reads deformation fields and matrices that have been generated by preceding nonlinear
procedures and, optionally, modes that have been generated by preceding natural frequency
extraction procedures;
computes a set of basis vectors that reproduce the nonlinear deformation fields and the
natural frequency modes when superimposed;
projects the operator data from the preceding nonlinear procedures onto the reduced
basis; and
writes the reduced basis and the projected operators to a
SIM document and optionally to a nonlinear flexible body
input file for use in the Simpack flexible body dynamics solver.
The term reduced basis refers to a set of basis vectors that might represent a set of
nonlinear deformation fields from preceding procedures when superimposed with appropriate
scaling factors. Such deformation fields might have been computed, for example, from ramping
up a load that acts on a finite element model in a nonlinear static analysis. Optionally,
the reduced basis can also represent a set of modes that might have been computed from one
or more natural frequency extraction procedures with varying predeformation. A reduced basis
can be used, for example, with hyperreduction analysis techniques or to set up a nonlinear
flexible body for use in the Simpack flexible body dynamics solver. Compared to the original finite element model, such
analysis techniques allow for a reduction of the computation time by several orders of
magnitude for nonlinear static or dynamic scenarios.
Generating Reduced Bases
As input data, the reduced basis generation procedure collects nonlinear deformation fields
and matrices from the generated SIM documents. It then
computes an initial set of orthonormal basis vectors, utilizing a singular value
decomposition of the nonlinear deformation fields. The singular value that is associated
with every basis vector determines if the basis vector is retained: Starting with the
smallest singular value, basis vectors are neglected until the sum of the associated
singular values exceeds a specified fraction of the overall sum. By default, this fraction
is 10−4.
Optionally, you can use the reduced basis generation procedure to collect the modes that
have been computed by preceding natural frequency extraction procedures. It then computes
additional basis vectors by means of a second singular value decomposition. By default,
basis vectors that are associated with the same fraction of the sum of singular values are
neglected as for the first singular value decomposition. The remaining basis vectors are
orthonormalized with respect to the first set of basis vectors. The first set of basis
vectors and the resulting residual vectors are then combined. If the
SIM documents from the preceding nonlinear procedures
contain the mass matrix of the undeformed finite element model, all basis vectors are
orthonormalized with respect to that mass matrix.
Finally, the reduced basis generation procedure projects all the matrices that are
contained in the binary SIM files from the preceding
nonlinear procedures onto the reduced basis.Abaqus/Standard stores the reduced basis and the projected operators in a new
SIM document. By default, this file is named
jobname_RBn.sim,
where jobname is the name of the input file or analysis job and
n is the number of the Abaqus step that generates the reduced basis.
Input File Usage
Use the following options to specify the reduced basis generation:
Use the following options to consider natural frequency modes for the reduced basis
generation:
** Natural frequency extraction (undeformed finite element model)
STEP, PERTURBATIONFREQUENCY
…
END STEP
** Nonlinear procedure with the operator output option (first deformation step)
STEP, NLGEOM=YESSTATIC
…
OPERATOR OUTPUT, NUMBER INTERVAL=1, SOLUTION, …
END STEP
** Natural frequency extraction (predeformed finite element model)
…
** Further alternating nonlinear procedures and natural frequency extractions
…
** Reduced basis generation procedure
STEPREDUCED BASIS GENERATE
fractions of the sums of singular values to neglect (nonlinear deformation fields, natural frequency modes)
SELECT EIGENMODES
modes to be considered from every one of the preceding natural frequency extractions
END STEP
Use the following option to specify the name of the file that the reduced basis
generation procedure creates:
Optionally, you can use the reduced basis generation procedure to generate a flexible body
input .fbi file for use in the Simpack flexible body dynamics solver. In Simpack, you can assign the .fbi file directly to a nonlinear flexible
body.
Input File Usage
Use the following options to generate a nonlinear flexible body input file:
To achieve good performance of downstream simulations in Simpack in terms of result accuracy and computation times, the reduced basis generation should
fulfill the following requirements:
In the assembled system, the nonlinear flexible body has one characteristic large and
nonlinear deformation shape. Usually, this deformation shape corresponds to a
compliant loading direction. For example, this might be the bending of a wind turbine
rotor blade in the flap-wise direction or the torsion of a twist beam in the rear axle
of a car assembly during a lane change maneuver at high speeds.
Abaqus generates nonlinear deformation fields and matrices for the compliant loading
direction by one or more nonlinear static procedures. When you define the loads and
boundary conditions for this procedure, it might be necessary to constrain the rigid
motion of the finite element model by adding appropriate connector elements and
constraints. In such cases, exclude the additional connector elements from the
operator output by specifying appropriate node and element sets that include only the
bare finite element model. In any case, you should exclude the boundary conditions
from the operator output.
The load and solution vectors, the mass matrix, the stiffness matrix, and the free
body response vector are generated and output from the nonlinear static procedures at
various deformation levels. Because only the mass matrix for the undeformed finite
element model is required, you need to output it only from the procedure that starts
from or ends with the undeformed model.
Natural frequency modes are computed for a sufficient number of deformation levels.
This is achieved by ramping up the load in the compliant direction of the model
step-by-step with multiple subsequent nonlinear static procedures. Between every two
such procedures, perform a natural frequency extraction. In addition, perform a
natural frequency extraction before the first and after the last nonlinear static
procedure. Typically, you need approximately 40 to 60 alternating nonlinear static
procedures and natural frequency extractions. The operator output is required only for
the last increment in every nonlinear static procedure.
The fractions of the sum of singular values to neglect are configured such that fewer
than 10 basis vectors are needed to represent the nonlinear deformation fields and
approximately 10 to 100 additional basis vectors are needed to represent the natural
frequency modes of the undeformed and the deformed finite element model are retained.
Typical values for such fractions lie in a range between 10−3 and
10−5.
Input File Usage
Use the following options to exclude boundary conditions and other auxiliary
elements that serve to constrain rigid motion during operator generation:
OPERATOR OUTPUT, NSET=name of set that contains all nodes of the bare finite element model, ELSET=name of set that contains all elements of the bare finite element model, BOUNDARY CONDITIONS=NO, ...
Use the following options to generate load, solution, mass, stiffness, and free body
response operators:
OPERATOR OUTPUT, LOAD, SOLUTION, MASS, STIFFNESS, FREE BODY RESPONSE, …
Use the following options to output operators only during the last increment when
using alternating nonlinear static procedures and natural frequency extractions:
Use the following options to specify the fractions of the sum of singular values to
neglect during reduced basis generation:
REDUCED BASIS GENERATE
fraction of singular value sum to neglect (solution vectors), fraction of singular value sum to neglect (eigenmode shapes)
Generating the Reduced Basis Using the Restart Capability
You can generate the reduced basis in the same job that contains the nonlinear procedures
and the natural frequency extractions. Alternatively, you can use the restart capability. In
that case, the job that generates the reduced basis must restart from the job that contains
the last nonlinear procedure or natural frequency extraction. To consider natural frequency
modes, request the generation of data for the restart analysis in all the natural frequency
extraction procedures.
Input File Usage
To consider natural frequency modes for the reduced basis generation, use the
following options to generate the data for the restart analysis in the first job (and in
all subsequent jobs):
** Natural frequency extraction (undeformed finite element model)
STEP, PERTURBATIONFREQUENCY
…
RESTART, WRITEEND STEP
** Nonlinear static procedure (first deformation step)
STEP, NLGEOM=YESSTATIC
…
OPERATOR OUTPUT, NUMBER INTERVAL=1, SOLUTION, …
END STEP
** Natural frequency extraction (predeformed finite element model)
…
** Further alternating nonlinear static procedures and natural frequency extractions
…
Specify all alternating nonlinear procedures and natural frequency extractions in the
first job, or split them into a number of subsequent jobs using the restart capability, as
appropriate. Use the following options to generate the reduced basis in the job that
restarts from the last of the preceding jobs: