Micromechanically based stochastic finite elements

Length scales and anisotropy

K. Alzebdeh, M. Ostoja-Starzewski

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

The present stochastic finite element (SFE) study amplifies a recently developed micromechanically based approach in which two estimates (upper and lower) of the finite element stiffness matrix and of the global response need first to be calculated. These two estimates correspond, respectively, to the principles of stationary potential and complementary energy on which the SFE is based. Both estimates of the stiffness matrix are anisotropic and tend to converge towards one another only in the infinite scale limit; this points to the fact that an approximating meso-scale continuum random field is neither unique nor isotropic. The SFE methodology based on this approach is implemented in a Monte Carlo sense for a conductivity (equivalently, out-of-plane elasticity) problem of a matrix-inclusion composite under mixed boundary conditions. Two versions are developed: in one an exact calculation of all the elements' stiffness matrices from the microstructure over the entire finite element mesh is carried out, while in the second one a second-order statistical characterization of the mesoscale continuum random field is used to generate these matrices.

Original languageEnglish
Pages (from-to)205-214
Number of pages10
JournalProbabilistic Engineering Mechanics
Volume11
Issue number4
DOIs
Publication statusPublished - Oct 1996

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stiffness matrix
Stiffness matrix
Anisotropy
anisotropy
estimates
continuums
matrices
mesh
Elasticity
elastic properties
potential energy
Boundary conditions
inclusions
methodology
boundary conditions
conductivity
microstructure
Microstructure
composite materials
Composite materials

ASJC Scopus subject areas

  • Mechanical Engineering
  • Safety, Risk, Reliability and Quality

Cite this

Micromechanically based stochastic finite elements : Length scales and anisotropy. / Alzebdeh, K.; Ostoja-Starzewski, M.

In: Probabilistic Engineering Mechanics, Vol. 11, No. 4, 10.1996, p. 205-214.

Research output: Contribution to journalArticle

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