Mixed stabilized finite element methods in nonlinear solid mechanics Part I: Formulation

This paper exploits the concept of stabilized finite element methods to formulate stable mixed stress/displacement and strain/displacement finite elements for the solution of nonlinear solid mechanics problems. The different assumptions and approximations used to derive the methods are exposed. The...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering Vol. 199; no. 37-40; pp. 2559 - 2570
Main Authors: CERVERA, M, CHIUMENTI, M, CODINA, R
Format: Journal Article
Language:English
Published: Kidlington Elsevier 01.08.2010
Subjects:
Approximation
C (programming language)
Displacement
Exact sciences and technology
Finite element method
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematical models
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Nonlinearity
Numerical analysis. Scientific computation
Physics
Sciences and techniques of general use
Solid mechanics
Structural and continuum mechanics
Solid mechanics
Nonlinear solid mechanics
High strain
Subgrid scale method
Stabilization
Irreducible operator
Displacement(deformation)
Large displacement
Modeling
Mixed method
Finite element method
Algebraic sub-grid scales
Stabilization methods
Orthogonal sub-grid scales
Mixed finite element interpolations
ISSN:0045-7825
Online Access:Get full text
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Summary:This paper exploits the concept of stabilized finite element methods to formulate stable mixed stress/displacement and strain/displacement finite elements for the solution of nonlinear solid mechanics problems. The different assumptions and approximations used to derive the methods are exposed. The proposed procedure is very general, applicable to 2D and 3D problems. Implementation and computational aspects are also discussed, showing that a robust application of the proposed formulation is feasible. Numerical examples show that the results obtained compare favorably with those obtained with the corresponding irreducible formulation.
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ISSN:0045-7825
DOI:10.1016/j.cma.2010.04.006