Papers on the Theory used in ADINA
Solution
Methods for Eigenvalue Problems in Structural Mechanics
Bathe,
Klaus-Jürgen; Wilson, Edward L. Source: International
Journal for Numerical Methods in Engineering, v 6, 213-266, 1973.
ISSN:
0029-5981 CODEN: IJNMBH
Publisher:
John Wiley & Sons, Ltd.
Abstract:
A survey of probably the most efficient solution methods currently in
use for the problems Kφ = ω2M
and Kψ = λKGψ is presented. In the eigenvalue problems the stiffness matrices K
and KG and the mass matrix M can be full or
banded; the mass matrix can be diagonal with zero diagonal elements.
The choice is between the well-known QR method, a generalized Jacobi
iteration, a new determinant search technique and an automated
sub-space iteration. The system size, the bandwidth and the number of
required eigenvalues and eigenvectors determine which method should
be used on a particular problem. The numerical advantages of each
solution technique, operation counts and storage requirements are
given to establish guidelines for the selection of the appropriate
algorithm. A large number of typical solution times are presented.
Keywords:
structural mechanics, eigenvalue problem, QR method, subspace
iteration
Stability
and Accuracy Analysis of Direct Integration Methods
Bathe,
Klaus-Jürgen; Wilson, Edward L. Source: International
Journal of Earthquake Engineering and Structural Dynamics, v 1,
283-291, 1973.
ISSN:
0098-8847 (print); 1096-9845 (online)
Publisher:
John Wiley & Sons, Ltd.
Abstract:
A systematic procedure is presented for the stability and accuracy
analysis of direct integration methods in structural dynamics.
Amplitude decay and period elongation are used as the basic
parameters in order to compare various integration methods. The
specific methods studied are the Newmark generalized acceleration
scheme, the Houbolt method and the Wilson θ-method. The advantages of
each of these methods are discussed. In addition, it is shown how the
direct integration of the equations of motion is related to the mode
superposition analysis.
Keywords:
Newmark generalized acceleration scheme, Houbolt method, Wilson
θ-method, mode superposition analysis
Eigensolution
of Large Structural Systems with Small Bandwith
Bathe,
Klaus-Jürgen; Wilson, Edward L. Source: J. Eng. Mech.
Div., v 99, 467-479, June 1973.
ISSN:
0044-7951
Publisher:
American Society of Civil Engineers
Abstract:
The basic technique for the accurate calculation of the smallest
(largest) eigenvalues and corresponding eigenvectors in large
generalized eigenvalue problems arising in dynamic and buckling
analysis are considered. This leads to the design of a very efficient
practical algorithm when the system has small bandwidth. The solution
technique combines an accelerated secant iteration in which the Sturm
sequence of the leading principal minors is used with vector inverse
iteration. Example analyses are presented to show typical convergence
characteristics and solution times.
Keywords:
buckling, computation, computers, dynamics, eigenvalues
Some chapters in books on the theory used in ADINA
Towards
a Model for Large Strain Anisotropic Elasto-Plasticity
Montáns,
Francisco Javier; Bathe, Klaus-Jürgen.
Source: Chapter in Computational Plasticity, E. Onate and R.
Owen, eds., 13-36, 2007.
ISBN:
1402065760; 9781402065767
Publisher:
Springer-Verlag
Finite
Element Formulation, Modeling and Solution of Nonlinear Dynamic
Problems
Bathe,
Klaus-Jürgen. Source: Chapter in Numerical Methods for Partial Differential
Equations, (S. W. Parter, ed.), 1979.
ISBN:
978-0120567614
Publisher:
Academic Press
Convergence
of Subspace Iteration
Bathe,
Klaus-Jürgen. Source: Formulations and Computational Algorithms in Finite
Element Analysis, (K.J. Bathe, J.T. Oden and W. Wunderlich,
eds.), 1977.
ISBN:
978-0-262-02127-2
Publisher:
M.I.T. Press
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