Adaptive analysis using the node-based smoothed finite element method (NS-FEM)

The paper presents an adaptive analysis within the framework of the node‐based smoothed finite element method (NS‐FEM) using triangular elements. An error indicator based on the recovery strain is used and shown to be asymptotically exact by an effectivity index and numerical results. A simple refin...

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Bibliographic Details
Published in:International journal for numerical methods in biomedical engineering 2011-02, Vol.27 (2), p.198-218
Main Authors: Nguyen-Thoi, T., Liu, G. R., Nguyen-Xuan, H., Nguyen-Tran, C.
Format: Article
Language:English
Subjects:
adaptive analysis
Asymptotic properties
Convergence
error indicator
Errors
Exact sciences and technology
Finite element method
finite element method (FEM)
Fundamental areas of phenomenology (including applications)
Mathematical analysis
Mathematical models
Mathematics
meshfree methods
Methods of scientific computing (including symbolic computation, algebraic computation)
node-based smoothed finite element method (NS-FEM)
Numerical analysis
Numerical analysis. Scientific computation
Physics
Sciences and techniques of general use
Solid mechanics
Static elasticity (thermoelasticity...)
Strain
Structural and continuum mechanics
upper bound
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Summary:The paper presents an adaptive analysis within the framework of the node‐based smoothed finite element method (NS‐FEM) using triangular elements. An error indicator based on the recovery strain is used and shown to be asymptotically exact by an effectivity index and numerical results. A simple refinement strategy using the newest node bisection is briefly presented. The numerical results of some benchmark problems show that the present adaptive procedure can accurately catch the appearance of the steep gradient of stresses and the occurrence of refinement is concentrated properly. The energy error norms of adaptive models for both NS‐FEM and FEM obtain higher convergence rate compared with the uniformly refined models, but the results of NS‐FEM are better and achieve higher convergence rate than those of FEM. The effectivity index of NS‐FEM is also closer and approaches to unity faster than that of FEM. The upper bound property in the strain energy of NS‐FEM is always verified during the adaptive procedure. Copyright © 2009 John Wiley & Sons, Ltd.
ISSN:2040-7939
2040-7947
2040-7947
DOI:10.1002/cnm.1291