Some applications of the mixed finite-element method to the solution of problems in solid mechanics

The paper analyzes and considers the application of the mixed finite-element method (FEM) to solve applied problems in solid mechanics. The general theory of mixed projection-mesh algorithms is developed. The reasonableness of the mixed method for elasticity, plasticity, and vibration problems is in...

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Bibliographic Details
Published in:Cybernetics and systems analysis Vol. 48; no. 5; pp. 749 - 761
Main Author: Chirkov, A. Yu
Format: Journal Article
Language:English
Published: Boston Springer US 01.09.2012
Springer
Springer Nature B.V
Subjects:
Accuracy
Algorithms
Approximation
Artificial Intelligence
Boundary conditions
Control
Efficiency
Finite element analysis
Finite element method
Materials elasticity
Mathematics
Mathematics and Statistics
Mechanics
Methods
Numerical analysis
Processor Architectures
Software Engineering/Programming and Operating Systems
Stress analysis
Studies
Systems Theory
Vibration
Ukraine
mixed approximation
theory of elasticity
theory of plasticity
free vibrations
finite-element method
plate bending
stability
ISSN:1060-0396, 1573-8337
Online Access:Get full text
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Summary:The paper analyzes and considers the application of the mixed finite-element method (FEM) to solve applied problems in solid mechanics. The general theory of mixed projection-mesh algorithms is developed. The reasonableness of the mixed method for elasticity, plasticity, and vibration problems is investigated and is used to formulate the conditions that ensure the stability and convergence of the mixed approximation for displacements, strains, and stresses. A special triangular finite element is set up for two-dimensional and axisymmetric problems. To solve problems of the bending, vibration, and stability of plates, a new hybrid finite element based on the Zienkiewicz triangle is proposed. The mathematical justification of the stability and convergence of the mixed approximation is supplemented with the numerical analysis, which confirms the efficiency of the developed algorithms.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:1060-0396
1573-8337
DOI:10.1007/s10559-012-9454-3