Basic Structural Nonlinearities - Nonlinear Stabilization

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© 2011 ANSYS, Inc. February 17, 20121

Lecture 5

Nonlinear Stabilization

ANSYS Mechanical

Basic Structural Nonlinearities




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.




• 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




• 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




• 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




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




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




... 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.




... 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).




... 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




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




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




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.




... Workshop

Please refer to your Workshop Supplement for instructions on:

W5A‐ PostBuckling with Stabilization

Basic Structural Nonlinearities - Nonlinear Stabilization

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