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:
These manuals describe in short form the theory used in ADINA Structures, Thermal, CFD and EM, and give hints for modeling problems correctly. For ADINA users: manuals
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
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.
Newmark generalized acceleration scheme, Houbolt method, Wilson
Bathe, Klaus-Jürgen; Wilson, Edward L. Source: J. Eng. Mech. Div., v 99, 467-479, June 1973.
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.
buckling, computation, computers, dynamics, eigenvalues
Montáns, Francisco Javier; Bathe, Klaus-Jürgen. Source: Chapter in Computational Plasticity, E. Onate and R. Owen, eds., 13-36, 2007.
ISBN: 1402065760; 9781402065767
Bathe, Klaus-Jürgen. Source: Chapter in Numerical Methods for Partial Differential Equations, (S. W. Parter, ed.), 1979.
Publisher: Academic Press
Bathe, Klaus-Jürgen. Source: Formulations and Computational Algorithms in Finite Element Analysis, (K.J. Bathe, J.T. Oden and W. Wunderlich, eds.), 1977.
Publisher: M.I.T. Press