Papers on the Theory used in ADINA
Computational
Issues in Large Strain Elasto-Plasticity: An Algorithm for Mixed
Hardening and Plastic Spin
Montáns,
Francisco Javier; Bathe, Klaus-Jürgen.
Source: Int. J. for Numerical Methods in Eng., v 63, 159-196, 2005.
ISSN:
0029-5981 CODEN: IJNMBH
Publisher:
John Wiley & Sons, Ltd.
Abstract:
In this
paper an algorithm for large strain elasto-plasticity with isotropic
hyperelasticity based on the Multiplicative decomposition is
formulated. The algorithm includes a (possible) constitutive equation
for the plastic spin and mixed hardening in which the principal
stress and principal backstress directions are not necessarily
preserved. It is shown that if the principal trial stress directions
are preserved during the plastic flow (as assumed in some algorithms)
a plastic spin is inadvertently introduced for the kinematic/mixed
hardening case. If the formulation is performed in the principal
stress space, a rotation of the backstress is inadvertently
introduced as well. The consistent linearization of the algorithm is
also addressed in detail.
Keywords:
large strains, computational plasticity, plastic spin, kinematic
hardening, cyclic plasticity, logarithmic strains
3D-Shell
Elements and Their Underlying Mathematical Model
Chapelle,
Dominique; Ferent, A.; Bathe,
Klaus-Jürgen. Source: Mathematical Models & Methods in
Applied Sciences, v 14, 105-142, 2004.
ISSN:
0218-2025
Publisher:
World Scientific Publishing Company
Abstract:
We focus
on a family of shell elements which are a direct generalization of
the shell elements most commonly used in engineering practice. The
elements in the family include the effects of the
through-the-thickness normal stress and can be employed to couple
directly with surrounding media on either surfaces of the shell. We
establish the "underlying" mathematical model of the shell
discretization scheme, and we show that this mathematical model
features the same asymptotic behaviors - when the shell thickness
becomes increasingly smaller - as classical shell models. The
question of "locking" of the finite element discretization
is also briefly addressed and we point out that, for an effective
finite element scheme, the MITC approach of interpolation is
available.
Keywords:
shells, general shell elements, asymptotic behaviors, locking
On Modeling Mixed
Hardening in Computational Plasticity
Bathe, Klaus-Jürgen; Montáns,
Francisco Javier. Source: Computers & Structures, v 82, 535-539,
2004.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher: Elsevier Ltd
Abstract: We address
herein the calculation of Prager’s hardening parameter in
computational plasticity when mixed hardening is considered. We
consider two approaches to evaluate the mixed hardening response;
namely, based on splitting the plastic strains and based on splitting
the plastic modulus. For a one-dimensional stress–strain curve
with nonlinear hardening, the proper calculation of Prager’s
hardening parameter is demonstrated and some comparisons and insight
are provided.
Keywords: Computational
plasticity, cyclic response, Prager’s rule, Mixed hardening
Finite Element
Developments for General Fluid Flows with Structural Interactions
Bathe, Klaus-Jürgen; Zhang, Hou.
Source: Int. J. for Numerical Methods in Eng., v 60, 213-232, 2004.
ISSN:
0029-5981 CODEN: IJNMBH
Publisher: John Wiley &
Sons, Ltd.
Abstract: The objective
in this paper is to present some developments for the analysis of
Navier-Stokes incompressible and compressible fluid flows with
structural interactions. The incompressible fluid is discretized with
a new solution approach, a flow-condition-based interpolation finite
element scheme. The high-speed compressible fluids are solved using
standard finite volume methods. The fluids are fully coupled to
general structures that can undergo highly non-linear response due to
large deformations, inelasticity, contact and temperature. Particular
focus is given on the scheme used to couple the fluid media with the
structures. The fluids can also be modelled as low-speed compressible
or slightly compressible media, which are important models in
engineering practice. Some solutions obtained using ADINA are
presented to indicate the analyses that can be performed.
Keywords: fluid flow,
incompressible, compressible, FSI, ADINA
On the Method of
Finite Spheres in Applications: Towards the Use with ADINA and in a
Surgical Simulator
De,
Suvranu;
Hong, Jung-Wuk; Bathe, Klaus-Jürgen. Source: Computational
Mechanics, v 31, 27-37, 2003
ISSN: 0178-7675 (Print)
1432-0924 (Online)
Publisher: Springer
Abstract: In this paper
we report some recent advances regarding applications using the
method of finite spheres; a truly meshfree numerical technique
developed for the solution of boundary value problems on
geometrically complex domains. First, we present the development of a
preprocessor for the generation of nodal points on two-dimensional
computational domains. Then, the development of a specialized version
of the method of finite spheres using point collocation and moving
least squares approximation functions and singular weight functions
is reported for rapid computations in virtual environments involving
multi-sensory (visual and touch) interactions.
Keywords: method of
finite spheres, meshfree method, ADINA, surgical simulation
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
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