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7/21/2019 Basic Structural Nonlinearities - Nonlinear Stabilization
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© 2011 ANSYS, Inc. February 17, 20121
Lecture 5
Nonlinear Stabilization
ANSYS Mechanical
Basic Structural Nonlinearities
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© 2011 ANSYS, Inc. February 17, 20122
Chapter Overview
This Lecture will present the use of Nonlinear Stabilization to solve global and
local nonlinear buckling problems
• It is assumed that the user has already covered Lecture 2
The Specific
topics
introduced
are:
A. Background on unstable structures
B. Understanding Nonlinear Stabilization
C. Controlling the Stabilization Force
D. Stabilization Input
E. Reviewing Results
F. Workshop
The capabilities described in this Chapter are generally applicable to ANSYS
Structural licenses and above.
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• Many structures require an evaluation of their structural stability. Thin
columns, compression members, and vacuum tanks are all examples of
structures where stability considerations are important.
• The instability
could
be
global
(such
as
a snap
‐through)
or
local
(such
as
yielding
or buckling at a concentrated load or support).
• Instability problems usually pose convergence difficulties and therefore require
the application of special nonlinear techniques.
A. Background on Unstable Structures
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• At the onset of instability (buckling) a structure will have a very large change in
displacement { u} under essentially no change in the load (beyond a small load
perturbation).
... Background on Unstable Structures
F F
StableUnstable
u
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• Nonlinear stabilization can be understood as adding an artificial damper or
dashpot element at each structural element node
• The solver calculates a damping force (f d) proportional to the relative pseudo
velocity
of
the
two
nodes
of
the
artificial
dashpot
element. – The pseudo velocity is calculated as a displacement increment divided by the time
increment of the substep
B. Understanding Nonlinear Stabilization
F
f d
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© 2011 ANSYS, Inc. February 17, 20126
With this dashpot model in view:
• Any DOF that tends to be unstable has a large displacement increment causing
a large damping (stabilization) force; this force, in turn, reduces the
displacements at the DOF so that stabilization is achieved.
• For the DOFs that are stable, the dashpot elements have little effect on the
results because the displacements and the stabilization forces are small relative
to the physical forces.
• The
coefficient
used
to
calculate
the
stabilization
force
is
also
referred
to
as
the
“damping factor”.
– Although it has the same physical meaning and unit as physical damping, it is
purely numerical in nonlinear stabilization.
... Understanding Nonlinear Stabilization
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There are two methods available in Mechanical for controlling the stabilization
force
• Energy
• Damping
factor
calculated
automatically
• Factor can vary from element to element.
• Best suited for local instability (i.e. plasticity)
• Damping• User defines a damping factor directly.
• Same factor used for all applicable elements.
• Recommended when user has a specific damping
factor in
mind.
• For challenging nonlinear problems, it is sometimes helpful to employ both methods,
starting first with the Energy method and switching to the Damping method in a
subsequent restart
C. Controlling the Stabilization Force
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... Controlling the Stabilization Force
Energy Method
• Energy Dissipation Ratio
– Ratio of the work done by stabilization forces to the
element potential energy.
– Should be large enough to circumvent the
divergence, but small enough to avoid excessive
stiffness. (Typically between 0 and 1.0)
It is a good practice to examine the energies after the solution has completed
because the energy dissipation ratio of the solution could be greater than the
ratio initially specified.
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... Stabilization Input• There are also three activation options for
controlling stabilization for the first substep
- NO: Stabilization is not activated (Default)
-
ON
NONCONVERGENCE:
Activate
Stabilization
only
when min time increment is reached and the analysis
has still not converged
- YES: Activate Stabilization regardless of time
increment for first substep.
• In most well posed problems, no stabilization is necessary at first substep
because the structure is initially stable, assuming the time increment is
reasonable.
– Stabilization is designed to overcome physical instabilities (i.e. properly
constrained models that fail due to buckling and/or localized material
yielding). It will not resolve numerical instabilities associated with ill
conditioned matrices (poorly constrained structures).
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... Stabilization Input
• In addition, user can receive feedback on
magnitude of Stabilization Forces relative to the
overall imbalance forces
- When the L2‐norm of the stabilization force exceeds
the L2
‐norm
of
the
internal
force
multiplied
by
the
stabilization force coefficient, the Solver issues a
message displaying both the stabilization force norm
and the internal force norm. Refer to Section
15.13.2 of Theory Manual for detailed description of
L2‐norm
calculations.
- Default is 0.2 (=20%)
- The message is intended to alert user to the
presence of an excessive stabilization force in the
run.
- User can choose to tighten or loosen this tolerance
depending on the application
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E. Reviewing Results• When
Stabilization
has
been
activated,
it
is
always
a good
practice
to
determine
the extent of its influence on results accuracy
– One way to do this is to post process the Strain Energy of the system and compare it
to the “Stabilization Energy” created by the artificial damping introduced to bring
about convergence
– As a general rule, the stabilization energy should be small (<<10% of strain energy) in
comparison
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It is also helpful to examine the reaction forces and moments to gain an
understanding of how much Stabilization forces are introducing fictitious loads
into model
... Reviewing Results
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Summary
• Many structures require an evaluation of their structural stability.
• Instability problems usually pose convergence difficulties and therefore
require the application of special nonlinear techniques.
• Nonlinear stabilization
can
be
understood
as
adding
an
artificial
damper
or
dashpot element at each structural element node
• There are two methods available in WB‐Mechanical for controlling the
stabilization force, Energy and Damping.
• When Stabilization has been activated, it is always a good practice to
determine the extent of its influence on results accuracy by postprocessing
the stabilization energy and comparing with strain energy as well as
examining the force and moment reactions.
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... Workshop
Please refer to your Workshop Supplement for instructions on:
W5A‐ PostBuckling with Stabilization