김경종
27 KiB
text_image
Vertical axis (Z-direction in 3D cases, Y-direction in 2D cases) H, wave height Wave of zero phase angle has a trough at the origin of the horizontal axis at time t=0. λ, wavelength Direction of wave travel horizontal position
Figure 6.11.1–1 Wave of zero phase angle.
to determine if the point of interest is above the instantaneous free surface. Similarly, a maximum wave elevation is used: any point above the maximum wave elevation is assumed to have no fluid loading.
For Airy and Stokes waves the minimum and maximum wave elevations are calculated from the wave theory.
For gridded waves Abaqus/Aqua allows the definition of a minimum wave trough elevation: z _ { m i n } in three-dimensional analysis or y _ { m i n } in two-dimensional analysis. The structure is always assumed to be immersed below this elevation. The maximum wave elevation is calculated as the still water elevation plus the difference between this elevation and the minimum wave trough elevation. If the minimum wave trough elevation is not specified for gridded waves, Abaqus/Aqua will compare the elevation of every point on the structure with the instantaneous fluid surface as defined by the gridded data. When defining this elevation, make sure that no wave trough ever drops below the minimum wave trough elevation specified.
Input File Usage: *WAVE, TYPE=GRIDDED, DATA FILE=file_name, MINIMUM=elevation
Wave kinematics, dynamic pressure, and extrapolation for Airy waves
A spatial (Eulerian) description of the wave field is used for all wave types; therefore, a structural point’s coordinates are used to evaluate the wave kinematics. In geometrically nonlinear analysis the structural point’s coordinates are its current coordinates. In geometrically linear analysis the wave kinematics are evaluated using the structural point’s reference coordinates.
In both geometrically linear and nonlinear analysis for both static and direct-integration dynamic procedures, submergence is calculated to the instantaneous water level at the current value of total time
for the analysis. Fluid loading is applied only to those points on the structure below the instantaneous water level.
When buoyancy loading is applied in conjunction with a gravity wave, the dynamic pressure due to the disturbance of the still surface is added to the hydrostatic pressure (measured to the still water level) to obtain the total buoyancy loading, except when the buoyancy loading described by a distributed or concentrated load definition overrides the fluid properties given for the Abaqus/Aqua analysis. Dynamic pressure is included for both static and dynamic procedures for Airy, Stokes, and gridded wave types; however, with gridded wave data you can choose to suppress this effect. See “Airy wave theory,” Section 6.2.2 of the Abaqus Theory Guide, and “Stokes wave theory,” Section 6.2.3 of the Abaqus Theory Guide, for a definition of dynamic pressure.
Although the linearized Airy wave theory assumes that the fluid displacements are small with respect to the wavelength and the fluid depth, these displacements may not be small with respect to the dimensions of the structure immersed in the fluid. As a result of the linearizing approximations special treatment is necessary to calculate the wave kinematics for points below the instantaneous water level but above the still water line. Abaqus/Aqua uses extrapolation with Airy wave theory: the wave velocity, acceleration, and dynamic pressure for points above the still water level but below the instantaneous free surface are taken to be the values evaluated from the wave theory at the still water level. See “Airy wave theory,” Section 6.2.2 of the Abaqus Theory Guide, for more details.
Reading the data that define gravity waves from an alternate file
The data for the gravity wave can be contained in an alternate file. See “Input syntax rules,” Section 1.2.1, for the syntax of the file name.
Input File Usage: *WAVE, INPUT=file_name
Visualization of gravity waves
In a three-dimensional analysis you can visualize gravity waves by meshing the free surface of the water with surface elements (see “General surface element library,” Section 32.7.2) and identifying elements as aqua visualization elements through the surface section definition.
Aqua visualization elements are used for postprocessing only and do not affect the solution. The following must be true for proper use of these elements:
- Aqua visualization elements can be connected to other visualization elements only through shared nodes. They cannot be connected in any way to any element in the model that is used during the analysis. This includes connections through shared nodes, kinematic constraints, or surface interactions. Abaqus issues an error message during input file preprocessing if these conditions are not met. For example, if you are doing an Abaqus/Aqua analysis of an offshore oil platform, the visualization elements cannot be connected to any element used to model the platform.
- Any boundary conditions or loads that are applied on the visualization elements are ignored.
- Density cannot be assigned to the visualization elements.
- Reinforcement layers cannot be defined for the visualization elements.
- To visualize the displacements, you must request displacement field output on the output database (.odb) file. During the analysis Abaqus computes the z-displacements of the elements using
whatever wave definitions you include in the model, including user subroutines. Only displacement output can be requested for these elements.
- The initial z-coordinates of the elements should be defined at the still water height; if they are not, Abaqus automatically adjusts them to the still water height during input file preprocessing.
Input File Usage: *SURFACE SECTION, ELSET =elset_name, AQUAVISUALIZATION=YES
Defining a wind velocity profile
You can define a wind velocity profile. Wind loading is applied only to elements above the still water surface elevation (defined in the fluid properties). If an element is above the still water depth but is submerged due to a wave, the wind loading will still be applied.
The wind profile is assumed to vary with height (the positive z-direction in three-dimensional models, the positive y-direction in two-dimensional models) according to the power law wind profile and has no variation in the horizontal plane. The power law wind velocity profile is given by
\mathbf {v} = \mathbf {v} ^ {0} \left(\frac {z}{z _ {0}}\right) ^ {\alpha},
where
\begin{array} { r l } { \mathbf { v } ( z , t ) } & { { } = v _ { x } ( z , t ) \hat { \mathbf { i } } + v _ { y } ( z , t ) \hat { \mathbf { j } } } \end{array} is the local wind velocity ( \hat { \bf i } is a unit vector along the local x-axis of the wind field, and is a unit vector along the local y-axis of the wind field);
\mathbf { v } ^ { 0 } ( t ) is the time-varying wind velocity at the reference height, , as described below;
α is a user-defined constant (default value 1/7);
z is the distance above the still water surface ( \mathrm { i } . \mathbf { e } . , z = 0 . 0 is the still water surface); and
z _ { 0 } is the reference distance above the still water surface where the time variation of the wind velocity is given.
The wind local system is defined by giving the direction cosines of the unit vector .
Input File Usage: *WIND
air density, , , , x-direction cosine for , y-direction cosine for ,
Prescribing the time variation of wind velocity at the reference height
The variation in time of the wind profile is defined by \mathbf { v } ^ { 0 } ( t ) , the wind velocity vector time history at a reference height z = z _ { 0 } . :
\mathbf {v} ^ {0} (t) = v _ {x} ^ {0} (t) \hat {\mathbf {i}} + v _ {y} ^ {0} (t) \hat {\mathbf {j}}.
The wind velocity component time histories v _ { x } ^ { 0 } ( t ) and v _ { y } ^ { 0 } ( t ) are given by
v _ {x} ^ {0} (t) = c _ {x} A _ {x} (t); \quad v _ {y} ^ {0} (t) = c _ {y} A _ {y} (t),
where c _ { x } and c _ { y } are user-defined as described above (with default values of 1.0) and A _ { x } ( t ) and A _ { y } ( t ) are time-dependent functions defined by referring to amplitude curves from the concentrated or distributed
load definitions used to apply the wind loading to the model. If no amplitude curve is referenced, the wind velocity components are the constant values v _ { x } ^ { 0 } ( t ) = c _ { x } and v _ { y } ^ { 0 } ( t ) = c _ { y } .
Geometrically linear versus geometrically nonlinear analysis
In geometrically linear analysis wind velocities are calculated based on the original coordinates of the structure. In geometrically nonlinear analysis the current coordinates of a point on the structure are used to calculate the wind velocity at that point.
Initial conditions
Initial conditions can be applied to the structure in an Abaqus/Aqua analysis in the same way as in static and dynamic analyses without Aqua loads. See “Initial conditions in Abaqus/Standard and Abaqus/Explicit,” Section 34.2.1.
Boundary conditions
Boundary conditions can be applied to the structure in an Abaqus/Aqua analysis in the same way as in static and dynamic analyses without Aqua loads. See “Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 34.3.1.
Defining contact at the seabed
Aqua loads are applied only above the seabed. To model the bottom of the sea using a contact plane, the elevation of the contact plane must be slightly higher than the seabed level to avoid ambiguity between the contact condition and applied loading. If the contact plane is at the same level as the seabed, there is a risk that round-off problems will cause Aqua loads not to be applied to nodes in contact with the seabed.
Loads
Steady current, wave, and wind loads are applied to nodes or elements of the structure using concentrated and/or distributed load definitions. Wind loads are applied only if the point is currently above the still fluid surface; fluid loads are applied only if the point is currently below the instantaneous fluid surface and above the seabed. Distributed loads are applied to partly immersed elements.
Concentrated and distributed load definitions cannot be used in eigenfrequency extraction steps, so the loads described below can be applied only in static and direct-integration dynamic steps.
Controlling the time variation and magnitude of Aqua loading
You have three ways to control the magnitude of an Aqua load as a function of time:
- You can reference a user-defined amplitude curve (“Amplitude curves,” Section 34.1.2) from the concentrated or distributed load definition to scale the entire load.
- You can specify a magnitude factor, M, for the concentrated or distributed load definition, which is used to scale all the load. This magnitude factor allows normalized amplitude curves to be defined and used for multiple loads. The default magnitude factor is always .
- You can reference individual user-defined amplitude curves to scale different components of the loading separately. For example, steady current velocity and wave velocity can be scaled separately by referencing different amplitude curves.
All of these scaling factors are cumulative.
Buoyancy loads
The calculated buoyancy of a structure depends on the orientation of the exposed surface area with respect to the vertical direction. This surface area is calculated automatically by Abaqus/Aqua for distributed buoyancy loading; however, you must specify the exposed area and direction cosines of the outward normal at a node for concentrated buoyancy loading.
Abaqus/Aqua uses a closed-end loading condition while computing the distributed buoyancy forces on all line elements. To obtain an open-end loading condition, concentrated buoyancy loading can be used to counteract the buoyancy load applied to the ends of the elements.
The buoyancy loads require the definition of fluid density, seabed and free surface elevation, and the gravitational constant. The default external fluid properties are defined for the model as described in “Defining the fluid properties.” You can override some of these properties by specifying them directly in the distributed or concentrated load definition. This provides for modeling situations where different parts of the structure are subjected to different buoyancy loads, such as a pipe inside another pipe where the static fluid surrounding the inner pipe is different from the fluid surrounding the outer pipe. Gravity waves (“Wave kinematics, dynamic pressure, and extrapolation for Airy waves”) do not affect the buoyancy loading when any external fluid property is overridden.
Specifying distributed buoyancy loads
To apply distributed buoyancy loads to elements immersed in a fluid, the effective outer diameter of beam, truss, and one-dimensional rigid elements must be specified. Provide the external fluid density, free surface elevation, and additional pressure to override the default fluid properties to model the situations described above. For situations where it is necessary to model the fluid inside an element, the effective inner diameter of the element must also be given, along with the density and free surface elevation of the fluid inside the element.
Distributed buoyancy loading can be applied to rigid surface elements. However, the effects of waves are ignored for these elements; the buoyancy loading is calculated to the still water level only. For proper application of a positive buoyancy force, the positive normal of R3D3 and R3D4 elements must point into the fluid.
Input File Usage: *DLOAD
element number or set, PB, M, effective outer diameter, internal fluid density, effective inner diameter, internal free surface elevation, external fluid density, external free surface elevation, additional pressure
Specifying concentrated buoyancy loads
For concentrated buoyancy loads applied to nodes immersed in a fluid, the load is calculated based on the sum of the hydrostatic pressure (measured to the still water level) and the dynamic pressure due to
wave action. The total pressure is multiplied by the exposed area associated with the node. The loading is automatically considered to be a follower force in geometrically nonlinear analysis (for elements that have rotational degrees of freedom); therefore, it is not necessary to specify that the load is a follower force. Provide the external fluid density, free surface elevation, and additional pressure to override the default fluid properties to model the situations described above.
Input File Usage: *CLOAD
node number or set, TSB, M, exposed area, local coordinate system data, external fluid density, external free surface elevation, additional pressure
Drag loads
Both waves and wind can cause drag loading on a structure. Fluid drag refers to drag caused by the structural member being immersed in the fluid defined by the fluid properties and the gravity waves and, thus, subject to steady current and wave loading. Fluid drag loading is provided by Morison’s equation. Fluid drag loads must be specified in terms of a normal (transverse) load and a tangential load.
Wind drag is generated on the portions of a structure that are above the still fluid surface defined by the fluid properties because these portions are exposed to the user-defined wind velocity profile.
Specifying distributed transverse fluid or wind drag loads
Distributed transverse drag is defined as follows (see “Drag, inertia, and buoyancy loading,” Section 6.2.1 of the Abaqus Theory Guide, for more details):
\mathbf {F} _ {D} = A \frac {1}{2} \rho C _ {D} D \Delta \mathbf {v} _ {f n} | \Delta \mathbf {v} _ {f n} |,
where
\mathbf { F } _ { D } is the force per unit length, transverse to the member;
A ( t ) is the current value of the amplitude curve referred to by the distributed load definition, multiplied by the user-defined magnitude factor, M;
\rho is the mass density of the fluid (given in the fluid properties) for fluid distributed drag or is the mass density of the air (given in the wind velocity profile) for wind distributed drag;
CD C _ { D } is the drag coefficient; and
D is the effective outer diameter of the member.
The relative fluid particle velocity in the normal direction, \Delta \mathbf { v } _ { f n } , is given by
\Delta \mathbf {v} _ {f n} = \Delta \mathbf {v} - \Delta \mathbf {v} \cdot \mathbf {t t},
\Delta \mathbf {v} = \mathbf {v} _ {f} - \alpha_ {R} \mathbf {v} _ {p},
where
\mathbf { v } _ { f } is the fluid particle velocity (see the discussion below);
\mathbf { v } _ { p } is the velocity of this point on the structure (zero during static steps);
\alpha _ { R } is the structural velocity factor; and
t is the unit vector along the axis of the element.
The effective outer diameter of the element, D ; the drag coefficient, C _ { D } ; and the structural velocity factor, \alpha _ { R } . , must be defined in the distributed load definition together with the distributed load type (fluid distributed drag or wind distributed drag).
The velocities due to steady current and waves can be scaled individually for fluid distributed drag by referring to different amplitude curves. Thus, the fluid particle velocity, \mathbf { v } _ { f } , at any time is
\mathbf {v} _ {f} = A _ {c} \mathbf {v} _ {c} + A _ {w} \mathbf {v} _ {w},
where
A _ { c } ( t ) is the current value of the first amplitude curve listed in the load definition or 1.0 if the amplitude reference is omitted,
Vc \mathbf { v } _ { c } is the steady current velocity defined in the fluid properties,
A _ { w } ( t ) is the current value of the second amplitude curve listed in the load definition or 1.0 if the amplitude reference is omitted, and
Vw { \bf v } _ { w } is the user-defined wave velocity.
The wind velocity is defined in components relative to the local axes \hat { \bf i } and \hat { \bf j } defined for the wind velocity profile. Each velocity component can be scaled independently by referring to different amplitude curves. The total wind velocity at any time, \mathbf { v } _ { f } , is
\mathbf {v} _ {f} = (c _ {x} A _ {x} \hat {\mathbf {i}} + c _ {y} A _ {y} \hat {\mathbf {j}}) \left(\frac {z}{z _ {0}}\right) ^ {\alpha},
where A _ { x } ( t ) and A _ { y } ( t ) are the amplitude references provided in the load definition for the velocity components in the local x- and y-directions, respectively. The values of c _ { x } , c _ { y } , z _ { 0 } , and \alpha are defined by the wind velocity profile; and z is the distance above the still fluid surface.
Input File Usage: Use the following option to define fluid distributed drag:
- DLOAD
element number or set, FDD, M, D,
C_{D},\alpha_{R},A_{c}(t),A_{w}(t)Use the following option to define wind distributed drag: - DLOAD
element number or set, WDD, M, D,
C_{D},\alpha_{R},A_{x}(t),A_{y}(t)
Specifying distributed tangential fluid drag loads
Distributed tangential fluid loading is a load in the tangential direction of an element due to skin friction. This type of loading is defined as follows (see “Drag, inertia, and buoyancy loading,” Section 6.2.1 of the Abaqus Theory Guide, for more details):
\mathbf {F} _ {t} = A \frac {1}{2} \rho_ {w} C _ {t} \pi D \Delta \mathbf {v} _ {f t} | \Delta \mathbf {v} _ {f t} | ^ {h - 1},
where
\mathbf { F } _ { t } is the force per unit length, tangent to the member;
A ( t ) is the amplitude curve referred to by the distributed load definition, multiplied by the userdefined magnitude factor, M;
\rho _ { w } is the mass density of the fluid (given in the fluid properties);
C _ { t } is the tangential drag coefficient;
D is the effective outer diameter of the member; and
\boldsymbol { h } is a constant (by default, h = 2 , for quadratic dependence of force on velocity).
The relative fluid particle velocity in the tangential direction, \Delta { \mathbf v } _ { f t } , is given by
\Delta \mathbf {v} _ {f t} = \left(\mathbf {v} _ {f} - \alpha_ {R} \mathbf {v} _ {p}\right) \cdot \mathbf {t t},
where
\mathbf { v } _ { f } is the fluid particle velocity (as defined above for distributed transverse fluid drag loading),
\mathbf { v } _ { p } is the velocity of this point on the structure (zero during static steps),
\alpha _ { R } is the structural velocity factor, and
t is the unit vector along the axis of the element.
The effective outer diameter of the element, D ; the drag coefficient, C _ { t } ; the structural velocity factor, \alpha _ { R } \mathbf { ; } ; and the exponent, h , must be defined in the distributed load definition together with the distributed load type (fluid drag tangential).
As with distributed transverse fluid loading, the velocities due to steady current and waves ( A _ { c } and A _ { w } ) can be scaled individually by referring to different amplitude curves.
Input File Usage: Use the following option to define fluid drag tangential:
*DLOAD
e l e m e n t n u m b e r o r s e t , \mathrm { F D T } , M , D , C _ { t } , \alpha _ { R } , h , A _ { c } ( t ) , A _ { w } ( t )
Specifying concentrated fluid or wind drag loads using a concentrated load definition
Concentrated fluid or wind drag loading applies a load normal to the end of an element. Such loading is automatically considered to be a follower force in geometrically nonlinear analysis (for elements that have rotational degrees of freedom).
The drag theory uses Morison’s equation (see “Drag, inertia, and buoyancy loading,” Section 6.2.1 of the Abaqus Theory Guide). The drag force is nonzero when the net flow is in the opposite direction of the outward normal to the exposed area and is zero when the net flow is in the direction of the normal:
\mathbf {F} _ {\mathrm{drag}} = \left\{ \begin{array}{l l} - A \frac {1}{2} \rho C _ {n} \Delta A (\Delta v _ {f t}) ^ {2} \mathbf {t} & \text {for} \quad \Delta v _ {f t} \leq 0, \\ 0 & \text {for} \quad \Delta v _ {f t} > 0, \end{array} \right.
where
A(t) is the amplitude curve referenced by the concentrated load definition multiplied by the user-defined magnitude factor, M ; \rho is the mass density of the fluid (given in the fluid properties) for transition section fluid drag or is the mass density of the air (given in the wind velocity profile) for transition section wind drag; C_n is the drag coefficient; \Delta A is the exposed area; and \Delta v_{ft} is the relative velocity between the structural member and the fluid particle along t and is given by t \cdot \Delta v_{ft} , where \Delta v_{ft} = (v_f - \alpha_R v_p) \cdot t t , as defined above for distributed tangential fluid drag loading.
The exposed area, \Delta A ; the drag coefficient, C _ { n } ; and the structural velocity factor, \alpha _ { R } , must be defined in the concentrated load definition together with the concentrated load type (transition section fluid drag or transition section wind drag).
As with distributed transverse fluid loading, the velocities due to steady current and waves ( A _ { c } and A _ { w } ) and the velocity components of the wind in the and \hat { \bf j } directions ( A _ { x } and A _ { y } ) can be scaled individually by referring to different amplitude curves.
Input File Usage: Use the following option to define transition section fluid drag:
*CLOAD node number or set, TFD, M, \Delta A , C _ { n } , \alpha _ { R } , A _ { c } ( t ) , A _ { w } ( t )
Use the following option to define transition section wind drag:
*CLOAD node number or set, TWD, M, , , , ,
Specifying concentrated fluid or wind drag loads using a distributed load definition
You can apply concentrated fluid or wind drag loading on the ends of elements. These loads have the same effect as specifying a concentrated load at a node using a concentrated load definition with concentrated load type transition section fluid drag or transition section wind drag, except that the normal to the exposed area cannot be specified when a distributed load definition is used; the normal to the end of the element is defined by the tangent to the element.
The load can be applied to the first end (node) of the element or to the second end (node 2 or 3, as appropriate) of the element. These loads are nonzero only when the net flow is in the opposite direction of the outward normal to the exposed area.
The loading is exactly the same as that described for the concentrated fluid or wind drag loading applied with a concentrated load definition. The “distributed” form of the loading is provided for convenience.
Input File Usage: Use the following option to define fluid drag on the first end of the element:
*DLOAD e l e m e n t n u m b e r o r s e t , \mathrm { F D 1 } , M , \Delta A , C , \alpha _ { R } , A _ { c } ( t ) , A _ { w } ( t )
Use the following option to define fluid drag on the second end of the element:
*DLOAD
element number or set, FD2, M, , C, , ,
Use the following option to define wind drag on the first end of the element:
*DLOAD
element number or set, WD1, M, , C, , ,
Use the following option to define wind drag on the second end of the element:
*DLOAD
e l e m e n t n u m b e r o r s e t , \mathrm { W D 2 } , M , \Delta A , C , \alpha _ { R } , A _ { x } ( t ) , A _ { y } ( t )
Neglecting the wave’s contribution to drag and inertia loading during a step
If the wave’s contribution to the drag and inertia loading should not be applied during a step, the concentrated or distributed load component definition must explicitly refer to an amplitude curve with a value of zero. This is the only way to prevent waves from contributing to the fluid velocities and accelerations used in the calculation of these concentrated or distributed load types.
Fluid inertia loads (added-mass effects)
Fluid inertia loading causes a structure to have increased inertial resistance to acceleration. This fluid “added-mass” effect is included automatically in a direct-integration dynamic step when fluid inertia loading is applied. Concentrated or distributed added mass must be defined to include the added-mass effect in an eigenfrequency extraction step.
Specifying distributed fluid inertia loads in a direct-integration dynamic step
Distributed fluid inertia loading is defined as follows (see “Drag, inertia, and buoyancy loading,” Section 6.2.1 of the Abaqus Theory Guide, for a more detailed description):
\mathbf {F} _ {I} = A \rho_ {w} \frac {\pi D ^ {2}}{4} \left[ C _ {M} \mathbf {a} _ {f n} - C _ {A} \mathbf {a} _ {p n} \right],
where
{ \bf { F } } _ { I } is the force per unit length, transverse to the member, caused by fluid inertia;
A ( t ) is the amplitude curve referred to by the distributed load definition multiplied by the userdefined magnitude factor, M;
\rho _ { w } is the mass density of the fluid (given in the fluid properties);
D is the effective outer diameter of the member;
C _ { M } is the transverse fluid inertia coefficient;
CA C _ { A } is the transverse added-mass coefficient;
\mathbf { a } _ { f n } is the transverse component of the fluid acceleration; and
apn { \bf a } _ { p n } is the transverse component of the beam acceleration (zero during static steps).