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For the theory used in ADINA, for structural analysis, CFD, and FSI, and also for the philosophy used in the program development, please refer to the publications given here:
You are welcome to download the second edition of the book, 6th printing, however, please note that the book is copyrighted and should only be used in the same manner as a purchased hardcopy of the book.
Improved versions will be made available here, from time to time, as the 7th printing, and so on.
"Finite Element Procedures", 2nd Edition (.pdf)
Solutions to exercises in the book "Finite Element Procedures", 2nd Edition, 2014 are given in this manual (.pdf)
The Chinese translation of the 2nd edition is also available: Vol. 1 Vol. 2

Solution Methods for Eigenvalue Problems in Structural Mechanics
Bathe, KlausJürgen; Wilson, Edward L. Source: International Journal for Numerical Methods in Engineering, v 6, 213266, 1973.
ISSN: 00295981 CODEN: IJNMBH
Publisher: John Wiley & Sons, Ltd.
Abstract: A survey of probably the most efficient solution methods currently in use for the problems Kφ = ω^{2}M and Kψ = λK_{G}ψ is presented. In the eigenvalue problems the stiffness matrices K and K_{G} 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 wellknown QR method, a generalized Jacobi iteration, a new determinant search technique and an automated subspace 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, KlausJürgen; Wilson, Edward L. Source: International Journal of Earthquake Engineering and Structural Dynamics, v 1, 283291, 1973.
ISSN: 00988847 (print); 10969845 (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 θmethod. 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
Eigensolution
of Large Structural Systems with Small Bandwith
Bathe, KlausJürgen; Wilson, Edward L. Source: J. Eng. Mech. Div., v 99, 467479, June 1973.
ISSN: 00447951
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
Towards
a Model for Large Strain Anisotropic ElastoPlasticity
Montáns, Francisco Javier; Bathe, KlausJürgen. Source: Chapter in Computational Plasticity, E. Onate and R. Owen, eds., 1336, 2007.
ISBN: 1402065760; 9781402065767
Publisher: SpringerVerlag
Finite
Element Formulation, Modeling and Solution of Nonlinear Dynamic
Problems
Bathe, KlausJürgen. Source: Chapter in Numerical Methods for Partial Differential Equations, (S. W. Parter, ed.), 1979.
ISBN: 9780120567614
Publisher: Academic Press
Convergence
of Subspace Iteration
Bathe, KlausJürgen. Source: Formulations and Computational Algorithms in Finite Element Analysis, (K.J. Bathe, J.T. Oden and W. Wunderlich, eds.), 1977.
ISBN: 9780262021272
Publisher: M.I.T. Press
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