Papers on the Theory used in ADINA
Some
Advances in the Analysis of Fluid Flows
Bathe,
Klaus-Jürgen; Zhang, Hou; Zhang, Xiaoli. Source: Computers & Structures,
v 64, no. 5/6, 909-930, 1997.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher:
Elsevier Ltd
Abstract:
We review
some new solution capabilities developed and available in the ADINA-F
CFD (computational fluid dynamics) program and present example
solutions. Unique features and advances are that incompressible and
compressible flows with structural interactions can be analyzed and
that a general radiation heat transfer analysis capability based on
specular and diffusive reflectivities and transmittance is available.
This paper is largely a continuation of the presentation given in
Ref. [1].
Keywords:
incompressible flow, compressible flow, CFD, ADINA, fluid structure
interaction; FSI
Advances
in Nonlinear Finite Element Analysis of Automobiles
Bathe,
Klaus-Jürgen; Guillermin, Olivier; Walczak, Jan; Chen, Heng-Yee. Source:
Computers & Structures, v 64, no., 5/6, 881-891, 1997.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher:
Elsevier Ltd
Abstract:
The
objective in this paper is to present some recent advances for the
finite element analysis of automobile structures. These advances
pertain to the development of effective basic finite element
procedures and the efficient solution of large systems of equations.
With these new procedures, it is possible to model much more
accurately (and reliably) the actual nonlinear physical behavior of
complex structures. The illustrative solutions given in the paper
include the solution of a roof-crush problem that was solved
appropriately, according to the actual physical situation, using
implicit time integration (resulting practically in a static
analysis).
Keywords:
finite element analysis, automobile, roof crush
On
Evaluating the Inf-Sup Condition for Plate Bending Elements
Iosilevich,
Alexander;
Bathe, Klaus-Jürgen; Brezzi, Franco. Source: Int. Journal for
Numerical Methods in Engineering, v 40, 3639-3663, 1997.
ISSN:
0029-5981 CODEN: IJNMBH
Publisher:
John Wiley & Sons, Ltd.
Abstract:
This
paper addresses the evaluation of the inf-sup condition for
Reissner-Mindlin plate bending elements. This fundamental condition
for stability and optimality of a mixed finite element scheme is, in
general, very difficult to evaluate analytically, considering for
example distorted meshes. Therefore, we develop a numerical test
methodology. To demonstrate the test methodology and to obtain
specific results, we apply it to standard displacement-based elements
and elements of the MITC family. Whereas the displacement-based
elements fail to satisfy the inf-sup condition, we fmd that the MITC
elements pass our numerical test for uniform meshes and a sequence of
distorted meshes.
Keywords:
Reissner-Mindlin plate elements, inf-sup condition
Displacement/Pressure
Based Mixed Finite Element Formulations for Acoustic Fluid-Structure
Interaction Problems
Wang,
Xiaodong; Bathe, Klaus-Jürgen. Source: Int. Journal for
Numerical Methods in Engineering, v 40, 2001-2017, 1997.
ISSN:
0029-5981 CODEN: IJNMBH
Publisher:
John Wiley & Sons, Ltd.
Abstract:
We
present reliable finite element discretizations based on
displacement/pressure interpolations for the analysis of acoustic
fluid-structure interaction problems. The finite element
interpolations are selected using the inf-sup condition, and emphasis
is given to the fact that the boundary conditions must satisfy the
mass and momentum conservation. We show that with our analysis
procedure no spurious non-zero frequencies are encountered, as
heretofore calculated with other displacement-based discretizations.
Keywords:
acoustic fluid, fluid structure interaction, mixed finite element
formulation, inf-sup condition
On
Mixed Elements for Acoustic Fluid-Structure Interactions
Wang,
Xiaodong; Bathe, Klaus-Jürgen. Source: Mathematical Models &
Methods in Applied Sciences, v 7, no. 3, 329-343, 1997.
ISSN:
0218-2025
Publisher:
World Scientific Publishing Company
Abstract:
In this
paper we investigate the performance of some mixed finite elements
used in the displacement/pressure (u/p) and
displacement-pressure-vorticity moment (u-p-Lambda) formulations for
acoustic fluid-structure interactions. In particular, we show that
certain elements pass a numerical inf-sup test and are valuable for
general applications. Also considered are macroelements that are
based on simple four-node elements.
Keywords:
fluid structure interaction, mixed finite element, inf-sup test
Finite
Element Analysis of Shell Structures
Bucalem,
Miguel Luiz; Bathe, Klaus-Jürgen. Source: Archives of
Computational Methods in Engineering, v 4, 3-61, 1997.
ISSN:
1134-3060 (print); 1886-1784 (online)
Publisher:
Springer
Abstract:
A survey
of effective finite element formulations for the analysis of shell
structures is presented. First, the: basic requirements for shell
elements are discussed, in which it is emphasized that generality and
reliability are most important items. A general displacement-based
formulation is then briefly reviewed. This formulation is not
effective., but it is used as a starting point for developing a
general and effective approach using the mixed interpolation of the
tensorial components. The formulation of various MITC elements (that
is, elements based on Mixed Interpolation of Tensorial Components)
are presented. Theoretical results (applicable to plate analysis) and
various numerical results of analyses of plates and shells are
summarized. These illustrate some current capabilities and the
potential for further finite element developments.
Keywords:
Mixed
Interpolation of Tensorial Components
A
Four-Node Quadrilateral Mixed-Interpolated Element for Solids and
Fluids
Pantuso,
Daniel; Bathe, Klaus-Jürgen. Source: Mathematical Models and
Methods in Applied Sciences, v 5, No. 8, 1113-1128, 1995.
ISSN:
0218-2025
Publisher:
World Scientific Publishing Company
Abstract:
A
four-node quadrilateral element is presented which shows promise for
general compressible and incompressible two-dimensional analysis of
solids and fluids. The element is based on a mixed interpolation of
displacements (velocities), pressure and strains (velocity strains).
We show that the element satisfies a numerical inf-sup test, and give
results of some analysis problems that demonstrate the capabilities
of the element.
Keywords:mixed-interpolated
element, inf-sup test
Some
Computational Issues in Large Strain Elasto-Plastic Analysis
G.
Gabriel; Bathe, Klaus-Jürgen . Source: Computers &
Structures, v 56, No. 2/3, pp. 249-267, 1995.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher:
Elsevier Ltd
Abstract:
The stress integration procedure proposed by Eterovic and Bathe [Int.
J. numer. Meth. Engng 30,
1099–1114 (1990).] is studied in detail. The elasto-plasticity
formulation is based on the use of the total logarithmic strains
and Cauchy stresses, and the Euler backward method of time
integration. The accuracy of the procedure is assessed in the
solution of various analysis
problems and is compared with the accuracy of other schemes. Two
important conclusions are reached. First, for a selected level of
accuracy, the use of the total strain
formulation, in general, allows larger
time steps than the use of a stress-rate based formulation (such as a
formulation based on the Jaumann stress rate). Second, the original
procedure of Eterovic and Bathe can be improved in accuracy by using
the trapezoidal rule with a measure to limit the magnitude of the
elasto-plastic
strain
increment per step. This improvement allows for the change of
principal stress directions during the incremental step. This
capability seems to be unique to this formulation and time
integration.
Keywords:
stress integration, large strain analysis, elasto-plastic
A
Mixed Displacement-Based Finite Element Formulation for Acoustic
Fluid-Structure Interaction
Bathe,
Klaus-Jürgen; Nitikitpaiboon, C; and Wang, Xiaodong. Source: Computers &
Structures, v 56, No. 2/3, 225-237, 1995.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher:
Elsevier Ltd
Abstract:
The
solutions of fluid-structure interaction problems, using
displacement-based finite element formulations for acoustic fluids,
may contain spurious non-zero frequencies. To remove this deficiency,
we present here a new formulation based on a three-field
discretization using displacements, pressure and a ''vorticity
moment'' as variables with an appropriate treatment of the boundary
conditions. We propose specific finite element discretizations and
give the numerical results of various example problems.
Keywords:
fluid structure interaction, mixed finite element
Finite
Element Analysis of Incompressible and Compressible Fluid Flows with
Free Surfaces and Structural Interactions
Bathe,
Klaus-Jürgen; Zhang, Hou; Wang, M. H. Source: Computers & Structures, v
56, No. 2/3, 193-213, 1995.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher:
Elsevier Ltd
Abstract:
We
present the current ADINA-F capabilities for fluid flow analysis. The
fluid can be considered to be an incompressible or compressible
medium. Free surfaces and the full interactions with structures in
two- and three-dimensional conditions can be analyzed. The basic
formulations and finite element discretizations used are described,
the techniques for the solution of the finite element equations are
briefly discussed, and the results of various demonstrative analyses
are given.
Keywords:
finite element, fluid structure interaction
An
Iterative Finite Element Procedure for the Analysis of Piezoelectric
Continua
Gaudenzi,
P; Bathe, Klaus-Jürgen. Source: J. of Intelligent Material
Systems and Structures, v 6, No. 2, 266-273, 1995.
ISSN:
1045-389X (print); 1530-8138 (online)
Publisher:
SAGE Publications
Abstract:
In this
paper an iterative finite element procedure is presented for the
analysis of two-and three-dimensional piezoelectric continua. The
procedure is applied to the steady-state analysis of two-dimensional
media subjected to mechanical and electrical loading.
Keywords:
piezoelectric continua, finite element
Error
Indicators and Adaptive Remeshing in Large Deformation Finite Element
Analysis
Lee,
Nam-Sua; Bathe, Klaus-Jürgen. Source: Finite Elements in
Analysis and Design, v 16, 99-139, 1994
ISSN:
0168-874X
Publisher:
Elsevier Science Publishers B. V.
Abstract:
We present and use a system of adaptive
procedures for large-deformation
finite element analysis
of elastic and elastoplastic problems using the h-refinement
approach. The procedures include a pointwise indicator
for error
in stresses, a pointwise indicator
for error
in plastic strain increments, a quadrilateral element
mesh generator for generating completely new meshes on the deformed
configuration of the body, and several mapping schemes for
transferring state variables and history-dependent variables
accurately across models. These procedures constitute the ingredients
of a proposed adaptive
scheme that is demonstrated to be effective in solutions of
two-dimensional stress analysis
problems including contact conditions. An important observation is
that with coarse finite
element
meshes and no error
indicator
used, crucial physical phenomena may be completely missed in the
analysis.
Keywords:
error indicator, adaptive remeshing, finite element
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