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Main formulations of the finite element method for the problems of structural mechanics. Part 2
The author offers a classification of Finite Element formulations, which allows orienting in a great number of the published and continuing to be published works on the problem of raising the efficiency of this widespread numerical method. The second part of the article offers examination of straight formulations of FEM in the form of displacement approach, area method and classical mixed-mode method. The question of solution convergence according to FEM in the form of classical mixed-mode method is considered on the example of single-input single-output system of a beam in case of finite element grid refinement. The author draws a conclusion, that extinction of algebraic equations system of FEM in case of passage to the limit is not a peculiar feature of this method in general, but manifests itself only in some particular cases. At the same time the obtained results prove that FEM in mixed-mode form provides obtaining more stable results in case of finite element grid refinement in comparison with FEM in the form of displacement approach. It is quite obvious that the same qualities will appear also in two-dimensional systems.
Main formulations of the finite element method for the problems of structural mechanics. Part 2
The author offers a classification of Finite Element formulations, which allows orienting in a great number of the published and continuing to be published works on the problem of raising the efficiency of this widespread numerical method. The second part of the article offers examination of straight formulations of FEM in the form of displacement approach, area method and classical mixed-mode method. The question of solution convergence according to FEM in the form of classical mixed-mode method is considered on the example of single-input single-output system of a beam in case of finite element grid refinement. The author draws a conclusion, that extinction of algebraic equations system of FEM in case of passage to the limit is not a peculiar feature of this method in general, but manifests itself only in some particular cases. At the same time the obtained results prove that FEM in mixed-mode form provides obtaining more stable results in case of finite element grid refinement in comparison with FEM in the form of displacement approach. It is quite obvious that the same qualities will appear also in two-dimensional systems.
Main formulations of the finite element method for the problems of structural mechanics. Part 2
Ignat’ev Aleksandr Vladimirovich (Autor:in)
Aufsatz (Zeitschrift)
Elektronische Ressource
Unbekannt
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