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Article information
1999 , Volume 4, ¹ 1, p.66-79
Ivanov G.V., Kurguzov V.D.
Iterative solution of the plane elasticity problems by the method of self-equilibrated residues
Presented here, is the iteration method of solving the static problems of solid mechanics. Every iteration begins with some approximation that does not satisfy the considered system of equations. Residues arising in the equations can be interpreted as the concentrated forces and moments applied to the nodes of the finite element mesh. The aim of the iterative process is to eliminate these concentrated forces and moments or to reduce them, in accordance with some criterion, to minimum values. Every iteration of the method leads to the decrease in the value of the positively determined quadratic functional that provides the convergence of the iterations. High rate of convergence is achieved by selecting such variations of displacements at which the residues turn to be self-equilibrated (the sum of the residues is equal to zero) within the limits of some area. Using the one-dimensional problem by way of example, the efficiency of different choices of the self-equilibrium area is considered. Presented here for the two-dimensional problem, are the equations of formation of residues self-equilibrated with respect to the thickness of layer packs.
[full text] Classificator Msc2000:- *74B05 Classical linear elasticity
- 74G15 Numerical approximation of solutions
- 74S05 Finite element methods
- 74S30 Other numerical methods
Keywords: self-equilibrated residues, variational method, iterative method, static problems, concentrated moments, finite element method, concentrated forces, positively defined quadratic functional, convergence, self-equilibrium area
Author(s):
Ivanov G.V.
Office: Lavrentiev Institute of Hydrodynamics of SB RAS
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave., 15
Kurguzov Vladimir Dmitrievich
Dr. , Professor
Position: Leading research officer
Office: Lavrentiev Institute of Hydrodynamics of SB RAS
Address: 630090, Russia, Novosibirsk, Ac. Lavrentiev ave., 15
Phone Office: (383) 333 21 79
E-mail: kurguzov@hydro.nsc.ru
Bibliography link:
Ivanov G.V., Kurguzov V.D. Iterative solution of the plane elasticity problems by the method of self-equilibrated residues // Computational technologies. 1999. V. 4. ¹ 1. P. 66-79
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