Simultaneous Relaxation in Structural Dynamics

by D. P. Flanagan, (M.ASCE), Student; Dept. of Civ. Engrg., Northwestern Univ., Evanston, I11. 60201,
T. Belytschko, (M.ASCE), Prof. of Civ. and Nuclear Engrg.; Dept. of Civ. Engrg., Northwestern Univ., Evanston, I11. 60201,

Serial Information: Journal of the Engineering Mechanics Division, 1981, Vol. 107, Issue 6, Pg. 1039-1055

Document Type: Journal Paper


The applicability of relaxation methods to implicit integration of structural dynamics problems is investigated. It is shown that although Jacabi interation is not competitive with explicit methods, conjugate gradient second order acceleration leads to schemes which are quite efficient, and its effectiveness is uneffected by the use of a consistent mass. For methods that require eigenvalue estimates, bounds are obtained by examining a single element and use of a theorem proved herein that the spectra of assembled positive definite matrices are always bounded by the unassembled element matrix. An energy based error criterion is developed for those methods.

Subject Headings: Relaxation (mechanics) | Structural dynamics | Matrix (mathematics) | Energy methods | Eigenvalues

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