In spite of the numerous differences between a structural model and a fluid model, the similarities allow the user to formulate a problem with a minimum of data preparation and obtain efficient solutions to large-order problems. The similarities of the fluid model to the structural model are as follows:
• The fluid is described by points in space and finite element connections. The locations of the axisymmetric fluid points are described by rings (RINGFL) about a polar axis and defined by their r-z coordinates. The rings are connected by elements (CFLUIDi) which have the properties of density and bulk modulus of compressibility. Each fluid ring produces, internally, a series of scalar points pnand pn*(i.e., harmonic pressures), describing the pressure function, P (f), in the equation
•
• where the set of harmonics 0, n and n* are selected by the user. If the user desires the output of pressure at specific points on the circular ring, he may specify them as pressure points (PRESPT) by giving a point number and an angle on a specified fluid ring. The output data will have the values of pressure at the angle f given in the above equation. The output of free surface displacements normal to the surface (FREEPT) are also available at specified angles, f. The Case Control command AXISYM = FLUID is necessary when any harmonic fluid degrees-of-freedom are included. This command may not be used when F = NONE on the AXIF Bulk Data entry (no harmonics specified).
• The input file may include all existing options except the axisymmetric structural element data. All existing Case Control options may be included with some additional fluid Case Control requests. All structural element and constraint data may be used but not connected
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to RlNGFL, PRESPT, or FREEPT fluid points. The structure-fluid boundary is defined with the aid of special grid points (GRIDB) that may be used for any purpose that a structural grid point is currently used.
• The output data options for the structural part of a hydroelastic model are unchanged from the existing options. The output values of the fluid will be produced in the same form as the displacement vectors but with format modifications for the harmonic data.
o Pressures and free surface displacements, and their velocities and accelerations, may be printed with the same request (the Case Control command PRESSURE = SET is equivalent to DlSP = SET) as structural displacements, velocities, and accelerations.
o Structural plots are restricted to GRID and GRIDB points and any elements connected to them.
o X-Y plot and Random Analysis capabilities are available for FREEPT and PRESPT points if they are treated as scalar points.
o The RINGFL point identification numbers may not be used in any plot request; instead, the special internally generated points used for harmonics may be requested in the X-Y plots and random analysis. (See “Hydroelastic Data Processing”for the identification number code.)
o No element stress or force data is produced for the fluid elements.
o As in the case of the axisymmetric conical shell problem, the Case Control command HARMONlCS = N is used to select output data up to the Nth harmonic.
Input Data
Several special Bulk Data entries are required for fluid analysis problems. These entries are compatible with structural entries. A brief description of the uses for each Bulk Data entry follows:
AXlF
AXIF controls the formulation of the axisymmetric fluid problem. It is a required entry if any of the subsequent fluid-related entries are present. The data references a fluid-related coordinate system to define the axis of symmetry. The gravity parameter is included on this entry rather than on the GRAV entry because the direction of gravity must be parallel to the axis of symmetry. The values of density and elastic bulk modulus are conveniences in the event that these properties are constant throughout the fluid. A list of harmonics and the request for the nonsymmetric (sine) coefficients are included on this entry to allow the user to select any of the harmonics without producing extra matrix terms for the missing harmonics. A change in this list, however, will require a RESTART at the beginning of the problem.
RINGFL
The geometry of the fluid model about the axis of symmetry is defined with RINGFL entries. The RINGFL data entries serve somewhat the same function for the fluid as the GRID entries serve in the structural model. In fact, each RINGFL entry will produce, internally, a special grid point for each of the various harmonics selected on the AXIF data entry. They may not, however, be connected directly to structural elements (see the GRIDB and BDYLlST entries). No constraints may be applied directly to RINGFL fluid points.
CFLUIDi
CFLUIDi defines a volume of fluid bounded by the referenced RlNGFL points. The volume is called an element and logically serves the same purpose as a structural finite element. The physical properties (density and bulk modulus) of the fluid element may be defined on this entry if they are variables with respect to the geometry. If a property is not defined, the default value on the AXlF entry is assumed. Two connected circles (RINGFL) must be used to define fluid elements adjacent to the axis of symmetry. A choice of three or four points is available in the remainder of the fluid.
GRIDB
GRIDB provides the same functions as the GRID entry for the definition of structural grid points.
It will be attached to a particular RINGFL fluid point. The particular purpose for this entry is to force the user to place structural boundary points in exactly the same locations as the fluid points on the boundary. The format of GRIDB is identical to the format of GRID except that one additional field is used to identify the RINGFL point. The GRDSET entry, however, is not used for GRIDB data, and no superelement partitioning is allowed.
GRIDB entries may be used without a fluid model. This is convenient in case the user wishes to solve the structural problem first and to add the fluid effects later without converting GRID entries to GRIDB entries. The referenced RINGFL point must still be included in a boundary list (BDYLIST; see below), and the AXIF entry must always be present when GRIDB entries are used. (The fluid effects are eliminated by specifying no harmonics.)
FREEPT, PRESPT
FREEPT and PRESPT are used to define points on a free surface for displacement output and points in the fluid for pressure output. No constraints may be applied to these points. Scalar elements and direct matrix input data may be connected to these points, but the physical meaning of the elements will be different from in the structural sense.
FSLlST, BDYLIST
FSLIST and BDYLIST define the boundaries of the fluid with a complete freedom of choice.
The FSLIST entry defines a list of fluid points which lie on a free surface. The BDYLIST data make up a list of fluid points to which structural GRIDB points are connected. Points on the boundary of the fluid for which BDYLlST or FSLIST data are not defined are assumed to be rigidly restrained from motion in a direction normal to the surface.
With both of these lists, the sequence of the listed points determines the nature of the boundary.
The following directions will aid the user in producing a list:
1. Draw the z-axis upward and the r-axis to the right. Plot the locations of the fluid points on the right-hand side of z.
2. If one imagines himself traveling along the free surface or boundary with the fluid on his right side, the sequence of points encountered is used for the list. If the surface or boundary touches the axis, the word AXIS is placed in the list. AXIS may be used only for the first and/or last point in the list.
3. The free surface must be consistent with static equilibrium. With no gravity field, any free surface consistent with axial symmetry is allowed. With gravity, the free surface must be a plane perpendicular to the z-axis of the fluid coordinate system.
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4. Multiple free surface lists and boundary lists are allowed. A fluid point may be included in any number of lists.
Figure 4-1illustrates a typical application of the free surface and structural boundary lists.
Figure 4-1. Examples of Boundary Lists
FLSYM
FLSYM allows the user an option to model a portion of the structure with planes of symmetry containing the polar axis of the fluid. The first plane of symmetry is assumed at f = 0.0 and the second plane of symmetry is assumed at f = 360° /M where M is an integer specified on the entry.
Also specified are the types of symmetry for each plane, symmetric (S) or antisymmetric (A). The user must also supply the relevant constraint data for the structure. The solution is performed correctly only for those harmonic coefficients that are compatible with the symmetry conditions, as illustrated in the following example for quarter symmetry, M = 4.
Plane 2
DMIAX is used for special purposes such as the specification of surface friction effects. DMIAX is equivalent to DMIG except harmonic numbers are specified for the degrees-of-freedom. A matrix may be defined with either DMIG or DMlAX entries, but not with both.