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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Veröffentlicht in:Cybernetics and systems analysis Jg. 48; H. 5; S. 749 - 761
1. Verfasser: Chirkov, A. Yu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Boston Springer US 01.09.2012
Springer
Springer Nature B.V
Schlagworte:
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
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Abstract 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.
AbstractList 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. Keywords: theory of elasticity, theory of plasticity, free vibrations, plate bending, finite-element method, mixed approximation, stability.
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.
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. [PUBLICATION ABSTRACT]
Audience Academic
Author Chirkov, A. Yu
Author_xml – sequence: 1
  givenname: A. Yu
  surname: Chirkov
  fullname: Chirkov, A. Yu
  email: chirkov@ipp.kiev.ua
  organization: G. S. Pisarenko Institute for Problems of Strength, National Academy of Sciences of Ukrain
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Cites_doi 10.1007/s11223-006-0017-6
10.1007/s11223-008-9059-2
10.1007/s11223-007-0034-0
10.1007/s11223-007-0049-6
10.1007/BF02165003
10.1023/A:1007498132504
10.1007/s11223-008-9005-3
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COPYRIGHT 2012 Springer
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Issue 5
Keywords mixed approximation
theory of elasticity
theory of plasticity
free vibrations
finite-element method
plate bending
stability
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– volume-title: Theremo-viscoplasticity [in Russian]
  year: 1987
  ident: 9454_CR7
– volume-title: The Variational Method and the Method of Monotone Operators [in Russian]
  year: 1972
  ident: 9454_CR10
– ident: 9454_CR15
– ident: 9454_CR18
– volume-title: Theory of Vibrations [in Russian]
  year: 1992
  ident: 9454_CR11
– volume: 39
  start-page: 437
  issue: 4
  year: 2007
  ident: 9454_CR20
  publication-title: Strength of Materials
  doi: 10.1007/s11223-007-0049-6
– volume-title: Brittle Fracture Mechanics [in Russian]
  year: 1974
  ident: 9454_CR21
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Snippet 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...
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SubjectTerms 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
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Title Some applications of the mixed finite-element method to the solution of problems in solid mechanics
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