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Computational Mechanics
Published in: Computational Mechanics 6/2017

24-07-2017 | Original Paper

A scaled boundary finite element formulation with bubble functions for elasto-static analyses of functionally graded materials

Authors: E. T. Ooi, C. Song, S. Natarajan

Published in: Computational Mechanics | Issue 6/2017

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Abstract

This manuscript presents an extension of the recently-developed high order complete scaled boundary shape functions to model elasto-static problems in functionally graded materials. Both isotropic and orthotropic functionally graded materials are modelled. The high order complete properties of the shape functions are realized through the introduction of bubble-like functions derived from the equilibrium condition of a polygon subjected to body loads. The bubble functions preserve the displacement compatibility between the elements in the mesh. The heterogeneity resulting from the material gradient introduces additional terms in the polygon stiffness matrix that are integrated analytically. Few numerical benchmarks were used to validate the developed formulation. The high order completeness property of the bubble functions result in superior accuracy and convergence rates for generic elasto-static and fracture problems involving functionally graded materials.
previous article A gradient crystal plasticity theory for large deformations with a discontinuous accumulated plastic slip
next article A new preconditioner update strategy for the solution of sequences of linear systems in structural mechanics: application to saddle point problems in elasticity

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Metadata
Title
A scaled boundary finite element formulation with bubble functions for elasto-static analyses of functionally graded materials
Authors
E. T. Ooi
C. Song
S. Natarajan
Publication date
24-07-2017
Publisher
Springer Berlin Heidelberg
Published in
Computational Mechanics / Issue 6/2017
Print ISSN: 0178-7675
Electronic ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-017-1443-y

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