Papers on the Theory used in ADINA
The
Finite Element Method
Bathe,
Klaus-Jürgen. Source: Chapter in
Wiley Encyclopedia of Computer Science and Engineering,
B.W. Wah (ed.), Dec 2008.
ISBN:
978-0-471-38393-2
Publisher:
John Wiley and Sons, Ltd
Abstract: The objective of this article is to give an overview
of finite element methods that are currently used extensively in academia and industry.
The method is described in rather general terms, the basic formulation is presented,
and some issues regarding effective finite element procedures are summarized. Various
applications are briefly given to illustrate the current use of the method. Finally,
the article concludes with key challenges for the further development of the method.
Keywords:
finite element method, structures, CFD, FSI, shells, meshing, mesh-glueing, locking, CAD,
error estimation
On
Finite Element Methods for Nonlinear Dynamic Response
Bathe,
Klaus-Jürgen. Source: Proceedings EURODYN 2008, Southampton, July 2008, M.J. Brennan (ed.)
Abstract: In this paper we briefly focus on the nonlinear analysis
of solids and structures when these undergo large deformations, possibly over long time
durations, and perhaps subjected to fluid-structure interactions. The analysis should be
conducted with finite element methods, including the time integration, that are reliable
and effective. The requirement of reliability is particularly important in nonlinear
finite element analysis because physical test data are frequently not available.
ISBN: 978-0-854-32882-6
Publisher: Institute of Sound and Vibration Research, University of Southampton, UK
Keywords:
finite element method, solids, structures, dynamics, time integration, FSI
A
4-node 3D-Shell Element to Model Shell Surface Tractions and
Incompressible Behavior
Kim,
Do-Nyun; Bathe, Klaus-Jürgen. Source: Computers &
Structures, in press.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher:
Elsevier Ltd
Abstract: We present in this paper a shell element that models
the three-dimensional (3D) effects of surface tractions, like needed when a shell
is confined between other solid media. The element is the widely used MITC4 shell
element enriched by the use of a fully 3D stress-strain description, appropriate
through-the-thickness displacements to model surface tractions, and pressure degrees
of freedom for incompressible analyses. The element formulation avoids instabilities
and ill-conditioning. Various example solutions are presented to illustrate the
capabilities of the element.
Keywords: shells, MITC4 element, 3D-shell model, surface tractions,
incompressible analysis, ill-conditioning
A
Model of Incompressible Isotropic Hyperelastic Material Behavior
using Spline Interpolations of Tension-Compression Test Data
Sussman,
Theodore; Bathe, Klaus-Jürgen. Source:
Communications in Numerical Methods in Engineering, in press.
ISSN:
1069-8299 (print); 1099-0887 (online)
Publisher:
John Wiley & Sons, Ltd.
Abstract: We present a model of incompressible isotropic hyperelastic
material behavior based on a strain energy description separable in terms of logarithmic
strains and piecewise spline interpolations of uniaxial tension-compression test data.
Valuable attributes are that no fitting of model constants is carried out and the model
replicates even physically complicated test data very accurately for small and large
strains and for tension and compression. The model is well suited for use in finite
element analysis.
Keywords: material modeling, finite element analysis, incompressible
materials, hyperelasticity, rubber-like materials
Benchmark
Problems for Incompressible Fluid Flows with Structural Interactions
Bathe,
Klaus-Jürgen; Ledezma, G. A. Source: Computers & Structures, v 85,
628-644, 2007
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher:
Elsevier Ltd
Abstract:
Various methods of analysis for the solution of fluid flows with
structural interactions have been proposed in the literature, and new
techniques are being developed. In these endeavors, to advance the
field, thorough evaluations of the procedures are necessary. To help
in establishing such evaluations, we present in this paper the
solutions of some benchmark problems. The results can be used to
evaluate existing and new formulations of incompressible fluid flows
with structural interactions.
Keywords:
incompressible fluid flows, Navier-Stokes equations, fluid-structure
interactions, benchmark problems, ADINA
Conserving
Energy and Momentum in Nonlinear Dynamics: A Simple Implicit Time
Integration Scheme
Bathe,
Klaus-Jürgen. Source: Computers & Structures, v 85, 437-445, 2007
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher:
Elsevier Ltd
Abstract:
We focus
on a simple implicit time integration scheme for the transient
response solution of structures when large deformations and long time
durations are considered. Our aim is to have a practical method of
implicit time integration for analyses in which the widely used
Newmark time integration procedure is not conserving energy and
momentum, and is unstable. The method of time integration discussed
in this paper is performing well and is a good candidate for
practical analyses.
Keywords:
nonlinear dynamics, implicit time integration, conservation of
momentum and energy, trapezoidal rule, composite scheme
Insight
into 3-node Triangular Shell Finite Elements: the Effects of Element
Isotropy and Mesh Patterns
Lee, Phill-Seung; Noh, Hyuk-Chun; Bathe,
Klaus-Jürgen. Source: Computers & Structures, v 85,
404-418, 2007.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher:
Elsevier Ltd
Abstract:
In this paper, we study the convergence characteristics of some
3-node triangular shell finite elements. We review the formulations
of three different isotropic 3-node elements and one non-isotropic
3-node element. We analyze a clamped plate problem and a hyperboloid
shell problem using various mesh topologies and present the
convergence curves using the s-norm. Considering simple bending
tests, we also study the transverse shear strain fields of the shell
finite elements. The results and insight given are valuable for the
proper use and the further development of triangular shell finite
elements.
Keywords:
shell structures, finite elements, triangular elements, MITC elements
The
CIP Method Embedded in Finite Element Discretizations of
Incompressible Flows
Banijamali,
Bahareh; Bathe,
Klaus-Jürgen. Source: Int. J. for Numerical Methods in Eng., v
71, 66-80, 2007.
ISSN:
0029-5981 CODEN: IJNMBH
Publisher:
John Wiley & Sons, Ltd.
Abstract: Quite
effective low-order finite element and finite volume methods for
incompressible fluid flows have been established and are widely used.
However, higher-order finite element methods that are stable, have
high accuracy and are computationally efficient are still sought.
Such discretization schemes could be particularly useful to establish
error estimates in numerical solutions of fluid flows. The objective
of this paper is to report on a study in which the cubic interpolated
polynomial (CIP) method is embedded into 4-node and 9-node finite
element discrefizations of 2D flows in order to stabilize the
convective terms. To illustrate the capabilities of the formulations,
the results obtained in the solution of the driven flow square cavity
problem are given.
Keywords:
incompressible flows, finite element discretization, CIP technique,
FCBI approach
A
Nine-node Quadrilateral FCBI Element for Incompressible Navier-Stokes
Flows
Kohno,
Haruhiko; Bathe, Klaus-Jürgen. Source: Comm. in Num. Methods in
Eng., v 22, 917-931, 2006.
ISSN:
1069-8299 (print); 1099-0887 (online)
Publisher:
John Wiley & Sons, Ltd.
Abstract:
We propose a nine-node flow-condition-based interpolation (FCBI)
finite element for the analysis of 2D incompressible flows. Emphasis
in the FCBI approach is on obtaining an element that is stable and
can be used in rather coarse meshes even when considering high
Reynolds number flows. The formulation of the element is presented
and the results obtained in the solution of some test cases are
given.
Keywords:
incompressible flows, flow-condition-based interpolation, FCBI
approach
On
a Composite Implicit Time Integration Procedure for Nonlinear
Dynamics
Bathe,
Klaus-Jürgen; Baig, M. M. I. Source: Computers & Structures, v 83, 2513 –
2534, 2005.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher:
Elsevier Ltd
Abstract: Transient
analysis of nonlinear problems in structural and solid mechanics is
mainly carried out using direct time integration of the equations of
motion. For reliable solutions, a stable and efficient integration
algorithm is desirable. Methods that are unconditionally stable in
linear analyses appear to be a natural choice for use in nonlinear
analyses, but unfortunately may not remain stable for a given time
step size in large deformation and long time range response
solutions. A composite time integration scheme is proposed and tested
in some example solutions against the trapezoidal rule and the Wilson
theta-method, and found to be effective where the trapezoidal rule
fails to produce a stable solution. These example results are
indicative of the merits of the composite scheme.
Keywords:
finite element method, composite integration, trapezoidal rule
A
Flow-Condition-Based Interpolation Finite Element Procedure for
Triangular Grids
Kohno,
Haruhiko;
Bathe, Klaus-Jürgen. Source: Int. J. Num. Meth. in Fluids, v
51, 673-699, 2006.
ISSN:
0271-2091 (print); 1097-0363 (online)
Publisher:
John Wiley & Sons, Ltd.
Abstract:
A flow-condition-based interpolation finite element scheme is
presented for use of triangular grids in the solution of the
incompressible Navier-Stokes equations. The method provides spatially
isotropic discretizations for low and high Reynolds number flows.
Various example solutions are given to illustrate the capabilities of
the procedure.
Keywords:
incompressible flows, stability,
accuracy, flow-condition-based interpolation
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