Papers on the Theory used in ADINA
On
Nonlinear Dynamic Analysis Using Substructuring and Mode
Superposition
Bathe,
Klaus-Jürgen; Gracewski, Sheryl. Source: J. Computers & Structures, v 13,
699-707, 1981.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher:
Elsevier Ltd
Abstract:
The solution of nonlinear dynamic equilibrium equations using mode
superposition and substructuring is studied. The objective is to
design schemes that in some analyses can significantly decrease the
computational effort involved when compared to a complete direct
integration solution. Specific schemes for mode superposition
analysis and substructuring are proposed. These techniques have been
implemented in ADINA. The results of a few sample analyses are
presented and recommendations are given on the use of these
procedures in practical analysis.
Keywords:
nonlinear dynamic analysis, substructuring, mode superposition
On
Thermo-Elastic-Plastic Analysis of Heat Treatment Processes Including
Creep and Phase Changes
Rammerstorfer,
F. G.; Fischer, D. F.; Mitter, W.; Bathe, K. J.; Snyder, M. D.
Source: J. Computers & Structures, v 13, 771-779, 1981.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher:
Elsevier Ltd
Abstract:
A method is described for calculating the stresses in a body during
heat-treatment and for calculating the remaining residual stress
distribution. Special attention is given to the
thermo-elastic-plastic material behaviour which is highly
temperature-dependent. A pseudo-plasticity effect due to
microstresses appearing during phase transformations is taken into
account. The stress analysis of a cylinder is performed using ADINA.
Calculated results are compared with results obtained experimentally.
Keywords:
heat treatment, residual stress distribution, thermo-elastic-plastic
material, ADINA
A
Simple and Effective Element for Analysis of General Shell Structures
Bathe,
Klaus-Jürgen; Ho, Lee-Wing. Source: J. Computers & Structures, v 13,
673-681, 1981.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher:
Elsevier Ltd
Abstract:
A simple flat three-node triangular shell element for linear and
nonlinear analysis is presented. The element stiffness matrix with 6
degrees-of-freedom per node is obtained by superimposing its bending
and membrane stiffness matrices. An updated Lagrangian formulation is
used for large displacement analysis. The application of the element
to the analysis of various linear and nonlinear problems is
demonstrated.
Keywords:
shell structure, finite element, updated Lagrangian formulation,
nonlinear analysis
The
Application of Quasi-Newton Methods in Fluid Mechanics
Engelman,
M. S.; Strang, G.; Bathe, K. J. Source: International Journal for
Numerical Methods in Engineering, v 17, 707-718, 1981.
ISSN:
0029-5981 CODEN: IJNMBH
Publisher:
John Wiley & Sons, Ltd.
Abstract:
The use of quasi-Newton methods is studied for the solution of the
nonlinear finite element equations that arise in the analysis of
incompressible fluid flow. An effective procedure for the use of
Broyden's method in finite element analysis is presented. The
quasi-Newton method is compared with the commonly employed successive
substitution and Newton-Raphson procedures, and it is concluded that
the use of Broyden's method can constitute an effective solution
strategy.
Keywords:
quasi-Newton methods, Broyden's method, finite element analysis,
nonlinear finite element equation, incompressible fluid flow
A
Solution Procedure for Thermo-Elastic-Plastic and Creep Problems
Snyder,
Mark D.; Bathe, Klaus-Jürgen. Source: J. Nuclear Engineering and
Design, v 64, 49-80, 1981.
ISSN:
0029-5493 (print); 1872-759X (online)
Publisher:
Elsevier Science B.V.
Abstract:
An effective solution procedure for finite element
thermo-elastic-plastic and creep analysis with temperature-dependent
material properties is presented. The material model employed is
summarized, the basic iterative equations are developed and the
solution procedure is theoretically analyzed and numerically tested
for its stability and accuracy properties.
Keywords:
thermo-elastic-plastic analysis, creep analysis, finite element
On
Finite Element Large Displacement and Elastic-Plastic Dynamic
Analysis of Shell Structures
Ishizaki,
Tairo; Bathe,
Klaus-Jürgen. Source: J. Computers & Structures, v 12,
309-318, 1980.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher:
Elsevier Ltd
Abstract:
Finite element procedures for nonlinear dynamic analysis of shell
structures are presented and assessed. Geometric and material
nonlinear conditions are considered. Some results are presented that
demonstrate current applicabilities of finite element procedures to
the nonlinear dynamic analysis of two-dimensional shell problems. The
nonlinear response of a shallow cap, an impulsively loaded
cylindrical shell and a complete spherical shell is predicted. In the
analyses the effects of various finite element modeling
characteristics are investigated. Finally, solutions of the static
and dynamic large displacement elastic-plastic analysis of a complete
spherical shell subjected to external pressure are reported. The
effect of initial imperfections on the static and dynamic buckling
behavior of this shell is presented and discussed.
Keywords:
shell structure, finite element, dynamic buckling, spherical shell
On
Some Current Procedures and Difficulties in Finite Element Analysis
of Elastic-Plastic Response
Bathe,
Klaus-Jürgen; Snyder, Mark D.; Cimento, Arthur P.; Rolph, W. Donald III.
Source: J. Computers & Structures, v 12, 607-624, 1980.
ISSN:
0045-7949 CODEN: CMSTCJ
Publisher:
Elsevier Ltd
Abstract:
Some finite element procedures for the analysis of elastic-plastic
response are presented and critically discussed: a consistent large
displacement and large strain formulation is summarized, a versatile
elastic-plastic model applicable to the analysis of metals and
geological materials is presented, the choice of an appropriate
finite element discretization is discussed, and some effective
methods for the solution of the nonlinear finite element equations
are briefly summarized. Finally, to illustrate the strength and
shortcomings of the procedures used, the results of some sample
analyses are presented and evaluated.
Keywords:
finite element, elastic-plastic response
Study
of Three-Node Triangular Plate Bending Elements
Batoz,
Jean-Louis; Bathe, Klaus-Jürgen; Ho, Lee-Wing. Source:
International Journal for Numerical Methods in Engineering, v 15,
1771-1812, 1980.
ISSN:
0029-5981 CODEN: IJNMBH
Publisher:
John Wiley & Sons, Ltd.
Abstract:
An assessment of flat triangular plate bending elements with
displacement degrees-of-freedom at the three corner nodes only is
presented, with the purpose of identifying the most effective for
thin plate analysis. Based on a review of currently available
elements, specific attention is given to the theoretical and
numerical evaluation of three triangular 9 degrees-of-freedom
elements; namely, a discrete Kirchhoff theory (DKT) element, a hybrid
stress model (HSM) element and a selective reduced integration (SRI)
element. New and efficient formulations of these elements are
discussed in detail and the results of several example analyses are
given. It is concluded that the most efficient and reliable
three-node plate bending elements are the DKT and HSM elements.
Keywords:
discrete Kirchhoff theory element, hybrid stress model element,
selective reduced integration element, plate bending element
An
Accelerated Subspace Iteration Method
Bathe,
Klaus-Jürgen; Ramaswamy, Seshadri.
Source:
J. Comp. Meth. In Appl. Mech. and Eng., v 23, 313-331, 1980.
ISSN:
0045-7825
Publisher:
Elsevier Science B.V.
Abstract:
The subspace iteration method for solving symmetric eigenproblems in
computational mechanics is considered. Effective procedures for
accelerating the convergence of the basic subspace iteration method
are presented. The accelerated subspace iteration method has been
implemented and the results of some demonstrative sample solutions
are presented and discussed.
Keywords:
subspace iteration method, finite element, eigenproblem
On Effective Implicit Time Integration in Analysis of Fluid - Structure
Problems
Bathe,
Klaus-Jürgen; Sonnad, Vijay. Source: International Journal for Numerical
Methods in Engineering, v 15, 943-948, 1980.
ISSN:
0029-5981 CODEN: IJNMBH
Publisher:
John Wiley & Sons, Ltd.
Abstract: An effective solution of fluid-structure systems
(and 'stiff and flexible domains' in general) can frequently be calculated using an implicit
time integration for the complete structural model with a lumped mass idealization
and the recently proposed BFGS method. In the analysis procedure used, the response
is calculated with implicit time integration for the fluid and the structure without
setting up a stiffness matrix of the fluid, and by satisfying the dynamic equilibrium
equations using the BFGS iterations.
Keywords:
fluid structure interaction, FSI, BFGS method, time integration
Some
Practical Procedures for the Solution of Nonlinear Finite Element
Equations
Bathe,
Klaus-Jürgen; Cimento, Arthur P. Source: J. Computer Meth. In Applied Mech.
and Eng., v 22, 59-85, 1980.
ISSN:
0045-7825
Publisher:
Elsevier Science B.V.
Abrstract:
Procedures for the solution of incremental finite element equations
in practical nonlinear analysis are described and evaluated. The
methods discussed are employed in static analysis and in dynamic
analysis using implicit time integration. The solution procedures are
implemented, and practical guidelines for their use are given.
Keywords:
nonlinear finite element, implicit time integration, dynamic analysis
A
Simple and Effective Pipe Elbow Element—Linear Analysis
Bathe,
Klaus-Jürgen; Almeida, Carlos A. Source: J. Applied Mech., v 47, 93-100,
September 1980.
ISSN:
0021-8936 (print); 1528-9036 (online)
Publisher:
American Society of Mechanical Engineers
Abstract: The formulation of a new, simple, and effective displacement-based
pipe bend element is presented. The displacement assumptions are axial, torsional,
and bending displacements that vary cubically along the axis of the elbow with plane
sections remaining plane, and a generalization of the von Karman pipe radial displacement
patterns to include the ovalization effects. The amount of ovalization varies cubically
along the elbow with full compatibility between elbows. The pipe bend element has been
implemented, and the results of various sample analyses are presented, which illustrate
the effectiveness of the element.
Keywords: pipe element, curved element, ovalization effects
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