Aqua load cases

Full submergence of structural members

Elements tested

B21
B21H
B22
B22H
B23
B23H
B31
B31H
B32
B32H
B33
B33H

ELBOW31
ELBOW31B
ELBOW31C
ELBOW32

PIPE21
PIPE21H
PIPE22
PIPE22H
PIPE31
PIPE31H
PIPE32
PIPE32H

RB2D2
RB3D2
R3D3
R3D4

T2D2
T2D2H
T2D3
T2D3H
T3D2
T3D2H
T3D3
T3D3H

Problem description

The structural member (beam, pipe, elbow, or truss) is kept straight and constrained, and it is moved to different positions and orientations in different steps; where appropriate, it is given a uniform velocity and acceleration. The structural member is subjected to various drag and buoyancy loads in the different steps. The problems are described in detail in the input files. The concentrated and distributed load procedures are tested in these problems. The effective axial force (output variable ESF1) for beam, pipe, and truss elements is also tested.

The features and load types tested in each problem in the various steps are:

Buoyancy, PB.
Normal drag, static, FDD.
Tangential drag, static, FDT.
Normal drag, dynamic, FDD.
Tangential drag, dynamic, FDT.
Inertial drag, FI.
Normal drag, dynamic, partial immersion, FDD.
End-drag, dynamic, FD1, FD2.
End-drag, dynamic, TFD (concentrated load).
Inertial end-drag, FI1, FI2.
Inertial end-drag, TSI (concentrated load).
Transition-section buoyancy, TSB.
End-drag, dynamic, (additional test), FD1, FD2.
End-drag, dynamic, (additional test), TFD (concentrated load).
Wind-drag, dynamic, WDD.
Wind end-drag, dynamic, WD1, WD2.
Wind end-drag, dynamic, TWD (concentrated load).

The individual steps are named alphabetically as listed above. These names appear in the step headings.

Model:

Length	10 $\sqrt{2}$
Orientation	45° with horizontal axis
Pipe section data	r = 1.0, t = 0.05

Material:

Young's modulus	30 × 10⁹
Poisson's ratio	0.3

Aqua – environment

Seabed elevation	0.0
Mean water elevation	40.0
Max. water elevation	40.0
Min. water elevation	40.0
Gravitational constant	32.2
Fluid mass density	1.987
Steady velocity specification: two-dimensional
( $v_{x}, v_{y}$ , elevation)	(2.0, 1.0, 0.0)
( $v_{x}, v_{y}$ , elevation)	(2.0, 1.0, 2000.0)
Steady velocity specification: three-dimensional
( $v_{x}$ , $v_{z}$ , elevation)	(2.0, 1.0, 0.0)
( $v_{x}$ , $v_{z}$ , elevation)	(2.0, 1.0, 2000.0)
( $v_{y}$ = 0.0)

Results and discussion

The correct total force can be determined analytically for the simple case of a straight structural member under drag or buoyancy loads, subjected to a uniform structural velocity or acceleration immersed in water with a constant velocity field. In all cases the reaction force at the beam nodes produced by Abaqus matches the analytical solution.

The analytically determined results are listed in the headings for each step in the input files.

Input files

eb22pxdb.inp: B21 elements.
eb2hpxdb.inp: B21H elements.
eb23pxdb.inp: B22 elements.
eb2ipxdb.inp: B22H elements.
eb2apxdb.inp: B23 elements.
eb2jpxdb.inp: B23H elements.
eb32pxdb.inp: B31 elements.
eb3hpxdb.inp: B31H elements.
eb33pxdb.inp: B32 elements.
eb3ipxdb.inp: B32H elements.
eb3apxdb.inp: B33 elements.
eb3jpxdb.inp: B33H elements.
exel1xdb.inp: ELBOW31 elements.
exelbxdb.inp: ELBOW31B elements.
exelbxdb.inp: ELBOW31C elements.
exel2xdb.inp: ELBOW32 elements.
ep22pxdb.inp: PIPE21 elements.
ep2hpxdb.inp: PIPE21H elements.
ep23pxdb.inp: PIPE22 elements.
ep2ipxdb.inp: PIPE22H elements.
ep32pxdb.inp: PIPE31 elements.
ep3hpxdb.inp: PIPE31H elements.
ep33pxdb.inp: PIPE32 elements.
ep3ipxdb.inp: PIPE32H elements.
er22sxdb.inp: RB2D2 elements.
er32sxdb.inp: RB3D2 elements.
er33sxdb.inp: R3D3 elements.
er34sxdb.inp: R3D4 elements.
et22sxdb.inp: T2D2 elements.
et2hsxdb.inp: T2D2H elements.
et23sxdb.inp: T2D3 elements.
et2isxdb.inp: T2D3H elements.
et32sxdb.inp: T3D2 elements.
et3hsxdb.inp: T3D2H elements.
et33sxdb.inp: T3D3 elements.
et3isxdb.inp: T3D3H elements.

Partial submergence of structural members

Elements tested

B21
B21H
B22
B22H
B23
B23H
B31
B31H
B32
B32H
B33
B33H

ELBOW31C
RB2D2
RB3D2

T2D2
T2D2H
T2D3
T2D3H
T3D2
T3D2H
T3D3
T3D3H

Problem description

The structural member is positioned vertically in both the two- and three-dimensional cases, such that one-half of the structure is below the seabed and only the top half is subject to fluid loads.

Nodes of each element are constrained to a single node whose reaction force is monitored.

The features and load types tested in each problem in the various steps are:

Static analysis with drag load FDD and no wave loads.
Static analysis: dummy step to zero out the loads.
Dynamic analysis with inertial load FI.

Model:

Height of the structure	2
Section data	r = 1.0 for beams, A = 1.0 for trusses

Material:

Young's modulus

1 × 10⁶

Aqua – environment

Seabed elevation	0.0
Mean water elevation	2.0
Gravitational constant	32.2
Fluid mass density	1.99
Steady velocity specification: 2D/3D
( $v_{x}$ , $v_{y}$ , $v_{z}$ , elevation)	(1.0, 0.0, 0.0, 0.0)
( $v_{x}$ , $v_{y}$ , $v_{z}$ , elevation)	(1.0, 0.0, 0.0, 2.0)

Airy wave parameters

Amplitude	0.1
Period	10.0
Phase angle	0.0
Direction of travel	(1.0, 0.0)

Results and discussion

The results match the analytically determined reaction force.

Input files

eb22cxd1.inp: B21 elements.
ebxxcxd1.inp: All beam elements.
exelcxd1.inp: ELBOW31C elements.
etxxcxd1.inp: All truss elements.

Submergence of a rigid box

Elements tested

R3D3

R3D4

Problem description

A box composed of three-dimensional rigid elements is immersed in water subject to a buoyancy load (PB). The buoyancy forces and moments produced are measured by the reaction force at the rigid body reference node in four distinct configurations: in the initial configuration, as well as in the configurations produced when the body is given 60° of heel and then followed by 10° and 20° of trim.

Results and discussion

The Abaqus values for the buoyancy forces match the analytical values exactly. Because analytical values are not readily available at the moment, these values are compared with values produced by an independent code and agree to within one-quarter of 1%. The expected results are listed in the input files.

Input files

er33sxdb.inp: R3D3 elements.
er34sxdb.inp: R3D4 elements.

Eigenfrequency extraction with added mass

Elements tested

B21

T3D2

Problem description

Frequencies of natural vibration are computed for slender structures with different boundary conditions, with and without the effect of added mass.

Model:

Length	1000
Beam section data (circular)	r = 3

Material:

Young's modulus	4.32 × 10⁹
Density	$ρ$ = 14.91

Aqua – environment

Seabed elevation	−100
Mean water elevation	100
Gravitational constant	32.2
Fluid mass density	2

Results and discussion

The analytically determined results and those given by Abaqus are listed at the top of each of the input files.

Input files

eb22cxd1.inp: Transverse vibration of simply supported beam.
eb22cxd2.inp: Transverse vibration of clamped-free cantilever beam.
eb22cxd3.inp: Longitudinal vibration of clamped-free cantilever beam.
et32pxdb.inp: Longitudinal vibration of clamped-free truss.

Spatial variation of steady current velocity

Elements tested

PIPE21

PIPE31

Problem description

Vertical structural members, fully submerged and constrained, are subjected to a steady current velocity that is uniform with respect to elevation but varies with position (x-coordinate for two-dimensional cases, and x- and y-coordinate for three-dimensional cases). The drag forces on the individual members can be determined analytically and compared to the nodal reaction forces.

The fluid velocity $v_{f}$ is equal to 2.8961.

Model:

Height of the structure	10
Pipe section data	r = 1.0, t = 0.05

Material:

Young's modulus

30 × 10⁶

Aqua – environment

Seabed elevation	0.0
Mean water elevation	40.0
Gravitational constant	32.2
Fluid mass density	1.987

Steady velocity specification: two-dimensional case

( $v_{x}$ , $v_{y}$ , $v_{z}$ , x-coord.)	( $1 v_{f}$ , 0.0, 0.0, 100.0)
( $v_{x}$ , $v_{y}$ , $v_{z}$ , x-coord.)	( $3 v_{f}$ , 0.0, 0.0, 300.0)
( $v_{x}$ , $v_{y}$ , $v_{z}$ , x-coord.)	( $3 v_{f}$ , 0.0, 0.0, 600.0)
( $v_{x}$ , $v_{y}$ , $v_{z}$ , x-coord.)	( $0 v_{f}$ , 0.0, 0.0, 900.0)

Steady velocity specification: three-dimensional case

( $v_{x}$ , $v_{y}$ , $v_{z}$ , x-coord., y-coord.)	( $2 v_{f}$ , 0.0, 0.0, 100.0, 200.0)
( $v_{x}$ , $v_{y}$ , $v_{z}$ , x-coord., y-coord.)	( $6 v_{f}$ , 0.0, 0.0, 300.0, 200.0)
( $v_{x}$ , $v_{y}$ , $v_{z}$ , x-coord., y-coord.)	( $6 v_{f}$ , 0.0, 0.0, 600.0, 200.0)
( $v_{x}$ , $v_{y}$ , $v_{z}$ , x-coord., y-coord.)	( $0 v_{f}$ , 0.0, 0.0, 900.0, 200.0)
( $v_{x}$ , $v_{y}$ , $v_{z}$ , x-coord., y-coord.)	( $1 v_{f}$ , 0.0, 0.0, 100.0, 800.0)
( $v_{x}$ , $v_{y}$ , $v_{z}$ , x-coord., y-coord.)	( $3 v_{f}$ , 0.0, 0.0, 300.0, 800.0)
( $v_{x}$ , $v_{y}$ , $v_{z}$ , x-coord., y-coord.)	( $3 v_{f}$ , 0.0, 0.0, 600.0, 800.0)
( $v_{x}$ , $v_{y}$ , $v_{z}$ , x-coord., y-coord.)	( $0 v_{f}$ , 0.0, 0.0, 900.0, 800.0)

Results and discussion

The results match the analytically determined reaction forces at select locations.

Input files

ep22pxd5.inp: PIPE21 elements.
ep32pxd5.inp: PIPE31 elements.
ep22pxd5_xpl.inp: PIPE21 elements in Abaqus/Explicit.
ep32pxd5_xpl.inp: PIPE31 elements in Abaqus/Explicit.

Dynamic pressure, closed-end buoyancy loads

Elements tested

PIPE21

PIPE22

PIPE31

Problem description

This problem tests the dynamic pressure implementation and closed-end buoyancy loading for the three Abaqus/Aqua wave options. A vertical pile is fully constrained and subjected to buoyancy loading. The Airy, Stokes, and gridded wave options are used to calculate the total reaction force on the structure during a direct-integration implicit dynamic analysis procedure. Distributed load type PB is used with a 50-element model, and concentrated load type TSB is used with a one-element model.

Model:

Height of the structure	175.0 (100.0 below and 75.0 above mean water elevation)
Pipe section data	r = 1.0, t = 0.25

Material:

Young's modulus

1 × 10⁶

Aqua – environment

Seabed elevation	100.0
Mean water elevation	1100.0
Gravitational constant	32.2
Fluid mass density	2.0

Results and discussion

The results agree well with the analytically determined peak total reaction force.

Input files

ep32pxx1.inp: Airy waves, PIPE31 elements.
ep23pxx2.inp: Stokes waves, PIPE22 elements.
ep32pxx3.inp: Gridded wave data with linear interpolation, PIPE31 elements.
ep23pxx3.inp: Gridded wave data with quadratic interpolation, PIPE22 elements.
pb_airy_p31_xpl.inp: Airy waves, PIPE31 elements in Abaqus/Explicit.
pb_airy_p21_xpl.inp: Airy waves, PIPE21 elements in Abaqus/Explicit.

Gridded wave file

Problem description

This problem illustrates the creation of the gridded wave file. The unformatted binary gridded wave files used in Dynamic pressure, closed-end buoyancy loads (ep32pxx3.inp and ep23pxx3.inp) are created from ASCII format files containing the gridded wave data using a Fortran program.

Results and discussion

The files gridwave_3d.binary and gridwave_2d.binary are created for use in Dynamic pressure, closed-end buoyancy loads.

Input files

gridwave_2d.inp: ASCII format file containing two-dimensional gridded wave data.
gridwave_3d.inp: ASCII format file containing three-dimensional gridded wave data.
gridfile_2d.f: Fortran program to convert the two-dimensional ASCII data file to a binary gridded wave file.
gridfile_3d.f: Fortran program to convert the three-dimensional ASCII data file to a binary gridded wave file.

Miscellaneous partial submergence tests for Stokes waves

Elements tested

B21

PIPE21

Problem description

This problem tests the implementation of the effective axial force output quantity ESF1. Coincident, one-element, vertical piles are partially submerged in a Stokes wave field such that the element integration points change between unsubmerged and submerged conditions during the analysis. The piles are fully constrained and subjected to distributed load type PB including internal fluid pressure. One pile is completely filled with internal fluid (Case A), and one is partially filled with internal fluid such that the element integration point is above the internal fluid free surface elevation (Case B). An amplitude variation is added to the distributed load definition in Cases A and B to produce, respectively, Cases C and D. Cases A and C use PIPE21 elements, and Cases B and D use B21 elements with general beam section to define the element properties. With the results from this analysis, the effective axial force output is tested using the postprocessing analysis procedure option.

Results and discussion

The effective axial force, ESF1, agrees with the analytical results for each case. The results are documented at the top of the xesf1gen.inp input file.

Input files

xesf1gen.inp: Input file for this analysis.
xesf1gep.inp: Input file that tests the postprocessing analysis procedure option.

Miscellaneous buoyancy loading

Elements tested

PIPE21

Problem description

This problem tests loading types PB and TSB when the fluid properties are prescribed as part of the loading. A general beam section procedure is used to describe the section properties.

Results and discussion

The results match the analytical solution.

Input files

pipepbtsb.inp: Input file for this analysis.