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Improved numerical dissipation for time integration algorithms in structural dynamics

TLDR
In this article, a new family of unconditionally stable one-step methods for the direct integration of the equations of structural dynamics is introduced and is shown to possess improved algorithmic damping properties which can be continuously controlled.
Abstract
A new family of unconditionally stable one-step methods for the direct integration of the equations of structural dynamics is introduced and is shown to possess improved algorithmic damping properties which can be continuously controlled. The new methods are compared with members of the Newmark family, and the Houbolt and Wilson methods.

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Lawrence Berkeley National Laboratory
Recent Work
Title
IMPROVED NUMERICAL DISSIPATION FOR TIME INTEGRATION ALGORITHMS IN STRUCTURAL
DYNAMICS
Permalink
https://escholarship.org/uc/item/18z548gt
Author
Hilber, Hans M.
Publication Date
1976-04-01
eScholarship.org Powered by the California Digital Library
University of California

-.
u u
Submitted
to
Earthquake
Engineering
and
Structural
Dynamics
LBL-4486
Preprint
C.
IMPROVED
NUMERICAL
DISSIPATION
FOR
TIME
INTEGRATION
ALGORITHMS
IN
STRUCTURAL
DYNAMICS
Hans
M.
Hilber,
Thomas
J.
R.
Hughes,
and
Robert
L.
Taylor
April
1976
Prepared
for
the
U.
S.
Energy
Research
and
Development
Administration
under
Contract
W
-7405-ENG
-48
For
Reference
Not
to
be taken from this
.room

DISCLAIMER
This document was prepared
as
an account
of
work sponsored
by
the United States
Government. While this document is believed to contain correct information, neither the
United States Government nor any agency thereof, nor the Regents
of
the University of
California, nor any
of
their employees, makes any warranty, express or implied, or
assumes any legal responsibility for the accuracy, completeness, or usefulness
of
any
information, apparatus, product, or process disclosed, or represents that its use would not
infringe privately owned rights. Reference herein to any specific commercial product,
process, or service
by
its trade name, trademark, manufacturer, or otherwise, does not
necessarily constitute or imply its endorsement, recommendation, or favoring by the
United
States Government or any agency thereof, or the Regents
of
the University
of
Califomia. The views and opinions
of
authors expressed herein do not necessarily state or
reflect those
of
the United States Government or any agency thereof or the Regents
of
the
University
of
California.

(
*
0 0
0
IMPROVED
NUMERICAL
DISSIPATION
FOR
TIME
INTEGRATION
. *
ALGORITHMS
IN
STRUCTURAL
DYNAMICS
Hans
M.
Hilber
Thomas
J.
R.
Hughes
Robert
L.
Taylor
Division
of
Structural
Engineering
and
Structural
Mechanics
Department
of
Civil
Engineering
and
Lawrence
Berkeley
Laboratory
University
of
California
Berkeley,
California
94720
April
1976
This
work
was
supported
in
part
by
the
U.
S.
Energy
Research
and
Development
Administration

o
u o
~
4 o
ABSTRACT
A new
family
of
unconditionally
stable
one-step
methods
for
the
direct
integration
of
the
equations
of
structural
dynamics
is
introduced
and
is
shown
to
possess
improved
algorithmic
damping
properties
which
can
be
continuously
controlled.
The new
methods
are
compared
with
members
of
the
Newmark
family,
and
the
Houbolt.
and
Wilson
methods.
i.

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A stabilised Petrov-Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics

TL;DR: This formulation is further enhanced for nearly and truly incompressible deformations with three key novelties, including a new conservation law for the Jacobian of the deformation is added into the system providing extra flexibility to the scheme.
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The Bathe time integration method revisited for prescribing desired numerical dissipation

TL;DR: In this article, the 3-point trapezoidal rule for the complete step with two Newmark parameters is used to smoothly prescribe desired numerical dissipation, from zero to very significant dissipation.
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Energy consistent algorithms for frictional contact problems

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References
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Journal ArticleDOI

A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft

TL;DR: A systematic procedure is developed for the calculation of the structural response of an airplane subject to dynamic loads, with particular attention given to determining the stresses developed due to flight through gusts.
Journal ArticleDOI

Stability and accuracy analysis of direct integration methods

TL;DR: In this article, a systematic procedure for the stability and accuracy analysis of direct integration methods in structural dynamics is presented, and the specific methods studied are the Newmark generalized acceleration scheme, the Houbolt method and the Wilson θ-method.
Journal ArticleDOI

Evaluation of numerical integration methods in elastodynamics

TL;DR: In this paper, the Newmark family of second-order difference approximations is compared with the original or extended Wilson and Houboult methods for the direct time integration of the spatially discretized equations of linear elastodynamics.
Journal ArticleDOI

Transient shell response by numerical time integration

TL;DR: In this paper, the authors show that the conditionally stable explicit schemes and the unconditionally stable implicit schemes can be divided into two classes: the conditionably stable explicit and implicit schemes.