Aqua load cases

This problem contains basic test cases for one or more Abaqus elements and features.

This page discusses:

ProductsAbaqus/StandardAbaqus/ExplicitAbaqus/Aqua

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:

  1. Buoyancy, PB.

  2. Normal drag, static, FDD.

  3. Tangential drag, static, FDT.

  4. Normal drag, dynamic, FDD.

  5. Tangential drag, dynamic, FDT.

  6. Inertial drag, FI.

  7. Normal drag, dynamic, partial immersion, FDD.

  8. End-drag, dynamic, FD1, FD2.

  9. End-drag, dynamic, TFD (concentrated load).

  10. Inertial end-drag, FI1, FI2.

  11. Inertial end-drag, TSI (concentrated load).

  12. Transition-section buoyancy, TSB.

  13. End-drag, dynamic, (additional test), FD1, FD2.

  14. End-drag, dynamic, (additional test), TFD (concentrated load).

  15. Wind-drag, dynamic, WDD.

  16. Wind end-drag, dynamic, WD1, WD2.

  17. 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 102
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
(vx,vy, elevation) (2.0, 1.0, 0.0)
(vx,vy, elevation) (2.0, 1.0, 2000.0)
Steady velocity specification: three-dimensional
(vx, vz, elevation) (2.0, 1.0, 0.0)
(vx, vz, elevation) (2.0, 1.0, 2000.0)
(vy = 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:

  1. Static analysis with drag load FDD and no wave loads.

  2. Static analysis: dummy step to zero out the loads.

  3. 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
(vx, vy, vz, elevation) (1.0, 0.0, 0.0, 0.0)
(vx, vy, vz, 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.

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.

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 vf 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

(vx, vy, vz, x-coord.) (1vf, 0.0, 0.0, 100.0)
(vx, vy, vz, x-coord.) (3vf, 0.0, 0.0, 300.0)
(vx, vy, vz, x-coord.) (3vf, 0.0, 0.0, 600.0)
(vx, vy, vz, x-coord.) (0vf, 0.0, 0.0, 900.0)

Steady velocity specification: three-dimensional case

(vx, vy, vz, x-coord., y-coord.) (2vf, 0.0, 0.0, 100.0, 200.0)
(vx, vy, vz, x-coord., y-coord.) (6vf, 0.0, 0.0, 300.0, 200.0)
(vx, vy, vz, x-coord., y-coord.) (6vf, 0.0, 0.0, 600.0, 200.0)
(vx, vy, vz, x-coord., y-coord.) (0vf, 0.0, 0.0, 900.0, 200.0)
(vx, vy, vz, x-coord., y-coord.) (1vf, 0.0, 0.0, 100.0, 800.0)
(vx, vy, vz, x-coord., y-coord.) (3vf, 0.0, 0.0, 300.0, 800.0)
(vx, vy, vz, x-coord., y-coord.) (3vf, 0.0, 0.0, 600.0, 800.0)
(vx, vy, vz, x-coord., y-coord.) (0vf, 0.0, 0.0, 900.0, 800.0)

Results and discussion

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

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.

Gridded wave file

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.