment stiffness against rotation, which is given by: \(M=F\frac{X^2}{L}\sin\alpha\) \(k\alpha=\frac{dM}{d\alpha}=F\frac{X^2}{L}\cos\alpha\approx F\frac{X^2}{L}\) where: F = wire tension L = wire length X = distance from center of gravity of the module, to the wire attachment point (on the module or at the bridle top point) α = rotation angle of the module (about vertical axis) The last approximation is for small angles. If a bridle arrangement is used, the expression is valid for a smaller than half the bridle angle (as larger angles will cause one of the bridle wires to go slack). There are three modelling alternatives for the heading control, depending on the focus of the analysis: If the focus of the analysis is on the dynamic tension in the liftwire only, a small linear yaw stiffness can be applied on the module, to prevent yaw drift due to numerical instability (change or create a new hydrostatic stiffness model element). A realistic heading control can be obtained by modelling the suspended dead-man load and a wire connection between this load and an imaginary point on the module, corresponding to the top point of the bridle (single wire coupling). This is accurate enough if no large yaw motions due to eccentric forces or moments are expected. If the heading control shall be studied more in detail, the wire from the dead-man load and the bridle should be modelled as accurate as possible (multiple wire coupling). A possible torque moment from the liftwire due to stretching can be included (edit or create a specified force model element), and a possible hydrodynamic yaw moment due to non-symmetric module geometry should be modelled as accurate as possible (edit or create slender elements). The final control of position before landing, including heading control, can be obtained by modeling bumpers and/or docking cones. These elements are described in separate sections. 1.5. Impulsive forces at lift-off and landing Impulsive forces are single events. In a situation with irregular wave excitation, a good statistical basis is needed for estimation of extreme impact forces to be expected. One method is to run a large number of simulations with calculation of impulsive forces, in order to acquire the statistics necessary to estimate extreme forces. This method is time consuming and may be unpractical. However, if the operation causes a series of impacts, the first impact is not necessarily the strongest. Several simulations should then be made in order to study the dynamic behaviour. Another method to estimate extreme forces at first impact is based on the assumption of high stiffness at the contact points, giving an impact duration much shorter than the predominant motion periods. Since the impact force is proportional to the relative velocity at impact, a stationary simulation without impact, with calculation of the relative velocity between the studied impacting members. The extreme force at first impact can then be derived from the estimated extreme relative velocity and the other parameters influencing the impact force. This can be done by use linear springs (fixed elongation couplings) to calculate the time history of the distance between the impacting bodies, and derive the relative velocity by post-processing the time series. Examples of arranged contact and measurement springs are given here: In the enclosed examples the input sequence for two simple, bi-linear springs are given: Simple, linear contact spring Body point MODULE_point7 is positioned at 10, 5, –3 (Ref. x and y close to MODULE position,z=–15m from MODULE, to avoid errors from x and y motion) Body point VESSEL_point5 is positioned at –30, 5, –5 Linear contact spring, combined with a distance measurement spring Body point MODULE_point6 is positioned at 10, 5, –3 on MODULE. (Ref. x and y close to MODULE position,z=–15m from contact point, to avoid errors from x and y motion) Body point VESSEL_point is positioned at –30, 5, –5. Compression, k=100000 kN/m if contact tension, k = 1 N/m if no contact Distance Measurement Spring Body point MODULE_point8 is positioned at origo of MODULE. Ref. x and z close to MODULE position,y=+60m from MODULE, to avoid errors from x and z motion Body point VESSEL_point6 is positioned at (x y z): 33 –50 20. The geometry of the above examples are shown in the below figure. Notice that the force depends on the distance between points. To avoid influence from relative motion in transverse direction, a spring length significantly longer than the actual distance is modelled. The model will be accurate for moderate angular motions. Arrange overlength on the unit subject to the smallest angular motions. Make sure that the initial relative location of the module and the vessel is correct, in the global coordinate system (see the body editor). In this example, if the initial vertical distance is Δ = 2 m: X (module) = X (vessel) - 30 - 10 = X (vessel) - 40 Y (module) = Y (vessel) + 5 - 5 = Y (vessel) Z (module) = Z (vessel) + 10 + 3 + 2 = Z (vessel) + 15 2. Connection and contact element models 2.1. Introduction Some of the connection models described in this chapter may be used for global body positioning or coupling between bodies (under different notations), while others can be applied only for one of the purposes. Models and available options are described in the next sections. 2.2. Distance calculations Notice that the position of all bodies are given in global coordinates, while the attachment points for coupling elements are given in local coordinates for each body In cases where stiff coupling elements are used between bodies, it is very easy to get a mismatch between the distance between the connection In cases where stiff coupling elements are used between bodies, it is very easy to get a mismatch between the distance between the connection points and the force - length relation of the coupling element. An error can easily result in an initial coupling force that is far from the intended value, and even unphysically large. The first symptom of this type of error is often serious problems in the calculation of static equilibrium. 2.3. Springs with specified relation between length and force The available model elements for positioning of a body and for coupling between bodies are: Positioning: Fixed force elongation Coupling: Fixed elongation coupling A linear or non-linear relation between length and elastic force and damping can be specified. 2.4. Simple wire coupling This is a simplified bi-linear (zero compression) wire model without mass and drag. Notice: In cases were a small mass (e.g. a spreader bar) is inserted between a vessel and a module subject to high dynamic loads, the stiffness proportional damping (Damping) can result in an unphysical load distribution due to numerical reasons. If strange results appear, reduce damping. Normal values are 1-2% of Ea (wire cross section stiffness). 2.5. Multiple wire coupling This feature can be used to model a branched system, e.g. crane wire and slings, without including the hook in the branch point. Use line damping only in one of the lines to avoid numerical convergence errors. 2.6. Lift line coupling This model is the deep-water alternative to the Simple Wire Coupling. Mass, buoyancy, drag and inertia forces are included. A simplified dynamic analysis method is used, assuming that the line forms a straight line. Numerical convergence problems may occur if this model is used for short lines (e.g. splash zone analysis and for lift in air). 2.7. Docking cone The docking cone model is one of the options available in the general spring models. The model can be used both as a global positioning element and a coupling element between bodies: Body positioning: Docking Cone Positioning Coupling element: Docking Cone Application examples: Example 1 2 fixed docking pins at the sea floor. Precision installation of a concrete platform, over pre-drilled wells. Cone and pin modelled oppositely. This example is taken from an analysis where a gravity-based structure should be positioned over pre-drilled wells. The required position accuracy was ensured by arranging two docking cones underneath the GBS and two docking piles on the seabed, at each side of the wellhead. When the docking cone model is used for global positioning, it is assumed that the cone is located at global coordinates and the piles is fixed to the body. The modelling is thus opposite to the real case, which is not important for the analysis. Water depth: 330 m Entry radius: 1.0 m Radius of parallel section (difference between pile and cylinder radius): 0.25 m Length of piles (i.e. cylinders): 8 m / 6 m image::platf2.gif[image] Example 2 4 coupling cones. Precision landing of a module on the deck of an FPSO. To be combined with 4 vertical contact springs. In this example it is assumed that the docking cylinders are 0.3 m high and are located 0.5 m inside the sides of the module. Assumed opening diameter equal to 0.3 m and a parallel section of 0.1 m below the cone. While 4 vertical support springs should be added, two of the docking cones may be omitted if angular levelling is under control, so that the corners land (close to) simultaneously. image::Conex1.gif[image] Docking cone used as hinge 2 horizontal coupling cones. Rotation shaft model for a level arm structure. To be combined with an axial spring. In this example a transverse arm attached to the deck of a vessel is modelled. Two docking cones model the bearings of the rotation axis. Notice that this model will easily give very short resonance periods, which numerically requires short time steps. Transverse oscillations should be filtered away, by post-processing. Include an axially directed spring to prevent axial sliding. image::Conex2.gif[image] image::e_hinge.gif[image] Model characteristics and limitations: The model will give a contact force when a point (representing the tip of a docking pin) enters into a cylinder and comes in contact with the internal cylinder walls. It will be detected if the entry into the cylinder opening is successful or not. Until a successful entry is made, the model will give zero forces. Rotation symmetric stiffness around the longitudinal axis is assumed. The contact force acts normal to the internal surface of the cylinder (which can be conical). The transverse relative motion between the two will be limited by the radial clearing at the respective longitudinal distance, DZ, see Figure 3. Outside this limit, structural stiffness will give a restoring force directed towards the centre. Friction forces are neglected. Any contact forces in longitudinal direction may be modelled by an additional spring. image::Cone.png[image] Figure 3: Docking cone - Relation between radial and contact force 2.8. Fender The fender model can be used both as a positioning element and as a coupling element, and expresses the contact force between a fender (point or cylinder) and a plane. The input data groups have different headings: Positioning element Point berthing fender Roller berthing fender Coupling element Point fender Roller fender The following characterises the fender model: Zero contact force for distances larger than a specified value Compression force normal to the plane calculated from a specified deformation - force relation In-plane friction proportional to the normal force (static and dynamic friction may be different). Shear stiffness and deformation of the fender included. The plane can have any position and orientation Fender examples The model is used for various applications, some of which are mentioned below. Notice that the fender plane of a berthing fender can also be the quay, which can be useful for modelling the contact between the quay and a curved ship’s side (by use of several fenders). Fixed berthing fender at ship’s side Ship alongside quay. Fixed fender attached to quay. Fender plane is ship’s side. To be combined with hawsers. Ship is laying alongside quay. Two fixed fenders are attached to quay, sliding on the ship’s side, which is the fender plane. Roller berthing fender at ship’s side Ship alongside quay. Roller fender with horizontal rotation axis attached to quay. Fender plane is ship’s side. No friction (and less wear) due to roll and heave motion. Ship is laying alongside quay. Two roller fenders with horizontal roller axis are attached to the quay. The ship’s side is the fender plane. Fender points: #1: ( 15, –1, 3 ) #2: (–15, –1, 3 ) Ship breadth: 20 m Global ship position: ( 0, –11, 0 ) Roller fenders between ships Ships side-by-side. Roller fender with horizontal axis attached to ship 1. Fender plane is side of ship 2. No friction due to vertical relative motion. Two ships are laying side-by-side. Two roller fenders are attached to SHIP1, sliding on the side of SHIP2, which is the fender plane. Global ship positions: Ship 2: (0, 15, 0) Ship 2: (0, –17, 0) Ship dimensions (both), L x B = 140 x 30 m Spherical fender pushes on ship’s stern Tug bow modelled as a spherical fender. Fender plane is ship’s stern. Friction only when fender slides, not when it rolls on the plane The bow of a tug pushing on the stern of a ship is modelled as a spherical fender. The spherical fender can also be modelled as a roller fender. In this case, if a roller fender with horizontal axis is specified, no vertical friction component will act in the contact between the fender and the sphere. Fixed fenders on module placed on a ship’s deck 4 equivalent fender elements are used as supports. Friction prevents module from sliding. Friction formulation simpler than using horizontal springs to avoid sliding, before lift-off. The friction included in the fender model makes it useful for modelling seafastening, i.e. take the vertical load and prevent the module from sliding along the deck. Two applications are particularly relevant, where a module is provisionally located on the deck of a transportation vessel: 1) before lift-off by a crane vessel 2) before the load transfer of a float-over deck mating operation Alternative models (bumpers or docking cones combined with vertical springs) can also be used, but they require an accurate initial position between the two bodies to avoid numerical troubles during the equilibrium calculation. Fixed berthing fender used for measuring distance from ship’s side to obstacle Fender characteristics giving a contact force 1.0 N per m distance. Can also be combined with realistic fender characteristics at contact In this example a berthing fender is used for measuring distance between the ship’s side and an earth-fixed obstacle. This can be accomplished in two ways: 1) by defining an imaginary ship side far enough away from the side to cover the range of distances that can be expected during the analysis 2) by defining a spherical fender with (similarly) large enough radius. A very low contact force is defined inside the imaginary ship’s side, corresponding to a spring stiffness of 1.0 N/m. The calculated force time series can be understood as distances, in the post-processor analysis. The distance between a detail on one body and a plane on another will be similar, with use of fender coupling elements. One relevant case is a float-over mating operation, where the vertical distance between the superstructure and its former supports on the deck of the installation vessel is important after the superstructure has been installed and the installation vessel shall move out. 2.9. Bumper The bumper element model is used to model contact force between a body and a globally fixed cursor or bumper, or contact forces between bodies: Positioning element: Bumper Data Coupling element: Bumper or Bumper Group These model elements are particularly useful in the analysis of offshore installation operations, where deflectors / bumper bars are used to guide a module to its correct position and to protect existing equipment from impact damages. The bumper element model defines a pair of lines (i.e. bumper bars) with specified location and length. Assuming that one line is fixed to a body, the other line can either be fixed to another body or have a globally fixed location. The contact force between the lines (i.e. cylinder bars) is defined through a specified distance / force relation, which can be non-linear and include damping. However, sliding friction between the bumper bars is not included. If the centre line of one cylinder approaches the other cylinder along the centreline of the latter (see Figure), the force specified for zero distance will be turned on at ’contact’ between centre lines. This will give a large transient force, and unintended numerical problems. Make thus sure that the bumper cylinders are long enough to avoid end contact. Example: In this example nearly vertical bumpers are modelled to guide a module down to its specified position on the deck of an FPSO. The bumper bars are tilted one meter outwards, in order to ease entry. The final control of horizontal position can be accomplished by docking cones, and the vertical supports by linear springs. 2.10. Ratchet A ratchet is a stick - slip element. Both a tension and a compression version can be specified. A tension ratchet will slide and reduce its length when the tension passes a specified minimum value (that can be zero). 2.11. Moment coupling A rotation axis is defined in the coordinate system of body no. 1. The coupling gives a moment about this axis (on both bodies) when body no. 2 rotates about the specified axis, relative to body no. 1. 3. Body data 3.1. Body types in SIMO 6 DOF - time domain 6 degrees of freedom. Total motion is simulated in time domain 6 DOF - separated analysis 6 degrees of freedom. Separation of motion calculation: 1) First order wave motion calculated in frequency domain, from motion transfer functions. 2) Low-frequency motion calculated in the time domain 3 DOF - time domain 3 translation degrees of freedom. Position dependent hydrodynamic coefficients are allowed Prescribed Used for control and study of dynamic forces on a body, without the influence from body motion 3.2. Body Location Data The initial location is defined by 3 coordinates and 3 directions, which defines the local, body-fixed coordinate system relative to the global system. For a system with stiff coupling elements between bodies or positioning springs with high stiffness, it is favourable that the initial position is not too far from the equilibrium position. Otherwise the equilibrium calculation may fail due to high forces in the first part of the iteration. 3.3. Structure mass and added mass Structure mass and added mass for 6 DOF body types should be imported from data calculated by a diffraction theory program, such as WAMIT or WADAM. For a 6 DOF body consisting of slender members, distributed hydrodynamic forces along slender elements can be modeled. The mass matrix will then be produced from the specified distributed structure mass and added mass. For 3 DOF bodies the centre of gravity and the structure mass should be given. Added mass data for 3 DOF bodies is specified in the small body hydrodynamic data model element. The user may want to give unphysical mass data, in order to make it possible to investigate special effects or simplified cases. Selected examples are given here. 3.4. Time Dependent Mass Model elements: Time-dependent point mass Time-dependent volume mass These model elements can be used to simulate a ballasting sequence and its influence on the static and dynamic response of a vessel. The data can also be used to model a sudden or gradual waterfilling of a subsea module after a specified time. The specified increase or decrease in mass both affect the gravity force and the mass matrix. 3.5. Retardation Functions For 6 DOF - time domain bodies the retardation function should be calculated when frequency dependent added mass and damping is imported into SIMA from diffraction theory programs, such as WAMIT or WADAM . 3.6. Hydrostatic Stiffness The stiffness is a 6x6 matrix, usually imported from WAMIT/WADAM results. If special load conditions shall be studied or no results are available from accurate analysis, stiffness values can be obtained from the well-known relations between waterplane area or metacentric height and stiffness: Degree of freedom: Body crossing water surface Body fully submerged Heave: \(k_{33}=\rho gA_{wp}\) 0 Roll: \(k_{44}=Mg \cdot GM_T\) \(k_{44}=k_{55} = \rho g \space V \cdot GB\) Pitch: \(k_{55}=\rho g \cdot M \cdot GM_L\) \(k_{44}=k_{55} = \rho g \space V \cdot GB\) The following notations are used: \(A_{wp}\) = Waterplane area \((m^2)\) \(GM_T\) = Transverse metacentric height (m) \(GM_L\) = Longitudinal metacentric height (m) \(GB\) = Distance from gravity to buoyancy centres (m) \(V\) = Submerged volume \((m^3)\) In some cases the stiffness matrix (alone or together with the damping matrix) can be used for a simplified position control. This feature is used mostly when other matters than the position control are focused. Examples: Yaw stiffness applied on the hanging object, in a single crane lift (replacing control wires etc.) Position control of a crane vessel, where the motion of the load and the crane wire tension are focused. 3.7. Linear and Quadratic Damping May be given in order to include viscous damping not calculated by linear diffraction theory programs. Useful for model calibration by comparison with experimental data. 3.8. First Order Wave Force Transfer Function For 6 DOF bodies this data should be calculated by a diffraction theory program such as WAMIT or WADAM and imported into SIMA. 3.9. First Order Motion Transfer Function For 6 DOF bodies this data should be calculated by a diffraction theory program such as WAMIT or WADAM and imported into SIMA. 3.10. First Order Diffracted Wave Transfer Function This data should be calculated by a diffraction theory program such as WAMIT or WADAM and imported into SIMA. Each point for which the transfer function from the incoming wave to the diffracted wave is given, will have an identifier. The wave forces on a body can be calculated from the diffracted wave at a specified point. This is useful in particular for cases where a small lifted module is lowered through the splash zone on the leeward side of the crane vessel, and where shadowing effects can reduce the wave forces significantly. Both for slender elements, fixed body elements and small body hydrodynamic data, diffracted wave kinematics can be used to calculate the wave forces. This is done by specifying the named diffratced wave for these elements. 3.11. Second Order Wave Drift Forces For 6 DOF bodies this data may be calculated by a diffraction theory program such as WAMIT or WADAM. 3.12. Quadratic Transfer Functions For 6 DOF bodies this data may be calculated by a diffraction theory program such as WAMIT or WADAM. Read either for forces at difference or sum frequencies. If sum frequencies are read, ringing forces on columns can optionally be included. 3.13. Wave Drift Damping A contribution to the system damping occurring when a moored vessel has slowly oscillating motion along the wave direction. 3.14. Wind Force Coefficients These are force coefficients, given for varying wind directions. Data based on wind tunnel tests or scaled from similar vessels should be used. 3.15. Linear and Quadratic Current Coefficients These are force coefficients, given for varying current directions. Data based on wind tunnel tests, towing tank tests or scaled from similar vessels should be used. 3.16. Small Body Hydrodynamic Data Input data used to calculate hydrodynamic forces, using small volume body theory. Comprises the submerged volume and added mass and damping in 3 directions. Position dependent correction coefficients can be specified and also soil reaction forces. Diffracted wave kinematics can be used to calculate the wave forces. This is done by specifying the named diffracted wave. 3.17. Distributed Element Forces Available in SIMA: Slender element Fixed body element Input data used to calculate hydrodynamic forces, using small volume body theory. Comprises the mass and submerged volume and added mass and damping in longitudinal and 2 transverse directions. Position dependent correction coefficients can be specified. Diffracted wave kinematics can be used to calculate the wave forces. This is done by specifying the named diffracted wave. 3.18. Specified Force These are static forces, transient ramp forces or harmonic forces. Several options for specification of magnitude and direction. 3.19. Positioning System Data This group comprises various optional systems used to control the global position of a body, such as: Thrusters, either controlled by a DP system or not. Catenary mooring lines (see here for how to convert to a RIFLEX model) Linear or non-linear springs connecting the body to a globally fixed point. Various guiding or contact element types The springs and contact elements can also be used for coupling elements between bodies.