Papers on the Theory used in ADINA
Towards Improving
the MITC9 Shell Element
Bathe,
Klaus-Jürgen; Lee, Phill-Seung;
Hiller, Jean-François;
Source: Computers & Structures, v 81, 477-489, 2003.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Abstract: Our objective
in this paper is to present some results regarding the predictive
capabilities of the MITC9 shell element when the tying points in the
element are changed. The MITC9 element is a general nine-node shell
element based on the formulation approach of using mixed-interpolated
tensorial components. Different tying points are very simple to
implement and are not decreasing the computational efficiency of the
element. Hence, the use of the “best” tying points is
clearly of value.
Keywords: MITC9 shell
element, mixed-interpolated tensorial components, tying points
Measuring
Convergence of Mixed Finite Element Discretizations: An Application
to Shell Structures
Hiller,Jean-François;
Bathe, Klaus-Jürgen. Source: Computers & Structures, v 81,
639-654, 2003.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Abstract:
We
consider the problem of assessing the convergence of mixed-formulated
finite elements. When displacement-based formulations are considered,
convergence measures of finite element solutions to the exact
solution of the mathematical problem are well known. However when
mixed formulations are considered, there is no well-established
method to measure the convergence of the finite element solution. We
first review a number of approaches that have been employed and
discuss their limitations. After having stated the properties that an
ideal error measure would possess, we introduce a new physics-based
procedure. The new proposed error measure can be used for many
different types of mixed formulations and physical problems. We
illustrate its use in an assessment of the performance of the MITC
family of shell elements.
Keywords:
mixed-formulated
finite elements, error measure, MITC shell elements
A Shell Problem
‘Highly-Sensitive’ to Thickness Changes
Bathe,
Klaus-Jürgen; Chapelle, Dominique; Lee, Phill-Seung.
Source: Int. J. for Numerical Methods in Eng., v 57, 1039-1052, 2003.
ISSN:
0029-5981 CODEN: IJNMBH
Publisher:
John Wiley & Sons, Ltd
Abstract:
In
general, shell structural problems can be identified to fall into one
of the categories of membrane-dominated, bending-dominated and mixed
shell problems. The asymptotic behaviour with a well-defined
load-scaling factor shows distinctly into which category a given
shell problem falls. The objective of this paper is to present a
shell problem and its solution for which there is no convergence to a
well-defined load-scaling factor as the thickness of the shell
decreases. Such shells are unduly sensitive in their behaviour
because the ratio of membrane to bending energy stored changes
significantly and indeed can fluctuate with changes in shell
thickness. We briefly review the different asymptotic behaviours that
shell problems can display, and then present the specific problem
considered and its numerical solution Using finite element analysis.
Keywords: shells,
asymptotic analysis, finite element solution
On the Asymptotic
Behavior of Shell Structures and the Evaluation in Finite Element
Solutions
Lee,Phill-Seung; Bathe,
Klaus-Jürgen. Source: Computers & Structures, v 80, 235-255,
2002.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Abstract:
The objective of this paper is to demonstrate how the asymptotic
behavior of a shell structure, as the thickness (t) approaches
zero, can be evaluated numerically. We consider three representative
shell structural problems; the original Scordelis–Lo roof shell
problem, a herein proposed modified Scordelis–Lo roof shell
problem and the partly clamped hyperbolic paraboloid shell problem.
The asymptotic behavior gives important insight into the shell load
bearing capacity. The behavior should also be known when a shell
problem is used to test a shell finite element procedure. We briefly
review the fundamental theory of the asymptotic behavior of shells,
develop our numerical schemes and perform the numerical experiments
with the MITC4 shell finite element.
Keywords: shells,
asymptotic behaviors, Ffnite element solutions
A
Flow-Condition-Based Interpolation Finite Element Procedure for
Incompressible Fluid Flows
Bathe,
Klaus-Jürgen; Zhang, Hou. Source: Computers & Structures, v 80,
1267-1277, 2002.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher:
Elsevier Ltd
Abstract:
The objective of this paper is to demonstrate how the asymptotic
behavior of a shell structure, as the thickness (t) approaches
zero, can be evaluated numerically. We consider three representative
shell structural problems; the original Scordelis–Lo roof shell
problem, a herein proposed modified Scordelis–Lo roof shell
problem and the partly clamped hyperbolic paraboloid shell problem.
The asymptotic behavior gives important insight into the shell load
bearing capacity. The behavior should also be known when a shell
problem is used to test a shell finite element procedure. We briefly
review the fundamental theory of the asymptotic behavior of shells,
develop our numerical schemes and perform the numerical experiments
with the MITC4 shell finite element.
Keywords:
shells, asymptotic behaviors, finite element solutions
A
Numerical Study of a Natural Convection Flow in a Cavity
Guo,
Yanhu; Bathe, Klaus-Jürgen. Source: Int.
J. Num. Meth. in Fluids, v 40, 1045-1057, 2002.
ISSN:
0271-2091 (print); 1097-0363 (online)
Publisher:
John Wiley & Sons, Ltd.
Abstract:
The solution to a benchmark problem of a differentially heated cavity
flow with Ra=3.4×105 and Pr=0.71 was
solicited for presentation at a special session entitled
‘Computational Predictability of Natural Convection Flows in
Enclosures’ which was held at the First MIT Conference on
Computational Fluid and Solid Mechanics. The objective of this paper
is to present the results obtained using the ADINA System.The 9-node
quadrilateral element in ADINA was used with various meshes. Periodic
solutions with a period of 3.42-3.43 were obtained. Compared with the
average values of the solution variables and the periods, the
calculated amplitudes of the periodic solutions were found to be more
sensitive to the spatial and temporal discretizations used. The flow
patterns, such as boundary layers, vortices, etc. were also studied
using a fine 40×120 element mesh. Vortices and their evolutions
were revealed inside the periodic flow field.
Keywords:
natural convection, unsteady cavity flow, ADINA
An
Evaluation of the Lyapunov Characteristic Exponent of Chaotic
Continuous Systems
Rugonyi,
Sandra; Bathe, Klaus-Jürgen. Source: Int. J. for Numerical
Methods in Eng., v 56, 145-163, 2003.
ISSN:
0029-5981 CODEN: IJNMBH
Publisher:
John Wiley & Sons, Ltd.
Abstract:
A procedure to calculate the Lyapunov characteristic exponent of the
response of structural continuous systems, discretized using finite
element methods, is proposed. The Lyapunov characteristic exponent
can be used to characterize the asymptotic stability of the system
dynamic response, and it is frequently employed to identify a chaotic
behaviour. The proposed procedure can also be used in the stability
characterization of fluid-structure interaction systems in which the
focus of the analysis is on the behaviour of the structural part.
Keywords:
stability analysis, Lyapunov characteristic exponent, chaotic
behaviour, non-linear dynamics, dynamic stability
A
Flow-Condition-Based Interpolation Mixed Finite Element Procedure for
Higher Reynolds Number Fluid Flows
Bathe,
Klaus-Jürgen; Pontaza, Juan P. Source: Mathematical Models and Methods in
Applied Sciences, v 12, no. 4, 525-539, 2002.
ISSN:
0218-2025
Publisher:
World Scientific Publishing Company
Abstract:
We present a (somewhat) new finite element procedure for the analysis
of higher Reynolds number fluid flows. While two-dimensional
conditions and incompressible fluid flows are considered, the scheme
can directly be used for three-dimensional conditions and also has
good potential for compressible flow analysis. The procedure is based
on the use of a nine-node element, optimal for incompressible
analysis (the 9/3 or 9/4-c elements), and a Petrov–Galerkin
formulation with exponential weight functions (test functions). These
functions are established from the flow conditions along the edge-
and mid-lines of the element. An important feature is that for low
Reynolds number flow, the weight functions are the usual biquadratics
and as higher Reynolds number flow is considered, the functions
"automatically" skew so as to provide the necessary
stability for the solution (the upwinding effect). Since the test
functions are calculated by the flow conditions, no artificial
constant is set by the analyst. The procedure is simple to implement.
We present some solution experiences and conclude that while the
procedure is not the "ideal" solution scheme sought, it has
some valuable attributes and good potential for further improvements.
Keywords:
finite elements, incompressible fluid flows
The Method of Finite
Spheres with Improved Numerical Integration
De,
Suvranu;
Bathe, Klaus-Jürgen. Source: Computers & Structures, v 79,
2183-2196, 2001.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Abstract: The method of
finite spheres was introduced as a truly meshless technique with the
goal of achieving computational efficiency in a mesh-free procedure.
In this paper we report several new numerical integration rules that
result in a significant reduction in computational cost.
Keywords: method of
finite spheres, meshless, mesh-free procedure, numerical integration
rules
Stability of Finite
Element Mixed Interpolations for Contact Problems
Bathe, Klaus-Jürgen; Brezzi,
Franco. Source: Proceedings della Accademia Nazionale dei Lincei, s.
9, v 12, 159-166, 2001.
ISSN: N.A.
Publisher: Accademia
Nazionale dei Lincei
Abstract: We consider
the formulation of contact problems using a Lagrange multiplier to
enforce the contact no-penetration constraint. The finite element
discretization of the formulation must satisfy stability conditions
which include an inf-sup condition. To identify which finite element
interpolations in the contact constraint lead to stable ( and optimal
) numerical solutions we focus on the finite element discretization
and solution of a ' simple' model problem. While a simple problem to
avoid the need for technicalities, the analysis of the finite element
discretizations to solve the problem gives valuable insight and
allows quite general conclusions on the use of different
interpolation schemes.
Keywords: contact
problems, elasticity, inf-sup condition
Optimal
Consistency Errors for General Shell Elements
Chapelle,
Dominique; Bathe, Klaus-Jürgen.
Source: C. R. Acad. Sci. Paris, t.332, Serie I, 771-776, 2001.
ISSN:
0764-4442
Publisher:
Académie des sciences/Éditions scientifiques et
médicales Elsevier SAS.
Abstract:
We obtain estimates for the consistency errors arising in general
shell element procedures, which are widely used in engineering
practice. These estimates improve a previous result by the same
authors. Moreover, numerical experiments indicate that these new
estimates are optimal. Further, we introduce a modified procedure for
which nominal convergence is recovered. These results are of much
practical significance.
Keywords:
shell element, error estimate
Towards
an Efficient Meshless Computational Technique: the Method of Finite
Spheres
De,
Suvranu;
Bathe, Klaus-Jürgen. Source: Engineering Computations, v 18,
170-192, 2001
ISSN:
0264-4401
Publisher:
MCB UP Ltd
Abstract:
Computational efficiency and reliability are clearly the most
important requirements for the success of a meshless numerical
technique. While the basic ideas of meshless techniques are simple
and well understood, an effective meshless method is very difficult
to develop. The efficiency depends on the proper choice of the
interpolation scheme, numerical integration procedures and techniques
of imposing the boundary conditions. These issues in the context of
the method of finite spheres are discussed.
Keywords:
method of finite spheres, meshless, interpolation scheme
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